Journal of Geophysical Research: Earth Surface

Morphodynamic evolution of experimental cohesive deltas

Authors


Abstract

[1] Here we describe new techniques for creating river-dominated (birds foot) deltas with strong channelization in the laboratory. The key to achieving strong self-channelization is the addition of a commercially available polymer to the sediment mixture. This polymer enhances the substrate strength increasing the critical erosion stress, an important geomorphic threshold. More importantly it increases the rate of cohesion onset to account for increased rates of morphodynamic evolution in small-scale experiments. A cyclic pattern of delta evolution is observed. The delta “avulsion cycle” begins with channel avulsion, erosion, and channel elongation and ends with channel backfilling and abandonment. This cycle appears to be universal but is subject to a range of controls, including sediment size distribution, sediment concentration, substrate cohesiveness, and Froude number. We propose that the observed depositional cycle is characteristic of an avulsion mechanism that is more complex than current models of fluvial systems, which generally explain avulsion probability as an upstream effect dependent on channel superelevation or levee slope. The experiments suggest that in many distributary channel systems, including deltas, alluvial, and deep water fans, downstream mediated topographic effects or “morphodynamic backwater effects” may dominate over upstream avulsion processes and control the surface mechanics and stratigraphy. The experimental observations are synthesized into a new depositional model for river-dominated deltas which emphasizes the importance of self-organization and feedback in delta surface evolution and stratigraphy.

1. Introduction

[2] Deltas, ubiquitous and dynamic features of the world's coastlines, are important sites for coastal cities and have been heavily engineered for ports and river navigation. In addition, because of their high deposition and subsidence rates, ancient deltas often contain significant hydrocarbon reserves [e.g., Ainsworth et al., 1999; Bohacs and Suter, 1997]. Recently, deltas have attracted increased attention because of coastal land loss issues related to storm surge and sea level rise associated with long-term climate changes.

[3] Despite their great economic and social importance our current understanding of delta surface processes, evolution, and related self-organization remains incomplete. This lack of understanding is largely a result of the intrinsic complexity of the processes involved, our inability to observe them over the long timescales necessary for natural delta evolution (e.g., 103–104 years for the Mississippi delta) and difficulties associated with collecting data in the coastal transition zone. Consequently, even the simplest end-member case, of a homopycnal, river-dominated delta under steady fluvial input, is not particularly well understood. This scenario, generally best approximated in nature by a river entering a small lake, has important implications as a baseline case for understanding all river-dominated deltas, and arguably provides insights into their wave- and tide-dominated cousins as well [e.g., Swenson, 2005; Jerolmack and Swenson, 2007].

[4] A delta is a variant of an alluvial fan where the sediment transport is significantly diminished at the coast (a downstream control) by the presence of standing water [Gilbert, 1884] and, like most alluvial fans, has a complex network of distributary channels on its surface [Olariu and Bhattacharya, 2006]. Perhaps the best-studied example, arguably the archetype, of an avulsing river-dominated delta is the Mississippi, whose Holocene history has been intensely scrutinized and has been a source for many important scientific concepts on delta evolution [Bates, 1953; Fisk et al., 1954; Gould, 1970; Morgan, 1970; Wright and Coleman, 1973; Wright, 1977] (also see Roberts [1997] for a comprehensive historical perspective). This body of work on the Mississippi led to the concept of delta lobe switching, “the fundamental depositional style that has shaped coastal environments of the Mississippi delta plain through Holocene time” [Roberts, 1997, p. 606]. The mechanism invoked to explain lobe switching is entirely autogenic. It begins with stream capture and the establishment of a well-defined channel network (the “fluvially-dominated regressive phase”) and ends with a “marine-dominated transgressive phase” involving marine reworking to form beaches, spits, barrier islands and, finally, submarine shoals as a result of lobe abandonment and subsidence [Roberts, 1997].

[5] The largest lobes of the Mississippi delta form in 1–2 ka cycles, far faster than the Holocene signal of sea level variation. Roberts [1997] calls this the “delta cycle,” which provides the context for the development of a range of morphodynamic structures observed on the present-day Louisiana coast. He suggests that the delta cycle is, in fact, a series of nested cycles that explain lobe formation over a range of scales from crevasse splays (<5 m thick, ∼100 years), through subdeltas (e.g., bayhead deltas) to the largest delta lobes (10–100 m thick, ∼1000 years). Avulsion cycles are also well documented on other large river-dominated deltas, most notably the Rhine-Meuse [e.g., Stouthamer and Berendsen, 2001].

[6] Avulsion cycles are a universal feature of distributary channel systems, including fluvial systems [Smith et al., 1989; Davies-Vollum and Kraus, 2001; Farrell, 2001; Slingerland and Smith, 2004], alluvial fans [Hooke, 1967] and submarine fans [Normark, 1970; Flood et al., 1991; Gardner and Borer, 2000]. Channels develop because sheet flow is fundamentally inefficient. Increased flow depth in channels leads to smaller bed surface areas and therefore less bed friction per unit flow volume. As a result, following avulsion there is a strong tendency for sheet flows to quickly channelize and extend basinward. Avulsion cycles are a consequence of this channel instability (positive feedback) and associated negative feedback mechanisms, but are subject to a range of controls that alter the channel character and dynamics. Apart from cohesiveness, the controlling variables include emergent properties like slope, Froude number and intrinsic structural scales (e.g., channel width and depth), which depend on imposed water discharge, grain size and sediment concentration [e.g., Paola, 2000]. Froude number is important because it governs hydrodynamic information transfer and therefore morphodynamic feedback along channels. In addition it controls the existence of specific hydraulic and morphodynamic structures.

[7] One way to study these processes and their controls is through the formation of small-scale physical models of river-dominated deltas in the laboratory. Unfortunately past experiments have been unable to reproduce the full range of complexity observed in natural deltas because of 2-D limitations [Jopling 1965], poorly developed, overly mobile channels [Shieh et al., 2001] and Froude supercritical flow [Sheets et al., 2007]. Previous studies have used simple noncohesive sand mixtures [e.g., Shieh et al., 2001; Sheets et al., 2002]. These may be analogous to coarse-grained (gravelly, Gilbert-type) deltas and alluvial fans, with highly mobile channels and weak channelization (large wetted area to total area). Weak channelization, however, limits the ability to generate complex river-dominated deltas at the experimental scale. For example, the experiments of Shieh et al. [2001], while quantitatively documenting the early stages of mouth bar extension and widening when fed by a fixed inlet, were unable to develop the later stages of morphodynamic evolution associated with self-formed channels. Noncohesive deltas express a smoother coastline due to the diffuse effect of faster channel migration [e.g., Shieh et al., 2001; Sheets et al., 2007].

[8] An experimental innovation described in this paper enables strong channelization (small channel width, slow channel migration, low-wetted area) at low Froude number, generating more realistic channel and shoreline patterns that approach the complexity of large-scale birds foot deltas like the Mississippi. The key to increased complexity is enhanced cohesion through the addition of an artificial polymer which increases the range of natural morphodynamic processes that can be reproduced. In real deltas it is expected that most, or at least some of, these cohesive effects are imparted by vegetation.

[9] The specific role of the polymer in experimental channel development remains equivocal but is likely to be associated with either transport thresholds or kinetics. The polymer increases substrate strength, enhancing hysteresis between deposition and erosion and increasing the critical erosive shear stress, an important geomorphic threshold [Schumm et al., 1987; Kim et al., 2006]. Perhaps more importantly it increases the rate of cohesion onset to match fast morphodynamic reaction rates in small-scale experiments. These rates are significantly larger than natural systems because of small channel depths and relatively large topographic growth rates associated with high sedimentation rates (i.e., high-sediment concentration) [e.g., Bryant et al., 1995, Tornqvist and Bridge, 2002]. Such effects are complex and poorly understood requiring further theoretical and experimental investigation. Ultimately, a full understanding of the influence of cohesion on channel cross section, channel pattern, and the evolution of distributary channel networks awaits the development of a comprehensive theory like that developed for sand and gravel bed rivers [e.g., Parker, 1978].

[10] In the meantime systematic empirical trends observed from controlled experiments may shed some light on these relationships. The cohesive experiments are compared to geometrically simpler experiments with less cohesion (e.g., “weakly cohesive” case with polymer but no clay) and noncohesive systems (e.g., pure sand) under similar conditions (steady forcing, similar grain size, no base level changes) enabling us to understand the effects of variable cohesion. In the cohesive deltas efficient routing of sediment and water through well-developed spatially and temporally persistent channels promotes low top set slopes and substantially subcritical Froude numbers. In contrast, inefficient sediment transport in noncohesive deltas due to coarser sediment, high sediment loads and inefficient sheet flow, develops steep Froude supercritical fan deltas that are starved of river load at the coast [e.g., Sheets et al., 2007; Orton and Reading, 1993; Postma, 1990; Schumm et al., 1987]. Sediment transport in these supercritical fans and fan deltas is typically disrupted by hydraulic jumps, which shorten the length scale and lifespan of the channels [e.g., Sheets et al., 2002; W. E. Weaver, Experimental study of alluvial fans, unpublished Ph.D. dissertation, Colorado State University, 1984].

[11] The primary objective of this research was to develop improved depositional models of river-dominated deltas under purely autogenic conditions. Current conceptual models of river-dominated deltas [e.g., Syvitski et al., 2005] are based on upstream avulsion mechanisms in fluvial systems [e.g., Mohrig et al., 2000; Slingerland and Smith, 2004]. They do not include feedbacks in the distributary channel system or the effects of differences in cohesion. Here we propose an alternative depositional model, where downstream controls dominate delta avulsion and avulsion cycles, and introduce the idea of upstream propagating “morphodynamic backwater” effects. These propagate through the distributary channel system and lead to strong spatial and temporal correlations in surface events and strong spatial organization of the stratigraphy. At present, observations documenting downstream control on avulsion in deltas are rather scarce [Bhattacharya et al., 2001; Bhattacharya, 2006].

2. Experimental Methods

[12] The results and observations presented in this paper are drawn from seven experiments with various degrees of cohesion (Table 1). The experiments were conducted at the ExxonMobil Upstream Research Company in a 5 × 3 × 1 m deep tank. The inlet condition in all experiments was a fixed channel 3.81 cm wide and 20 cm deep (Figure 1) located at the center of a wall (Agg2, long wall; other experiments, short wall). From this inlet, the deltas were free to expand radially, over a 180 degree angle. The basin floor was a flat and horizontal plate supported from below, with 20 cm spaces between the tank sidewalls and the plate. As a result, the deltas could prograde off the edges of the plate into “deep water” if allowed to grow large enough, but hydraulic wall effects were kept to a minimum. Base level (basin water depth) was held constant using a weir system (6.35 cm above the flat plate for all experiments). As the delta aggraded, the bed of the inlet channel was free to aggrade, thereby raising the inlet point.

Figure 1.

Experimental arrangement and location of stratigraphic cross sections. (top) Overhead image of Agg1 experimental delta with flow patterns highlighted in black and (bottom) perspective topographic scan taken at end of Agg2 experiment. Inlet position and positions of stratigraphic sections shown in Figure 10 denoted by vertical arrow and dashed lines, respectively. X, Y, and Z scales in cm.

Table 1. Experimental Conditionsa
Delta ExperimentQw (l m−1)Qs (l m−1)Runtime (h)FrReWetted Width (cm)Channel Width (cm)Channel Depth (cm)Width/DepthSediment Mixture and Channel Pattern
  • a

    Here Qs is sediment discharge, Qw is water discharge, Fr is Froude number, and Re is Reynolds number.

  • b

    Run intermittently.

7200.08142.6739076.27.620.1445.40Strongly cohesive, bifurcation dominant
8200.04161.3178138.15.440.3653.52Strongly cohesive, bifurcation dominant
9200.02720.5958585.085.082.322.18Strongly cohesive, avulsion dominant
14200.03552.7739019.0519.090.14139.6Weakly cohesive, bifurcation dominant
15200.03381.9039010.8810.880.1762.43Weakly cohesive, bifurcation dominant
Agg1100.012000.6139053.813.811.722.20Strongly cohesive, avulsion dominant
Agg2100.01150b0.2139053.813.813.461.09Strongly cohesive, avulsion dominant
Mississippi River1 · 101210−2 g/l0.110710%10510350–100Cohesive, avulsion dominant

[13] Sediment and water were mixed outside the basin and delivered at a fixed rate through the inlet channel at low concentrations (∼1:500 for Agg1 and Agg2; for others see Table 1). The cohesive sediment mixture comprises a near uniform distribution of sediment grades ranging from bentonite clay to coarse sand (Figure 2), combined with a small amount (approximately 100 g/50 kg sediment) of a commercially available shale stabilizing polymer developed for oil well drilling applications (i.e., New-Drill Plus, Baker Hughes Inc). The sediment moves primarily as bed load in the channels but a portion of the finer sediment that would normally travel as suspended load is attached to the bed load material by the action of the polymer. Coarse bed load accumulates in the channels and at the edge of channel mouth bars while the remaining fine suspended load accumulates overbank on the fluvial surface, (e.g., floodplain deposits and levees), or in the offshore prodelta.

Figure 2.

Experimental delta sediment mixture; cumulative grain size distributions for major grain size components. A typical mixture (e.g., Agg2) comprises 50 lb G800 ceramic microspheres (3M), 25 lb #3 blasting sand, 25 lb #5 blasting sand, 2.5 quarts bentonite (Aquagel), 2.5 quarts fine kitty litter (Better Way, flushable), 10 lb #12 glass spheres, and 80 g Newdrill Plus polymer (Baker-Hughes). The mixture creates channels without kitty litter but this component creates roughness on the fluvial surface that enhances channel formation. This roughness may be analogous to vegetation in real deltas.

[14] Various combinations of water discharge, cohesiveness and sediment discharge were simulated, including cohesive low concentration (Agg1, Agg2, Delta9), cohesive high concentration (Delta7, Delta8) and lower cohesion (Delta14, Delta15). These experiments were part of a general investigation of controls on channelization (>20 experiments) that led to the selection of particular experiments for further analysis. A number of experiments were run with polymer but without clays in order to highlight internal stratigraphy, which is obscured by clays in the cohesive experiments (Delta14, Delta15). While this approach made the stratigraphy more visible, the polymer increases sediment cohesiveness best with the presence of clay and, consequently, these experiments developed geometries characteristic of sandy noncohesive deltas.

[15] The cohesive Agg1 experiment was run continuously for 200 h, producing a radially symmetric delta (Figure 1) approximately 11 cm thick and 5 cm above “sea level” at its thickest point. The most cohesive experiment, Agg2, was run intermittently over a 2 month period to facilitate topographic scanning and consequently had the longest set-up time (Table 1). The Agg2 experiment ran for 150 h, not including pauses every 2 h for ultrasonic topography scanning (approximately 4 h duration) (Figure 1). Throughout all experiments, digital images of delta evolution were taken on 5 min intervals and rhodamine dye was injected on 15 min intervals to aid in visualization of the flow patterns. A rapid series of images (6–8 at ∼1 sec interval) was taken during dye release to enable measurement of flow velocity in the channels.

[16] These experiments were not rigorously scaled because we do not understand all of the important scaling variables, particularly those associated with cohesion. However, given that natural sediment loads (total load), based on the pre-1960 Mississippi River, [e.g., Syvitski, 2006] are approximately 1/1000 that of the experiments (10−6 g/cc for the Mississippi versus 10−3 g/cc for Delta9), and the grain sizes are about the same (both fine-medium sand), the morphodynamic reaction rate will be speeded up 106 times on the basis of relative channel depths of 10 m and 1 cm, respectively. A similar speed-up factor (∼106) is predicted on the basis of the ratio of a typical time for lobe growth in the Mississippi (103 years) versus the experiments (∼10 h). This dependence of morphodynamic reaction rate on sedimentation rate suggests that in addition to increased cohesion, decreased sedimentation rates are important for the promotion of strong channelization, and this prediction is confirmed experimentally in this study.

[17] Our general scaling philosophy was to focus on the aspects of scaling most likely to influence the mesoscale structure such as channel patterns, applying a general “similarity of process” methodology [Hooke, 1968]. This involved selecting for further study those experiments that exhibited the best channel development (longest channels, smallest channel widths) within the dynamic regime of interest (e.g., low Froude number, bed load dominated). Additional criteria included the observation of geologically reasonable surface processes such as channel and bar patterns and realistic internal stratigraphy. The experimental deltas include compaction and related subsidence (∼1 mm/day) such that flooding is observable on abandoned delta lobes. Even this small amount of differential subsidence can significantly influence subsequent morphodynamics in a manner similar to natural deltas, making the experiments a useful analog for the study of substrate-sedimentation interactions [Morgan, 1970]. Another useful aspect of the experimental cohesion is that it suppresses bed forms that might interfere with channel formation.

[18] Table 1 includes typical nondimensional scaling variables for the experiments as well as characteristic values for fundamental emergent properties like channel width and depth. Mean channel depth (d) is calculated on the basis of the known water discharge (Qw), estimates of flow velocity (v) in medial channels (i.e., 1/2 way down the delta from an advancing dye front), and the total wetted width of the active flow (W). Implicitly this approach assumes a rectangular channel cross section with area (A). Depth is calculated from: A = Q/v and d = A/W. Losses through infiltration or other processes were assumed to be negligible. Average channel width (w) is calculated by dividing the total medial wetted width (W) by the number of active channels (n).

[19] Although the gross stratigraphic packaging and large-scale spatial patterns of the experimental deposits appear to be remarkably similar to natural birdsfoot deltas [e.g., Roberts, 1997], a number of aspects of natural deltaic stratigraphy are not reproduced well in the experiments. In particular, natural deltas typically have larger proportions of suspended load and larger ocean depths which leads to the development of thicker and more depositionally diverse marine sections than are observed in the experiments. Consequently progradational (i.e., coarsening up) stratigraphy is poorly represented in the experimental deltas. Furthermore, the experiments do not develop all of the detailed facies observed in real deltas because of both the inability to properly scale certain morphodynamic instabilities (e.g., ripples or dunes, and in-channel bars) and the lack of certain processes, such as waves, tides and biological activity. We assume that missing morphodynamic structure below the characteristic channel depth would add another level of detail without grossly affecting the general vertical grain size patterns. That is, small-scale organization is controlled by (i.e., “slaved”) to the large-scale structure and should not substantially affect the cycles described in this paper [Haken, 1983; Werner, 1999].

[20] In the heterogeneous delta environment, which spans the transition between alluvial and marine processes, the flow is subject to diminishing gravity forces as the ambient fluid that surrounds the sediment-laden flow changes from air (delta top) to water (delta front). At the coastline the effective gravity forces and the dynamics are reset and as a result the Froude number is commonly formulated differently (and has a different value) in the subaerial and submarine realm. On the subaerial delta surface the Froude number can be approximated via the standard formulation for open channel flows (Fr)

equation image

where U is the depth-averaged velocity, g is gravitational acceleration, and h the flow depth. Beyond the shoreline, the appropriate formulation for the Froude number in the marine realm is commonly called the densimetric Froude number (Fr′)

equation image

where

equation image

with ρa the ambient fluid density, ρf the density of river mouth flow, and g′ the densimetric gravitational acceleration (reduced gravity).

3. Experimental Results

3.1. Channel and Mouth Bar Patterns as a Function of Cohesion and Sediment Concentration

[21] The experiments demonstrate a range of channel patterns as a function of sediment mixture cohesion and sediment concentration. In particular, cohesion and sediment concentration influence both channel width and overall wetted area on the delta top (Figure 3) by affecting bank strength and sedimentation rate. Narrower and fewer channels lead to increased channel depths and lower Froude numbers, bringing the dynamic conditions in the experiment closer to those in natural deltas (Table 1). For example, the experiments shown in Figure 3 demonstrate that under identical discharge and sediment mixture, increased concentration leads to increased wetted width, decreased channel depth and ultimately increased flow friction. This, in turn, leads to increased channel slopes and an increase in Froude number (see Figure 3 and Table 1).

Figure 3.

Overhead images indicating how delta-channel patterns change as a function of sediment concentration. All three experiments were run with the same water discharge and sediment mixture. (left) Delta9 has the lowest sediment concentration (C0), lowest normalized wetted width (i.e., ratio of active flow width to delta width at half the distance down delta), and lowest Froude number. The channel pattern is dominated by branching caused by avulsion; bifurcation occurs only in the most distal channel reaches. (right) Delta7 has a larger sediment concentration, larger normalized wetted width, shallower flow, and substantially higher Froude number. This channel pattern is bifurcation dominant, radiating from the fixed inlet. A comparison between the shorelines of Delta9 and Delta7 indicates that avulsion dominated systems have a more complex, rugose coastline than bifurcation-dominated systems. (middle) The Delta8 channel pattern is intermediate between bifurcation dominant and avulsion/bifurcation dominant.

[22] On the basis of this exploratory study of delta behavior, and the experiments of Sheets et al. [2002], we recognize three channel pattern regimes depending of the measured Froude number and degree of cohesion. In order of increasing sediment concentration, these are (1) persistent branching channels, associated with cohesive sediments, subcritical flows (relatively strong gravitational forces) and relatively few, avulsive channels; (2) persistent radiating channels, associated with cohesive sediments, but supercritical flow (relatively strong inertial forces) and bifurcation; and (3) broken channels, associated with noncohesive sediments, and consequent hydraulic jump formation (oscillation around critical flow).

[23] Persistent branching channels (illustrated in Delta9 in Figure 3 (left)) are the focus of this paper and are best illustrated in the lowest Froude number experiments (Agg1 and Agg2, Table 1). Proximal-medial (i.e., mature) channel patterns are primarily the result of avulsion, a gravitational instability, and therefore subcritical Froude numbers on relatively low gradients (Fr < 0.6 in the experiments). Most natural, input-dominated deltas are characterized by this channel pattern. In these deltas, bifurcation, the gravitational deflection of an inertial flow, is restricted to distal regions near the shoreline where gradients following avulsion are steeper and channels are shallower and more depositional. This interpretation is supported by the presence of bed forms on mouth bars typically associated with near-critical flow (small antidunes on mouth bars, e.g., Fr > 0.7 [Chanson, 2000]). This indicates that Froude ratio is typically highest near the shoreline, and gradually decreases in an upstream direction (i.e., proximally).

[24] Persistent radiating channels (Figure 3 (right)) are dominated by bifurcation and large wetted areas associated with weaker cohesion or high sediment loads. Channels are generally straight, and radiate from the fixed inlet because of supercritical flow (1.3 < Fr < 2.6). This channel pattern developed in both low concentration, relatively weakly cohesive experiments (polymer but no clay; Delta 14 and Delta15), and higher concentration, strongly cohesive sediment mixtures (Delta7 and Delta8). In effect, these bifurcation dominant deltas remain immature; they essentially remain in the late inertial bar stage of bar development (discussed in more detail in section 4.3). These deltas are geometrically simpler, with relatively smooth coastlines and simpler stratigraphy than their lower Froude number cousins. An important aspect of higher Froude number systems is that upstream information propagation is inhibited. This has important implications for delta surface processes and stratigraphy, as much of the delta is effectively out of communication with the shoreline. There is no obvious, natural-scale analog for this channel pattern.

[25] The broken channel pattern is also associated with supercritical flow, but noncohesive sediments. As described by Sheets et al. [2002], the natural analogs for this pattern are most likely steep alluvial fans and fan deltas where channel segments are generally very short in comparison to distance to the coast or fan terminus. An interesting difference between the two supercritical channel patterns is their ability to modulate Froude number. Froude number measurements indicate that, in the noncohesive case, hydraulic jump and cyclic step formation [e.g., Sun and Parker, 2005], lead to oscillation around critical flow. Flow acceleration leads to supercritical values, and jumps return the flow to subcritical conditions. In contrast, the cohesive experiments seem unable to “break” channelization with a hydraulic jump, and tend toward very high Froude numbers (Fr for Delta7 is 2.6). Channel patterns associated with supercritical flow may be more common in deep water distributary systems where Froude numbers are generally higher than in shallow water systems [e.g., Pirmez and Imran, 2003; Normark, 1970].

[26] Like channel patterns, mouth bar stacking patterns are also a function of both Froude ratio and cohesiveness because they respond to, and influence, the mechanisms of channel migration. In strongly cohesive deltas, bars generally extend and widen symmetrically (Figure 4 (left)). In noncohesive systems, bank erosion tends to be asymmetric, and widening may occur to one side, resulting in a lateral offset stacking pattern (Figure 4 (right)). Froude number also influences these mouth bar patterns. In high Froude number cases (e.g., Figure 4 (left)) the tendency to back up through progressive upstream accretion is reduced, making the system more likely to move laterally at the bar scale. Such systems only move backward once a significant thickness of sediment has built up through deposition of multiple bars. In summary, strong cohesion (and lower Froude numbers) leads to strong back-stepping at the bar scale, while weaker cohesion (and higher Froude numbers) leads to laterally shifting strata at the bar scale.

Figure 4.

Schematic of bar stacking patterns in experimental deltas made from cohesive (Delta 9) and noncohesive (Delta 15) sediments. Backstepping bar patterns dominate in cohesive substrates and at lower Froude numbers, while sidestepping (compensational stacking) dominates in noncohesive deltas at higher Froude numbers. Cohesive systems tend to backstep at the bar scale then sidestep at the lobe scale. Noncohesive deltas tend to sidestep at the bar scale and then back up and sidestep.

3.2. Cohesive Experiments (Agg1 and Agg2)

[27] The forgoing analysis of channel splitting mechanisms and associated channel patterns suggests that branching channels (Agg1 and Agg2) are the best analogs for natural birds foot deltas. Exaggerated cohesion and low-sediment concentration promotes strong flow channelization, low Froude number and the most complex channel patterns. One measure of the degree of channelization and flow localization is the fraction of subaerial delta surface area occupied by flow at any given time. In these experiments, the wetted fraction is typically substantially smaller than observed in the less cohesive experiments (0.05–0.2 versus 0.2–0.4 as given by Sheets et al. [2002]) and is closer to wetted fractions we have estimated from satellite photos in the modern Mississippi delta (i.e., up to ∼0.1 on the distributary lobes and much less on the delta plain).

[28] The cohesive experimental deltas typically exhibit 3 or more orders of channel branching with a broad range of length scales (e.g., channel lengths, widths and depths). We note here that the channel cross-sectional aspect ratios (width:depth) observed in the experiments are far smaller than those observed in natural systems (1–2 in the strongly cohesive experiments, versus 100 for typical natural channels, see Table 1). We would argue, however, that comparable Froude ratios lead to more natural development of the landscape, as indicated in the channel patterns and evolution of the distributary channel system. We note that the lowest calculated Froude number (0.21) and lowest aspect ratio channels are associated with Agg2, the most cohesive experiment. This increased cohesion is the result of a longer set-up time. Although Agg2 had the same sediment mixture as Agg1 and Delta9, (Fr, 0.59 and 0.61 respectively), it was run intermittently over 2 months to facilitate topographic scanning. In contrast Agg1, Delta 9 and the other experiments were run continuously over a few days and as a result were less cohesive.

3.2.1. Statistical Analysis of the Shoreline (Cohesive Experiments Agg1 and Agg2)

[29] One way to quantify fundamental length scales in the experimental deltas is to analyze the evolution of their shorelines (Figure 5). This analysis shows that the increase in the mean distance from the inlet to shoreline (dashed line) is increasing at a gradually diminishing rate. This increase is a consequence of the constant sediment discharge and water depth in a radial expanding system. Note that compaction produces dips in this trend around 60 and 100 h, during long pauses in the experiment.

Figure 5.

Measurements of shoreline dynamics during the Agg2 experiment. Maximum shoreline is calculated as the maximum distance between the inlet and any point along the shoreline. Mean shoreline is the radius of a semicircle with the same map view area as the subaerial experimental delta. Standard deviation (σ) of the shoreline is the expected distance a randomly chosen point on the shoreline falls with respect to the mean radius. Gray area on the shoreline plot represents a major episode of delta extension which is keyed to gray area on the time series plot, indicating sudden extension in maximum coastline position and increase inshoreline standard deviation.

[30] The plot of maximum distance from the inlet to the shoreline, however, increases in discrete events (solid black line in Figure 5) leading to roughening of the shoreline as indicated by shoreline standard deviation, σ, in Figure 5. As is the case in the mean distance measurement, dewatering leads to pronounced dips in this trend (gray portion of the trace in Figure 5). Major progradation generally occurs at times immediately following the development of a relatively symmetrical map pattern, as indicated by relatively low values of shoreline standard deviation immediately preceding jumps in maximum distance to the shoreline. These major progradation events are associated with channel entrenchment and a collapse of the distributary system to a single channel, as indicated by the anticorrelation between shoreline standard deviation and wetted area (Figure 6). These large shoreline excursions (ca. 5, 30 and 120 h) can be considered as an oscillation around grade, a complex response to a gravitational instability associated with channel overextension.

Figure 6.

Time series plot of the number of wet (pink dye) delta top pixels and shoreline standard deviation (also illustrated in Figure 5) indicates that these data are anticorrelated. Large shoreline excursions occur when the channel system incises and collapses to a single channel.

[31] The steps observed in the maximum distance to shoreline plot define important time and length scales in this distributary system. The time between these individual events increases as the experiment progresses, because increasing amounts of sedimentation and time are necessary to approach symmetry. However, the major shoreline excursions are all of similar length, constrained by the degree to which the system can extend before becoming inefficient. These length scales represent the largest extension events and are diminished by subsequent channel splitting. Channel splitting within a lobe is most frequent just prior to avulsion, when the channel pattern is strongly influenced by depositional topography. As a result, only the largest events are revealed in the shoreline statistics (e.g., Figure 5). For example, the greatest contribution of inertially deposited bars to signal (i.e., mean shoreline position) as opposed to noise occurs when all the flow is contained in a single channel soon after a major avulsion event.

3.2.2. Surface Observations: Avulsion Cycle for Cohesive Experimental Deltas

[32] The cyclic shoreline behavior observed in the preceding analysis can be explained by characteristic autogenic cycles that provide a context for all the surface dynamics and stratigraphic packaging. A specific example from the Agg2 experiment aptly illustrates a characteristic experimental avulsion cycle from the topography and isopach maps in Figure 7. Following avulsion, an incisional channel forms and extends across the delta top. Incisional channel formation is most rapid immediately following avulsion as the relatively steep gradient induces strong erosion and the highest flux at any stage of the cycle. A jet forms at the coastline, and the channel extends further via deposition and progradation (112–114 h), a constructional channel extension process.

Figure 7.

Flow patterns, topographic scans, and isopach maps on 2 h intervals over an 8 h period during the Agg2 experiment. Note initial channel extension (112–114 h), subsequent flow bifurcation (116–118 h), and occurrence of overbank flow and deposition late in the avulsion cycle (120 h). Jet (inertial) and lobe length scales are annotated. Contour marked on images is 1 cm above the flat plate.

[33] The flow field images indicate a gradual loss of flow confinement following initial channel incision and extension (114–120 h). The mouth bar underlying the channel widens during this period as the flow is lifted and increasingly affected by topography (116–118 h). Isopach maps (Figure 7) highlight the gradual shift of deposition to the bar margins as the flow is lifted and forced to spread during bar growth. The increasing influence of topography leads to backpressure on the flow, which, in turn, leads to bed aggradation and upstream overbank flow (120 h), a process we have termed morphodynamic backwater and will discuss in more detail. As overbank flow increases, the delta surface is “tested” by thin flows and rivulets that form on steeper gradients and tend to develop into incipient channels, a sort of “finding phase,” separate from the “entrenched phase” earlier in the cycle. Since there will be no avulsion without a favorable potential energy gradient, rapid bed and levee aggradation associated with channel backflooding may be a trigger for avulsion of the flow from the now superelevated channel. As a result, avulsion is strongly influenced by bar and lobe growth downstream (downstream control).

[34] Lower-order, lobe scale flow patterns can be complex and may affect flow over the entire delta. Figure 8 demonstrates an upstream migrating wave of overbank flooding or morphodynamic backwater associated with the growth of a large downstream lobe in the Agg2 experiment. These morphodynamic backwater events do not propagate upstream monotonically. While the overall progression is upstream, there is at least one period during which the system steps toward the shoreline as a new inertial bar is formed (Figure 8c) before continuing back toward the inlet. Figure 9 shows upstream migration of channel bed sedimentation as the morphodynamic backwater effect progresses.

Figure 8.

Sequential overhead images illustrating overbank flooding associated with the growth of a large lobe during the Agg2 experiment. Runtimes indicated in upper left of each photo. The maximum upstream extent of overbank flow is marked with a green dot. Ultimate backflooding is observed all the way to the fixed inlet, 1.8 m upstream and approximately 5 cm above base level. Average postavulsion channel slope is approximately 1:200. Estimated hydraulic backwater length (discussed in text) is shown in Figure 8e for comparison. Stratigraphic section positions for Figure 9 indicated by dashed black lines in Figure 8f.

Figure 9.

Stratigraphic cross sections along (A-A′) and perpendicular to (B-B′) a distributary channel in the Agg 2 experiment (sections are shown at different scales). Topographic scan times (indicated in legend) correspond to those in Figures 7 and 10. Intersection of A and B cross sections indicated by dashed black lines. Plan view positions of these cross sections are indicated by black dashed lines in Figure 8f. Note the low-angle upstream accretion in the cross section A associated with morphodynamic backwater effects. Further, the cross section B indicates that channel bed and levee aggradation are roughly contemporaneous up to the point when a new channel is formed.

[35] Upstream controlled channel avulsion is relatively rare in the experiments, presumably because of the effectiveness of downstream control. It was observed in extreme cases when channels prograded to the edge of the experimental plate (i.e., into deep water), effectively removing any downstream control. This represented a pure example of upstream controlled avulsion, as channel superelevation was due only to local gradual aggradation in the absence of any downstream effects. Experimental upstream avulsions occurred on much longer time scales than those associated with downstream effects. An incidental observation relating to channel filling is that, in most cases, a channel abandoned by upstream avulsion was left empty, unlike most backfilled channels which leave very little topographic evidence on the delta top. It was observed that the gravity-driven process of advective flow down levees dominated levee growth. The rate and height of levee growth was strongly dependent on the specifics of the grain size distribution, particularly in the silt size range. Apparently these particles were just suspended in channelized flow, but were deposited rapidly in overbank flow.

[36] The experiments indicate that distributary systems like deltas may be more erosive than is currently thought, with cutting localized in time and space to very specific parts of the avulsion cycle. The degree of erosion depends on the order of the channel that avulses. Erosion occurs immediately following avulsion as the channel extends (incisional channel extension) and, as a result, much of the material in incipient mouth bars early in the lobe cycle is erosionally sourced from the delta top (e.g., Figure 7). Later, as the deposit grows, channel erosion decreases and the material deposited at the edges of the growing mouth bar is more likely to be externally sourced from the fluvial system upstream of the delta. Another phase of erosion is associated with more mature phases of delta growth, as lower-order streams associated with the developing fluvial system (coastal plain) build out over the underlying delta, causing the entire system to prograde (e.g., Figures 1 and 3 (left)).

3.2.3. Subsurface Observations/Stratigraphy (Agg1/Agg2)

[37] The experimental stratigraphy can be subdivided into two general parts, an upper fluvial fan stratigraphy dominated by channel surfaces and fills as well as overbank sedimentation, and a lower, submarine portion of clinoform strata and marine mud (see delta cross sections in Figure 10). Favorable comparisons of the experimental stratigraphy with seismic data from natural deltas give us some confidence that the cohesive experiments generate realistic geometries. In particular, the mouth bar geometry and “double downlap” growth patterns (Figure 10) are qualitatively similar to those observed in seismic interpretations of natural deltas [McKeown et al., 2004].

Figure 10.

Strike-oriented stratigraphic sections from the Agg2 delta reconstructed from topographic scans. Positions of sections are indicated in Figure 1. Labels 1, 2, and 3 indicate Figure 11 thin section locations. Light gray and dark gray shading indicate weak and strong morphodynamic stages of bar growth, respectively.

[38] The 2.5 cm wide thin-sectioned cores of the strata (Figure 11) document a bimodality of laminae thickness showing thin-bedded subaerial laminae deposited atop thick-bedded laminae from submarine portions of the delta. The cores also show several important delta facies in the experimental deposits including: (1) coarse bed load deposits/lags at the base of a persistent distributary channel (top core 1, mantling an erosional surface cut into distributary mouth bar facies); (2) thinly bedded, fine-grained overbank/levee sediments overlying distributary mouth bar deposits (top cores 2 and 3); and (3) fining upward sedimentation associated with bar deposition during avulsion cycles (bottom cores 1–3, and repeated twice in core 3, indicated by open triangles).

Figure 11.

Thin sections (30 mm wide slabs) taken from sediment cores of the Agg1 experiment. Analogous stratigraphic positions are indicated in Figure 10. Section 1 shows proximal bar deposition followed by thick channel “lag” coarse-grained deposits. Section 2 shows proximal bar deposits topped by continuous overbank/levee deposits. Section 3 shows at least two bar packages overlying and separated by prodelta mud. Fining upward packages are indicated by open triangles and major stratigraphic boundaries by black lines. Note missing portion of section 2.

4. Discussion

4.1. Fundamental Autogenic Cycles

[39] Experimental observations presented in the foregoing sections suggest three fundamental nested autogenic cycles controlling river-dominated delta evolution.

[40] 1. The inertial bar cycle is the smallest of these, and is associated with an inertial jet instability at the channel mouth [Syvitski et al., 1998]. A bar cycle involves progradational channel extension from the shoreline, aggradational mouth bar growth and widening and ultimately channel bifurcation [e.g., Edmonds and Slingerland, 2007], at which point this cycle may begin again.

[41] 2. The avulsion (lobe) cycle operates at a larger scale, and is associated with gravitational channel instability (avulsion). An avulsion cycle is characterized by initial incisional channel extension followed by the development of a network of channels and hierarchically arranged bars associated with avulsion and bifurcation. The terminal elements of lobes are composite mouth bars deposited by the inertial bar cycle. Lobes are usually hierarchically arranged into larger lobes that are associated with avulsion on different orders of the distributary channel network.

[42] 3. The delta cycle (inferred but not observed in the experiments) is the smallest scale over which the delta is on average progradational, requiring delta extension over distances significantly longer than the lobe scale. A delta cycle contains all of the hierarchical, higher-order elements and cycles listed above in a nested fashion, i.e., 1 inside 2, inside 3. In the following discussion we present our interpretation for the mechanics of these autogenic cycles and their relation to the preserved stratigraphy.

4.2. Positive Feedback, Fundamental Length Scales, and Landscape Inertia: A Source of Landscape “Noise”

[43] Perhaps the most striking behavior associated with the exaggerated cohesiveness in the experimental deltas is low channel mobility. Relatively stable channels lead to a type of “landscape inertia,” whereby the system tends to extend or prograde in a single direction for a prolonged period of time, locally overshooting the long-term equilibrium deposit trajectory (grade), and creating irregularity in the deposit coastline (e.g., Figures 5 and 6). Such behavior contrasts with a system of highly mobile channels where sedimentation is quasi-diffusive, and the deposit planform approaches an ideal semicircular coastline. Here channels rapidly adjust to the path of steepest descent, creating less noise in the shoreline shape. The degree to which landscape inertia affects channel patterns may be related to the flow momentum, resulting in turbulent jets, or to landforms, such as subaerial or subaqueous levees, that confine the flow to a particular course. Evidence for landscape inertia in natural deltas like the Holocene Mississippi is the strongly irregular planform and channel gradients that are well below those at which avulsion is theoretically predicted [Aslan et al., 2005].

[44] Early stages of the delta experiments revealed that Froude supercritical flow in the inlet slot generally went through a hydraulic jump to Froude subcritical conditions prior to exiting the channel and becoming unconfined. The densimetric Froude number (Fr′), however, is likely to be supercritical immediately downstream of the inlet, as by definition g′ in equation (2) is vanishingly small in homopycnal systems like the experiments. In natural systems this situation will occur when the flow from the channel has moved sufficiently far offshore to become fully submerged so that the ambient water depth is substantially larger than the channel depth (at least twofold) [Bates, 1953; Ramsayer, 1974]. A sudden decrease in the gravity force at the channel mouth leads to excess inertia and rapid mixing with the ambient water in the form of an inertial, turbulent jet.

[45] The jet region is characterized by rapid flow deceleration, perturbing sediment transport at the coast and causing a strong downstream limit on the extension length of channels [e.g., Bates, 1953]. Once a channel reaches the coast it must fill vertical space in order to be lifted back to the elevation of the fluvial surface before it can propagate efficiently. Inertial behavior on floodplains has been described as the progradational phase of alluvial channel extension [Slingerland and Smith, 2004], or the aggradational channel extension phase of Mohrig et al. [2000].

[46] The inertial (bar) length scale (“inertial bar scale” in Figure 7) is constrained by channel width, the local discharge at a channel mouth and sediment size [e.g., Shieh et al., 2001]. It sets a length for individual mouth bars, a fundamental building block of delta stratigraphy. The absolute limit to this length scale is not well understood, but is longer than simple jet theory would predict and appears to be governed by water depth, the rate of shoaling due to bed load deposition, the rate of subaqueous levee deposition, and their influence on jet hydraulics [Edmonds and Slingerland, 2007; Rowland and Dietrich, 2006]. In the experiments, inertial regions are often characterized by adverse (i.e., positive) bed slopes because of the dominance of inertial over gravitational forces.

[47] In contrast to bar length scales set by flow inertia the tendency toward a long-term equilibrium state (grade) sets an upper limit on the lobe length scale (“lobe scale” in Figure 7). This limit represents the maximum distance a channel can prograde before its gradient becomes too low to efficiently transport sediment. The deposition rate at the shoreline is typically much higher than at any other point upstream in the experiments, leading to a shallowing of the channel profile. In principle, upstream channel aggradation could keep pace with shoreline deposition, maintaining the channel profile during progradation, but this is rarely the case in deltas. An important control on the lobe length scale, therefore, is the degree to which depositional landforms (such as subaerial levees) force channels to maintain a particular channel course. Mechanisms of subaerial levee development are well documented by Adams et al. [2004]. They include deposition of sediment advected overbank by flow and diffusion in regions of lateral shear adjacent to a flooded channel. The relative impact of each process is dependent on the amount of standing water on the floodplain.

4.3. Weak and Strong Morphodynamic Interaction

[48] In both experimental fan and delta systems, the onset of sudden sediment transport inefficiency is related to supercritical conditions, either by high gradients on the delta top (e.g., hydraulic jumps in supercritical fan deltas, Fr > 1 [e.g., Sheets et al., 2002], as discussed earlier) or the presence of standing water offshore (e.g., in cohesive birds foot deltas, Fr′ > 1). As a result spatial and temporal oscillation around critical flow appears to be an important theme in the surface dynamics.

[49] For example, surface maps of delta evolution (Figure 7) and time lapse topographic surface cross sections (Figure 10) indicate that vertical bar and lobe growth and widening represent a transition from inertially dominated bar deposition to gravitationally influenced flow bifurcation and, ultimately, gravitationally dominated avulsion. This transition can be illustrated with reference to energy conservation through a simplified Bernoulli equation for flow energy conservation along a streamline

equation image

where U is flow velocity, g is gravitational acceleration, y is flow thickness, z is bed elevation, p is pressure, and γ is the specific weight of the fluid. All three terms in this formulation are in units of length (head) and subscripts refer to locations either in the channel or on the bar. This equation can be simplified, however, as the flows are open to the atmosphere, (i.e., open channel flow) and pbar = pchan. This leaves only the relative velocity and elevation terms (the first two terms on each side of the equation). While energy conservation is a weak assumption in this case, because the early stages of bar growth are dominated by highly dissipative turbulent jets, experimental observation suggest that the stages of bar evolution can be understood heuristically through the terms in equation (4).

[50] Bar evolution involves a transition between two distinct stages. The first is a “weak” morphodynamic stage, in which the velocity (or inertial) term dominates and the effect of gravity is weak. During this stage, the flow is strongly inertial and changes in the form of the bar will have relatively little impact on flow patterns. Deposits associated with this stage are elongated in the flow direction and are essentially a passive response to the flow field, predominantly aggradational, generating a cross-stream symmetric profile (dark gray-shaded strata in Figure 10). A number of previous delta studies have focused on this weak morphodynamic stage, for example Shieh et al. [2001] and the “inertial stage” of Wright [1977].

[51] The second phase of bar development is a “strong” morphodynamic stage, in which the gravitational term dominates and flow interacts strongly with the evolving bed. The inertial flow is gradually lifted up to the fluvial surface by submarine sedimentation (increase in both y and z), leading to increased influence of the elevation term in equation (4). This involves a transition from jet-like flow to boundary layer flow with suppressed turbulence. A balance of inertial and gravitational forces leads to bifurcation associated with a V-shaped subaerial region developed on the bar surface (the middle ground bar [Edmonds and Slingerland, 2007]). The deposits of this stage are characterized by well-developed clinoforms extending outward from the edge of the aggradational core (light gray-shaded strata in Figure 10) and bidirectional downlap. This strong morphodynamic stage is similar to the “friction-dominated” stage of Wright [1977] and, in fact, the friction effect grows significantly as the bar shoals. While we acknowledge that friction must be important during this stage, it is likely that the decrease in Froude number associated with increase in bed elevation drives the majority of flow spreading. The geometric evolution from weak to strong morphodynamics has been quantitatively documented by planview bar length:width ratios by Shieh et al. [2001].

[52] This full cycle of weak to strong morphodynamic evolution is usually observed only in places where the Froude number is initially high and inertia dominates significantly over gravity, for example on a delta edge or flooded fan/delta surface [e.g., McKeown et al., 2004]. In cases where the Froude number can evolve very quickly with small increases in bar height, the inertial stage may be very short or nonexistent, changing rapidly to the strong morphodynamic stage. Bar stratigraphy in such cases (e.g., well-drained alluvial fans or deep water fans) should record little to no aggradational (jet) core, as observed in the experiments of Sheets et al. [2002]. Rather, the lobes seem to grow in a geometrically self-similar state by a spreading gravity flow over the convex bar, which resists rechannelization [Sittoni, 2005].

4.4. Negative Feedback: Morphodynamic Backwater and Channel Backfilling

[53] A general observation of the cohesive “branching” deltas is that channel extension and bar deposition lead to morphodynamic adjustment over a substantial portion of the delta. This adjustment represents a form of negative feedback (self-regulation or homeostasis), compensating for extension beyond grade during the avulsion cycle. Bar deposition near the shoreline leads to an upstream migrating flow disturbance, which causes sedimentation to propagate up the channel. This sedimentation, in turn, leads to increased overbank flow, rapid bed and channel levee aggradation and, ultimately, induces failure of the channel banks at an advantageous point, producing channel avulsion.

[54] The morphodynamic backwater effect we propose is initiated by sedimentation associated with a hydraulic backwater effect (“backwater deposits” [Senturk, 1994; Batuca and Jordaan, 2000]) that occurs as an incipient bar lifts and decelerates channelized flow. This phenomenon has been modeled in two-dimensional systems, like a single channel or a flume, using the shallow water equations [Chang, 1982; Hotchkiss and Parker, 1991]. However, the influence of deposition at the channel terminus and associated backwater effects in three-dimensional distributary channel networks and on channel and lobe evolution is more complicated.

[55] Since the experimental gradients are relatively high (Table 1), the hydraulic backwater length in these experiments is relatively short. The ratio of characteristic experimental flow depths of 2–3 cm to experimental channel slopes of 0.02–0.03 would result in experimental backwater lengths on the order of 1 m using a common approximation for hydraulic backwater length [e.g., Paola, 2000; G. Parker, One-Dimensional Sediment Transport Morphodynamics With Applications to Rivers and Turbidity Currents, internet E-book, 2005, available at http://vtchl.uiuc.edu/people/parkerg/morphodynamics_e-book.htm]. Channel bed sedimentation precipitated by the hydraulic backwater deceleration, however, can propagate upstream rapidly (i.e., backwater deceleration → deposition → more proximal backwater deceleration → etc.). As a result, the length scale of the morphodynamic backwater effect can be substantial, considerably longer than the simple hydraulic backwater length. For example, in Agg2 (Figure 8) overbank flooding associated with backwater effects extends all the way to the fixed inlet, approximately 1.8 m from the shoreline, considerably longer than the rough 1 m estimate (Figure 8). This suggests the presence of morphodynamic backwater through which bar and lobe formation has a substantial influence throughout the experimental delta.

[56] While the controls on hydraulic backwater are well understood and include channel slope, Froude number and flow thickness [Chow, 1959], controls on the morphodynamic backwater length are poorly constrained. Presumably, processes that affect the magnitude, length and migration speed of the hydrodynamic wave, as well as the sediment transport variables that control the coupling of the morphodynamic wave, are important. For example, variables that control the channel bed aggradation rate, like the proportion of bed load versus suspended load, may affect morphodynamic coupling. Three-dimensional observations of the experiment suggest that the upstream limit to the morphodynamic length is geometrically constrained. Channels are typically backfilled to some point at which another, more geometrically advantageous channel path presents itself (e.g., a steeper path to shoreline).

[57] The most important implication of a limit on the morphodynamic backwater length is that there is some portion of the system above which deposition and channel dynamics operate in the absence of influence from the shoreline. One might expect the morphodynamic backwater length to be limited by channel gradient in the distributary system itself. In particular, as slope often increases nonlinearly from coastline to coastal plain, there might be a limit associated with increasing proximal flow velocities. Circumstantial evidence for this is the tendency for “nodal” avulsion styles in many sedimentary systems [Slingerland and Smith, 2004], where multiple avulsions occur from the same nodal point.

[58] The strength of morphodynamic backwater in the experiments varies with Froude number as predicted by backwater theory [Chow, 1959]. They were strongest in the cohesive, low Froude number experiments (e.g., Delta9, Agg1, Agg2), where flow backflooding was typically strong after the development of a single inertial bar (Figure 4). In the more bifurcation-dominated deltas (e.g., Delta7, Delta14, Delta15) backflooding usually occurred after a greater accumulation of bars. It is interesting to note that backflooding is still prevalent in noncohesive, supercritical experiments [Sheets et al. 2007; Sittoni, 2005; W. E. Weaver, unpublished Ph.D. dissertation, 1984]. Here the mechanics of backflooding must be somewhat different, as the hydraulic backwater length in supercritical flows is extremely short. Rather, upstream migrating deposition appears to be associated with hydraulic jumps.

[59] The persistence of morphodynamic backwater effects in the experiments suggests that feedback in distributary channel systems may be far more important to geomorphology and stratigraphy than is currently thought. Channel filling strata are often explained as a consequence of postavulsion waning flow, and internal storeys as a consequence of reoccupation of abandoned channels [Mohrig et al., 2000; Slingerland and Smith, 2004]. The presence of morphodynamic backwater, however, implies that the internal architecture of many channel fills, at least in deltaic deposits, might reflect downstream avulsion cycle events, and may be more predictable than previously thought. For example, a major trunk distributary channel might record a hierarchical arrangement of storeys associated with repeated avulsion cycles in more distal, higher-order channels. These storeys might record both erosion and deposition as the gradient of the system evolves during an avulsion cycle.

[60] The experimental results may also have important implications for quantitatively analyzing and modeling bifurcation processes in distributary channel systems. Analyses of the stability of adjacent bifurcates [e.g., Slingerland and Smith, 1998; Bolla-Pittaluga et al., 2003; Federici and Paola, 2003] do not generally include feedback in the distributary channel network through more than two bifurcates. The observation that morphodynamic backwater effects can propagate long distances implies that distributary channel networks need to be analyzed over much larger regions, and over more nodes, as has been done in solving hydrological problems in tributary river networks [e.g., Saco and Kumar, 2002].

4.5. Avulsion: A Gravitational Instability

[61] The final phase in each of the various cycles discussed here, bar, avulsion, and delta scale, is abandonment of that particular portion of the delta. This can occur intrinsically, as part of deltaic autocyclicity (“downstream” control) or via abandonment of an entire region due to “upstream” controlled channel avulsion. Downstream controlled abandonments fall into two categories, bifurcation around emergent topography during the bar cycle (discussed earlier) and channel avulsion resulting from the morphodynamic backwater effect.

[62] The basic requirement for successful channel avulsion is that there exists a sufficient potential energy gradient at the point of avulsion such that an incipient channel can rapidly extend and become the preferred course. In the case of upstream controlled avulsion, the source of the favorable gradient is typically gradual channel bed and levee superelevation above the floodplain caused by local aggradation. Upstream controlled avulsion may be common in environments where downstream influences are negligible, such as fluvial systems in continental interiors or in deltas where the offshore conditions create an effective sediment sink. One might expect, however, that downstream effects must become important as rivers approach the shoreline, particularly if the offshore bathymetry is shallow. One caveat is that the presence of backwater itself is not a sufficient condition to drive backwater avulsions. This effect must exceed the influence of local aggradation, something which will be very difficult to evaluate in many cases.

[63] In backwater mediated avulsions the development of a significant potential energy gradient is primarily associated with the morphodynamic wave of deposition, which leads to increased channel bed and overbank sedimentation, as well as increased overbank flow. This is particularly evident in the overhead images of channel and overbank flow (Figure 8) and down and across channel cross sections presented in Figure 9. The time lapse overhead images show increasing overbank flow as far upstream as the inlet toward the end of the avulsion cycle. The down channel topographic cross sections show gradual upstream accretion of channel fill strata with time. The channel cross sections show channel bed and levee aggradation at times corresponding to increased overbank flow. Ultimately a favorable gradient is developed that captures flow, and the avulsion cycle begins again.

[64] A final thought on avulsion relates to the observation that avulsion cycle dynamics involve a transition from an inertial instability associated with a channel mouth jet (progradational extension) to a gravitational instability associated with channel extension (incisional extension). Unsuccessful (“failed”) avulsions may be associated with inertial flow downstream of a channel breach that locally evolves through multiple bar cycles, but because of a lack of favorable gradient is unable to reach the threshold conditions for the onset of gravitational channel extension. The result of this is a local crevasse splay deposit, an important component of natural deltaic stratigraphy.

4.6. Delta Processes, Fractals, and Distance From the Shoreline

[65] A number of researchers have documented the fractal nature of tributary systems generally attributed to multiple scales (orders) of erosional bifurcation [Rodriguez-Iturbe and Rinaldo, 1997]. However, the existence of the particular cyclic mechanisms and fundamental scales presented in this discussion suggests that delta distributary channel networks are not fractal. They can be expected to be organized differently at different distances from the shoreline and with removal from shoreline-related phenomena like morphodynamic backwater [Morisawa, 1985; Syvitski et al., 2005; Jerolmack and Swenson, 2007]. Consequently on some small deltas channel patterns are dominated by bifurcation (i.e., fossilized mouth bar patterns) [Edmonds and Slingerland, 2007]. At the other end of the spectrum lie purely alluvial dynamics where lower-order channels are generally split by upstream-mediated avulsion [Mohrig et al., 2000]. For example, on the Mississippi delta plain, bayhead deltas are dominated by bifurcation (e.g., Wax Lake bayhead delta) while larger-scale splitting (e.g., the Atchafalaya River) is dominated by upstream avulsion [Roberts, 1997].

[66] The range of channel characteristics in proportion to distance from the shoreline can be thought of as reflecting channel maturation. That is, young channel geometries are dominated by their initiation (genetic) mechanism, whereas mature channels evolve to efficiently deliver sediment and water to the delta front. Distal reaches of the experimental channels are wide and shallow, reflecting their juvenile status and origin via depositional jets. More proximal and mature channel reaches have generally lower cross-sectional aspect ratios, tend to be more deeply incised into older strata, and are the domain of gravity flows, frictionally dominated boundary layer flows with well-developed and coarse traction deposits. This change in channel cross section and mechanics associated with delta maturation can be observed in any river-dominated delta, for example, the Mississippi delta, as one traverses up river from a distal to a proximal position along the channel network. It may explain, for example, why meanders never occur in the distal delta distributaries.

[67] A transition from downstream dominant to upstream dominant avulsion processes may represent a fundamental difference between deltaic and alluvial systems. Since sedimentary systems tend to decrease in slope (and Froude number) as time progresses, channel patterns may also imply evolutionary stages of landscape evolution (i.e., maturity or time since deposition). For instance immature landscapes may be associated with Froude supercritical conditions (e.g., alluvial fans or delta termini) while fluvial systems may tend to greater landscape maturity (i.e., lower slope and Fr).

[68] In summary we note that deltas generally evolve from inertial to gravitational dominated dynamics and from downstream to upstream-mediated channel splitting mechanisms. Channel and channel network patterns evolve appreciably during avulsion cycles, as slope is gradually modified via sedimentation and abruptly changed via avulsion. This slope evolution may exert an important control on smaller-scale structures like bed forms, channel and bar patterns that develop at various times and locations during an avulsion cycle. Indeed, friction associated with these structures and their dependence on gradient and Froude number, adds another source of feedback to avulsion cycles that is not present in the cohesive experimental deltas.

4.7. Stratigraphy in the Context of the Autogenic Cycles

[69] The observation that surface processes can be understood through the characterization of a series of nested cycles implies that deltaic stratigraphy should reflect this. In particular, we should be able to identify characteristic vertical and lateral stacking patterns and grainsize trends associated with bar, avulsion and delta cycles. The bar cycle generally involves a transition from weak to strong morphodynamics, as does the avulsion cycle, with its early stages comprising one or more bar cycles and later stages associated with strong morphodynamic backwater effects. This transition from inertial to gravitational flow is associated with a general loss in flow competence as friction increases and flow becomes increasingly unconfined. One might expect this loss in flow competence, in turn, to lead to increasingly proximal deposition of coarser-grained sediment load and a general fining upward of the deposits at a particular location. Though the general loss in flow competence records an overall cyclic transition from positive to negative feedback, the stratigraphic details will be a consequence of nested cycles at multiple scales. For example, as is shown in Figure 8, morphodynamic backwater recedes slowly upstream in response to lobe growth but will also intermittently reverse this overall tend as smaller channels extend, erode and then backfill.

[70] Bar cycle stratigraphy is relatively straightforward to interpret. The lowest portions of the cores shown in Figure 11 show key aspects of characteristic bar cycle stratigraphy. These packages generally fine upward, but comprise sedimentation from both the positive and negative feedback stages of the bar cycle. Passive settling during the inertial stage is recorded by a uniform grain size lower bar in core 1 (indicated by white bar). This uniform grain size succession is absent in the other cores because of missing material (core 2) or a more lateral position (core 3). The negative feedback stage of the bar cycle is recorded as a fining upward cap above the uniform grain size base present in all three cores. This pattern is repeated twice in core 3, where the lower bar sequence did not build all the way to the water surface and therefore there was additional room for a second, thinner bar sequence. The upper bar sequence in core 3 shows more rapid fining because of deposition in shallower water, and therefore more rapid morphodynamic evolution. Because of the relatively small aerial influence of the bar cycle, it is likely that very little of the stratigraphy higher up in the cores is related to individual bars.

[71] Multiple avulsion cycle patterns are recorded in all three cores, though they are more difficult to discern. Core 1 shows a partial bar succession followed by an erosionally based, coarse-grained, distributary channel filling succession. The bar and some lower portion of the channel fill correspond to the first avulsion cycle, though the upper portion of the channel fill must correspond to a series of subsequent avulsion cycles that were fed through this distributary channel. Cores 2 and 3 show initial avulsion cycles with well-preserved bar sequences at their bases (two bar sequences in core 3). The overbank stratigraphy overlying these, however, is more difficult to interpret. The fine-grained layering corresponds to increased overbank deposition during backwater conditions associated with multiple avulsion cycles, though without chronostratigraphic information we cannot break out individual events. One possible interpretation is given (Figure 11), though each of the individual layers apparent in the upper third of core 3 might correspond to a separate avulsion cycle.

[72] Avulsion and breach of the upstream subaerial levees usually begins slowly. The trigger is lobe accretion because of inefficient overbank flow and the formation of many small channels near the end of lobe development (driven by channel backfilling and morphodynamic backwater). As a result, a typical (lower-order) lobe at the end of the avulsion cycle is a topographic high containing filled channel deposits encased in muddy levees. The lobe may have little or no surficial evidence of the original channel network, just a smooth convex cross section that will deflect subsequent flows (e.g., see the surface of the delta in Figures 1, 3, 7, and 8). Channel fills fine upward and may even end up as a mud plugged channel contained in sandy channel fills, because of the slow redirection in water discharge from the old lobe to the new channel. This stratigraphy is in turn encased in the fine overbank and levee deposits of the floodplain.

[73] All of the deltaic experiments presented here were shorter-lived and smaller than we would expect for a full-scale delta cycle at experimental scales. This is indicated by the fact that morphodynamic backwater effects were able to propagate across the entire delta, from shoreline to inlet, even at the end of the experiment. Delta cycles which are associated with upstream controlled avulsion, should leave an overall progradational package at a particular location, followed by a major marine flooding surface. The progradational part of the delta cycle is most obvious in core 1 of Figure 11, where bar deposits are overlain by coarser channel deposits, and underlain by thin prodelta deposits. None of the experiments were allowed to run long enough, nor were they large enough, to evolve to the point where upstream controlled avulsion led to a major abandonment.

4.8. A Depositional (or Conceptual) Model for River-Dominated Deltas

[74] The process interpretations presented above provide the basis for a new depositional model for river-dominated deltas. Overall, deltaic surface processes can be understood in the context of three nested autogenic cycles [e.g., Roberts, 1997; Jerolmack and Swenson, 2007]. From smallest to largest these cycles are: (1) the inertial bar cycle, associated with a transition from the dominance of inertial to gravitational forces at the shoreline; (2) the avulsion cycle, associated with gravitational channel extension, formation of multiple bars (making a lobe) and, ultimately, morphodynamic backwater and backwater controlled avulsion (i.e., downstream controlled); and (3) the delta cycle, associated with delta growth integrated over a number of prograding and aggrading lobes before regional abandonment by upstream controlled avulsion processes. These nested cycles provide a context for understanding and linking many aspects of natural deltaic evolution, including avulsion, channel formation and bifurcation, and the evolution of mouth bars, lobes and stratigraphy [cf. Roberts, 1997].

[75] Further, we propose the following three stages of deltaic evolution at the lobe (avulsion cycle) scale. Stage 1, positive feedback (channel extension and inertial bar formation) involves sheet flow exiting a channel and extending across the fluvial surface via incisional channel extension to the coast, forming a jet where the channelized flow debouches into standing water. Channel extension proceeds via a progradational stage, forming a narrow, primarily aggradational mouth bar that extends basinward under the evolving jet (i.e., weakly morphodynamic bar growth).

[76] Stage 2, negative feedback (bar aggradation and morphodynamic backwater) can be broken into two steps. The first step involves bar aggradation above the point where the incipient topography affects the flow (i.e., strongly morphodynamic bar growth). Gravitational forces begin to rival inertial forces, leading to flow widening and flow bifurcation, leaving a V-shaped subaerial region on the bar surface and ending the bar cycle. At this point, gravitational forces in a bifurcate channel may overwhelm inertial forces and the bar cycle repeats. The second step of negative feedback involves a morphodynamically mediated backwater effect. As the bar grows, a hydraulic backwater effect propagates slowly upstream, and is immediately followed by a wave of channel bed aggradation. As the lobe continues to grow and channel bed aggradation increases, overbank flow drives accelerated subaerial levee growth. The combined effect of bed aggradation and levee growth is superelevation of the channel, and ultimately avulsion, due to gravitational instability.

[77] Stage 3, channel avulsion involves the progressive overbank flooding associated with the upstream migrating morphodynamic backwater wave, which ultimately leads to the “discovery” of a more favorable path to the shoreline. While there may be any number of failed avulsions (creating potentially substantial deposits) as flooding progresses upstream, the first path steep enough to promote incisional channel extension will be the site from which a new avulsion cycle begins.

5. Conclusions

[78] Progress in experimental morphodynamics has been hindered by the inability to create realistic experimental models of cohesive, river-dominated (birds foot) deltas with complex channel patterns and irregular coastline shapes approaching natural complexity. The root of this problem is apparently associated with a discrepancy in timescales between the activity of natural cohesion and the rapid morphodynamic evolution rates in small-scale experiments. In the experiments presented here we address this problem by creating strongly cohesive sediment mixtures using artificial polymers. The resulting cohesive deltas are Froude (Fr) subcritical and are characterized by well-developed channelization, low-wetted area, and slow channel migration rates. These new techniques provide the basis for solving many problems in fluvial and deltaic systems that were previously inaccessible to experiment, and allow the formulation of new hypotheses regarding many aspects of deltaic behavior.

[79] Perhaps most importantly, the experiments allow the isolation and identification of a series of paired positive and negative feedback cycles that control deltaic evolution across a range of time and length scales. These cycles represent the tendency for deltaic systems to oscillate around long-term stability because of the presence of intrinsic instability in morphodynamic systems. While a particular instability will tend to drive the system away from equilibrium (e.g., channelization), the nature of morphodynamic systems requires self-regulation (e.g., deposition and lowering of the slope) and a return to quasi-equilibrium conditions.

[80] This sort of behavior leads to three important cycles characteristic of deltaic evolution. The smallest and most rapid of these is the bar cycle, involving a transition from inertial to gravitational flow and deposition at a channel mouth. At intermediate length and time scales the avulsion cycle dominates, wherein multiple bar cycles may integrate to promote morphodynamic backwater effects that can propagate upstream over surprisingly long distances. The largest scale of evolution is the delta cycle, associated with long-term behavior of major distributary channels, and, ultimately, upstream controlled avulsion and abandonment of large regions of the delta.

[81] The combination of hydraulic backwater and deposition at the terminus of distributary channels produces morphodynamic backwater effects that can propagate significant distances upstream. This effect is particularly pronounced in the deltaic environment, because of the nature of the subaerial-submarine interaction at the shoreline. However, we also expect morphodynamic backwater effects to be important in a variety of distributary systems where channel fills and upstream accretion have been recognized [e.g., Gardner and Borer, 2000]. It will be advantageous to include analysis of possible downstream influence in future mechanistic studies in these environments.

[82] In particular, the pervasiveness of downstream effects in the experiments suggests that similar phenomena should be considered as potential influences on channel (multiple storeys) and overbank (levee and splay distribution) deposition far removed from the shoreline. Further, avulsion dynamics in many regions might be better understood as a consequence of downstream control. While morphodynamic backwater effects make deltaic evolution more complicated than previously thought, implying linkages between surface processes in many parts of the delta, the recognition of this phenomenon should allow more sophisticated and accurate models of deltaic behavior.

Acknowledgments

[83] The inception of this industrial physical modeling effort was part of the Shapes project (∼2000–2005). We would like to thank John Van Wagoner, Shapes team members, and ExxonMobil management for enthusiastically supporting and participating in the development of a dynamic experimental sedimentology/stratigraphy program at ExxonMobil Upstream Research Company. Neal Adair, David Awwiller, Dave Giffin, and John Leiphart are thanked for assisting with various aspects of the experiments at EMURC. Roger Bloch, John Martin, Doug Edmonds, Rudy Slingerland, and Juan Fedele stimulated useful discussions of delta dynamics. In addition we thank Jana van Alstine for loading the Agg2 data into Petrel, from which the cross sections in Figure 9 were generated. The authors are also grateful to Paul Dunn, who carefully and insightfully reviewed this manuscript and to reviewers David Mohrig, Janok Bhattacharya, and Miles Hayes for useful editorial suggestions. Finally, we would like to thank Chris Paola for the stimulating experimental and theoretical work at SAFL and specifically for access to the DB-03 overhead images.

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