Water Resources Research

Mixing and circulation at the confluence of two rivers entering a meandering reservoir

Authors


Abstract

[1] A field data set collected under different conditions is analyzed to characterize the spatial arrangement of two large inflows (Ebro and Segre) with distinct physical-chemical characteristics as they join at the upstream end of Ribarroja reservoir in northern Spain. Given the short average residence time of water in the reservoir, the spatial arrangement of the rivers at their confluence and their mixing rates are likely the drivers of the stratification patterns observed near the dam. In winter, inflows have similar densities—Δρ/ρ0O(10−5)—and their spatial distribution is largely determined by inertial forces, and in particular, by the discharge ratio. Downstream of the confluence, both rivers flow side by side and largely unmixed over long distances. In summer, with Δρ/ρ0 of O(10−3), the flow fields at the confluence are largely controlled by buoyancy forces. Atmospheric forcing during strong wind events and centrifugal forces caused by the meandering shape of the reservoir induce significant tilting of the isotherms, leading to localized high mixing rates. Mixing, in general, though is weak at this time of the year. In fall and early winter, density differences are largely controlled by conductivity differences between the incoming flows. The warmer Ebro water, with larger thermal inertia, flows beneath the colder Segre water. The spatial arrangement of the inflows is largely controlled by the discharge ratio and mixing between sources is strong, likely as a result of mixed water being denser than either of the incoming flows.

1. Introduction

[2] Stratification in the water column provides one of largest physical constraints for biological growth in lake ecosystems, controlling the vertical rate at which mass is transferred, and, hence, determining the environmental conditions in which biogeochemical reactions occurs and biota develops. Stratification, for example, is tightly linked to the oxygen dynamics in lakes and reservoirs. Under stratified conditions, the vertical transfer of oxygen is reduced and oxygen levels in the deeper layers of eutrophic systems tend to decrease, getting even to levels close to zero. Under those conditions, the oxidation state of many water quality constituents change, modifying their physical and chemical behavior (F. J. Rueda et al., The value of reservoir operations in the water treatment process for urban supply, submitted to Water Resources Management, 2011). Stratification develops as a result of a subtle balance between processes that alter the density of water over depth and other processes that mix parcels of fluid within the water column. In natural lakes, with negligible through flows, heat fluxes tend to warm up the surface layers, and, the mechanical energy imparted by the wind in the water column, either directly or through shear-generation will mix water parcels. Water flowing over a solid bottom may also introduce the necessary turbulent kinetic energy to mix the water column. Hence, one expects weaker stratifications in rivers and reservoirs with large throughflow rates [Schräder, 1958] or with small residence times. Straškraba and Mauersberger [1988], in fact, developed an empirical relationship between the average residence times and reservoir stratification characterized by the temperature difference between the surface and a depth of 30 m in summer (see also Straškraba [1999]). Hydraulic forcing can also be a source of stratification [Tundisi, 1984] when large inflows from rivers with different characteristics enter a lake or a reservoir. Ribarroja reservoir, in northern Spain, is a case example of reservoir that stratifies as a result of hydraulic forcing [Prats et al., 2010]. The two largest inflows into the reservoir (Ebro and Segre rivers) enter at its upstream end and have distinct physical-chemical characteristics that vary at seasonal, and even shorter, time scales. Given the short average residence time of water in Ribarroja, stratification patterns observed near the dam are expected to be largely controlled by the relative magnitude of the inflows from Ebro and Segre rivers and the rates at which these two sources mix as they travel downstream.

[3] The extent to which basin scale stratification develops in hydraulically stratified reservoirs, in general, and the particular stratification patterns existing near the dam will depend on (1) the spatial distribution of the different sources of water as they enter the reservoir and (2) the rate at which they mix downstream of their confluence. The behavior of single inflows, in turn, critically depends on their density ρ relative to that of the surface of the reservoir ρ0, ambient stratification and circulation, inflow rates [Fischer et al., 1979], and the particular geometry of the receiving basin near the inflow regions [Johnson et al., 1987; Fleenor and Schladow, 2000]. In long, narrow, straight, and quiescent basins with simple geometries in which lateral motions are restricted, the pathways of distribution of single inflows and their relevant time and spatial scales have been thoroughly studied in the literature through laboratory experiments [e.g., Wells and Wettlaufer, 2007; Wells and Nadarajah, 2009, and references therein], numerical simulations [e.g., Chung and Gu, 1998; Bournet et al., 1999; Kassem et al., 2003], and analysis of field data [e.g., Fischer and Smith, 1983; Hebbert et al., 1979; Dallimore et al., 2001]. According to these studies, an inflowing stream will push the stagnant ambient water until its inertia is arrested, at some distance from the inflow section, due to density differences. At this point, a stream having less density than the lake surface will separate from the bottom, riding on top of the water column as an overflow. The denser stream water will plunge, in turn, beneath the surface, and it will flow downward along the bottom as a gravity-driven density current, gradually entraining water until it reaches the level of neutral buoyancy where the densities of the flowing current and the ambient fluid are equal [Stevens et al., 1995; Ahlfeld et al., 2003]. The level of neutral buoyancy can even be the bottom of the basin [Hebbert et al., 1979; Finger et al., 2006]. Once the density currents reach their depth of neutral buoyancy, they will form intrusions that spread horizontally into the main body of the reservoir. The behavior of buoyant river inflows can be interpreted as the interplay between inertial and buoyancy forces, and hence can be parameterized in terms of the internal Froude number, Fi = U/(g′h)1/2, where U represents the inflow velocity, h the depth of the channel, and g′ (= g Δρ/ρ0) the reduced gravity calculated from the density differences between lake and river water. Upstream of the plunge/lift point, it is assumed that motion is dominated by inertial forces and Fi >> 1. Downstream, in turn, buoyancy forces dominate the motion and Fi << 1. At the plunge/lift point, Fi is O(1), and most expressions proposed to determine the location of the plunge/lift points are based on this condition.

[4] Describing the pathways of distribution of river water under realistic conditions with more complex inflow geometries [Rueda and MacIntyre, 2010], with several inflows interacting [Marti et al., 2011], or with strong circulation in the receiving basin, however, remains a major challenge in the study of inflows in reservoirs. The inflow of Segre River into the upstream end of Ribarroja reservoir (Figure 1) is a case example where those conditions hold. The reservoir is constructed on the Ebro River channel, has an elongated and meandering planform and typically exhibits large throughflow rates. Segre River enters the left margin of the reservoir shortly downstream of a dam that regulates the inflows from the Ebro River. Being able to describe and understand the spatial arrangement of Ebro and Segre waters (the largest inflows) near their confluence and the mixing rates of both masses as they travel downstream appears to be the key to understanding stratification as observed near the dam and, hence, is important for water quality management. However, it is a challenging task for several reasons. First, because of the strong cross-flows along the Ribarroja reservoir, the rate of mixing of river and reservoir water may not conform to classical models for inflows into quiescent ambient waters. Second, the flow downstream of the confluence may be stratified, depending on the density difference between the rivers. Many studies exist that study circulation patterns of stratified flows within curved or meandering channels, but most of them are aimed at describing flows in laboratory settings [e.g., Corney et al., 2006; Chao et al., 2009; Cossu and Wells, 2010], estuarine environments [Lacy and Monismith, 2001], or in submarine channel bends [Parsons et al., 2010].

Figure 1.

Ribarroja reservoir (gray rectangle: area of study—confluence between Ebro and Segre rivers), bathymetry of the confluence and location of ADCP Jj, Fj, and Nj transects (gray solid lines) for the 2009 campaign. Gray dashed line: location of cross-section A immediately downstream of the junction corner. Star: location where cameras were deployed during the July experiment; triangles: location of thermistor chains E, S, and C during the February experiment. Dots: locations where CTD profiles a–f were collected on day 50 (February experiment).

[5] Our general goal in this work is to describe the spatial distribution of water from the Ebro (here on E-) and Segre (here on S-) rivers as they enter the Ribarroja reservoir and to understand the physical processes controlling the rate of mixing between these two rivers at and downstream of their confluence, at the upstream end of the reservoir. Based on previous records collected in 1998, an experimental plan was laid out in which a series of field campaigns were conducted near the confluence of the S- and E-rivers (see Figure 1). The field data collected in those campaigns are presented and interpreted using scaling arguments.

2. Study Site

[6] Ribarroja reservoir (41°18′N, 0°21′E) is the second of a chain of three reservoirs (Mequinenza-Ribarroja-Flix) constructed along the lower reaches of E-River for hydroelectric power generation (Figure 1). It is warm, monomictic, and mesoeutrophic, and is used for fishing, navigation, irrigation, and urban supply, in addition to being for hydropower. The basin is relatively shallow, with an average depth of 9.8 m, reaching values of up to 34 m near the dam. The free surface elevation is kept nearly constant and close to 70 m above sea level. Its area A and volume V when full are 2152 ha and 2.07 × 108 m3, respectively. With an average throughflow Q of 300 m3 s−1 (mean value from 1998), the nominal residence time of Ribarroja (=V/Q), is approximately 8 days. This value ranges from ∼3 days to less than a month [e.g., Cruzado et al., 2002], depending on throughflow rates. Throughflows, in turn, typically vary from ∼200 m3 s−1 in summer to nearly 800 m3 s−1 in winter. Peak flows after storm events can be larger than 2000 m3 s−1 [Prats et al., 2010]. The reservoir has an elongated and meandering shape (Figure 1), with the two largest inflows (Segre S- and Ebro E-rivers) occurring at the northwest end. Inflows from the E-River are regulated by Mequinenza dam, which discharges directly into Ribarroja reservoir 3 km upstream of the confluence of the S-River into the E-River. Only the hydroelectric intakes, releasing deep hypolimnetic water with stable temperatures throught the year, are operated on a regular basis [Prats et al., 2010]. Inflows from S-River, in turn, are largely unregulated and exhibit larger seasonal variations in temperature. Stratification in the reservoir, hence, is largely subject to hydraulic control exhibiting changes at seasonal scales. The strongest stratification develops in summer time, with a thermocline located between 5 and 10 m and a nearly anoxic hypolimnion, primarily formed by cold hypoxic waters released from the hypolimnion of Mequinenza dam [Prats et al., 2010]. Winds are highly variable with daily-averaged values ranging from 1 to nearly 10 m s−1. Winds are strongly periodic (with 24 h periods), predominantly from the southeast during summer (from May to September), and from the East in the first 3 months of the hydrologic year. From January to March, winds are predominantly from the north and northeast, veering to southeasterly winds in April. The strongest winds are commonly associated with southeasterly winds, but gusts of strong winds from the north and northwest occasionally develop.

3. Material and Methods

3.1. Approach

[7] Three different scenarios or modes for the behavior of the E- and S-rivers at their confluence were identified based on a preliminary analysis of existing information on river inflows and water temperatures, collected in 1998 (Figure 2). It was assumed in this analysis that water density would be largely controlled by its temperature, given that no other water properties had been observed at that time. Furthermore, this assumption is commonly used when studying freshwater bodies [e.g., Horne and Goldman, 1994; Goudsmit et al., 2002; Prats, 2011]. Scenario 1 corresponds to the first few months of the year, when large inflow rates (average values of ∼200 m3 s−1) are observed both in the E- and S-rivers. Peak inflows in S-River occur in December and May, probably associated with rainfall events and ice-off from the Pyrenees, respectively. Inflows from E-River exhibit several peaks during this period of time, probably due to withdrawals from Mequinenza after major rainfall events. E- and S-temperatures are similar, especially during the first and coldest part of the year. S-temperatures tend to be warmer, though, toward the end of this period. In Scenario 2 (summer time), inflow rates are lower (∼100 m3 s−1) from both sources, and decreasing, in the case of E-River. By the end of the period, the inflows from E-River are negligible. Large temperature differences between the sources exist, with the warmer temperatures observed in the S-River. Finally, Scenario 3 corresponds to fall and beginning of winter conditions. The warmer temperatures are from E-River and inflow rates are similar to those in Scenario 2. Other studies conducted in Ribarroja already point to the existence of these three scenarios [e.g., González, 2007; Prats, 2011].

Figure 2.

Scenarios (Sc) first proposed after analysing daily inflow rates from Ebro and Segre rivers, and water temperature in 1998. ΔT is the depth-averaged temperature difference between the Segre and Ebro rivers (ΔT=TS − TE).

3.2. Field Experiments

[8] Three field experiments were conducted in 2009 to characterize the spatial distribution of E- and S-waters in their confluence (see Table 1), under the three scenarios identified in the analysis of historical data. The first field experiment was conducted in late winter, from 18 February to 20 February (days 49–51); the second in summer, on 21 and 22 July (days 202–203); and the third, in late fall, on 25 and 26 November (days 329–330). Wind (speed and direction), air temperature, relative humidity, and solar radiation records for the days of the three experiments were collected at a meteorological station existing on a floating platform deployed near the dam. Water velocity, temperature, conductivity, and turbidity were collected along several transects. Water velocity profiles were collected using a boat-mounted Acoustic Doppler Current Profiler (ADCP). Two ADCPs (1200 kHz and 600 kHz RDI-Workhorse) were used in the first experiment, and only one (1200 kHz) in all others. The 1200 kHz-ADCP was operated in two different working modes, depending on the depth of the reservoir along the transect. The high-resolution coherent mode 5 was used in the shallowest transects. The default Mode 1 was used in the deeper portions of the lake. The maximum bin size was 0.5 m in all cases. The ADCP transects will be referred to as Fj, Jj, and Nj for the February, July, and November campaigns, respectively, where j is the number of the transect in Figure 1. Temperature, conductivity, and turbidity profiles were collected at several points along the transects using Seabird SBE-19 conductivity-temperature-depth (CTD) profilers. SBE-19 recorded at a rate of 20 Hz while free falling through the water column, giving a vertical resolution of O(10−2) m. The number of CTD profiles taken along each transect varied, and the distance between two consecutive profiles ranged from 100 to 300 m. The observations were mainly analyzed on a transect-by-transect mode. CTD data collected upstream of the confluence along the E- and S-rivers were used as references to characterize the properties of the sources (E- and S-water) in an end-member analysis of the mixed water downstream of the confluence. In this analysis, any given sample at and downstream of the confluence is assumed to be the result of a conservative mixture of two sources of water (end members) [e.g., Boyle et al., 1974]. The bathymetry of the confluence was reconstructed from an existing bathymetry map of the upper midhalf of the reservoir (Figure 1), and additional data collected with the ADCP during the field experiments in 2009.

Table 1. Summary of Experiments Conducted at Ribarroja Reservoir—Dates and Measurements
ExperimentObservation From BoatObservations From Autonomous Instrumentation
February2009Day 49▪ CTD profilesDays 49–51▪ Thermistor chains (Ebro, Segre, and confluence)
Days 50–51▪ CTD profiles and▪ Velocity profile observations with a RDI 1200 kHz and a RDI 600 kHz ▪ Wind, air temperature, relative humidity, and solar radiation (meteorological station)
July 2009Days 202–203▪ CTD profiles and ▪ Velocity profile observations with a RDI 1200 kHzDay 202▪ Photographs of the confluence
Days 202–203▪ Wind, air temperature, relative humidity, and solar radiation (meteorological station)
November 2009Days 329–330▪ CTD profiles and ▪ Velocity profile observations with a RDI 1200 kHzDays 329–330▪ Wind, air temperature, relative humidity, and solar radiation (meteorological station)

[9] During the first experiment, three thermistor chains were deployed upstream of the E- (chain E) and S- (chain S) rivers and downstream of the confluence (chain C) to characterize daily changes in water temperature. Chains S, E, and C had 5, 13, and 14 HOBO H20-001 temperature loggers (resolution 0.02°C, accuracy ±0.2°C), respectively, arranged at about ∼0.4 m intervals close to the surface and 1 m closer to the bottom, except for chain E, where a constant interval of 1 m was used. On the second campaign, several cameras were deployed near a high point located at the confluence to the left of E-River on day 202 (Figure 1). A series of photographs were taken from 11 A.M. to nearly 5 P.M.

[10] The equation of state of Chen and Millero [1986], as reported in Pawlowicz [2008], was used to calculate density from temperature and salinity data. Salinity or total dissolved solids (TDS), in turn, was estimated from specific conductivity C0 (μS cm−1) and temperature (°C) records as follows [Pawlowicz, 2008]

display math(1)

[11] The scaling factor λ in equation (1), here set to 0.8, is known to vary between 0.55 and 0.9 mg L−1 (μS cm−1)−1 in general usage, but can be as high as 1.4 mg L−1 in meromictic saline lakes [Pawlowicz, 2008]. The large variations (of up to 30%) in the value of the scaling factor are indicative of the extreme sensitivity of salinity values to changes in the ionic composition of water. Water samples collected in November 2009 were analyzed to determine their ionic composition. Using the results of that analysis, as proposed by Pawlowicz [2008], the correlation between TDS and specific conductivity gives an average value of 0.8 ± 0.2 mg L−1 (μS cm−1)−1 for the scaling factor, for both rivers, which makes the former assumption reasonable. No information was available on whether the ionic composition of the water from Mequinenza or S-River changes in time. Hence, 0.8 is assumed valid for all experiments. The contribution of suspended solid SS concentration in the density calculations was in all cases assumed neglible, based on the observed turbidity differences (Table 2). The turbidity records Turb collected at the inflow sections were first converted to SS (mg L−1) using the following empirical equation (R2 = 0.97) developed for the study site

display math(2)
Table 2. Average Values at Segre and Ebro Inflow Sections Before Entering the Reservoir Obtained From ADCP and CTD Casts
DayTransectQa (m3 s−1)uE-Wb (m s−1)uN-Sc (m s−1)T (°C)Turb (ntu)SC25d (µS cm−1)Tae (°C)U10f (m s−1)
  1. a

    Q, inflow rate.

  2. b

    uE-W, average E-W velocity (positive value if eastward).

  3. c

    uN-S, average N-S velocity (positive value if northward).

  4. d

    SC25, specific conductivity (T = 25°C).

  5. e

    Ta, average temperature of air at the time when transects where collected.

  6. f

    U10 = average wind speed (10 m height) at the time when transects where collected.

  7. g

    F, February; J, July, N; November. Numbers account for transects in Figure 1. S, Segre; E, Ebro.

50S-F1g−96−0.050−0.108.217.4713.710.62.9
 E-F37300.468−0.0848.19.7801.2  
51S-F1−116−0.054−0.117.413.2722.58.51.8
 E-F36240.371−0.040     
202S-J1−50−0.021−0.05124.161.1909.327.78.4
203E-J3–52200.146−0.03120.85.21061.728.77.0
329S-N2−120.007−0.01010.918.2838.89.01.9
 E-N52530.163−0.00314.27.41758.2  
330S-N2−69−0.006−0.06610.317.6833.614.40.8
 E-N51720.108−0.00314.18.81743.4  

[12] The contribution of SS to density (ΔρSS) was then calculated as follows [Ford and Johnson, 1983]:

display math(3)

where SG is the specific gravity of suspended solids. Given that almost 95% of the suspended sediment load from the E-River [Roura, 2004] is retained upstream in Mequinenza, S-River is the largest source of suspended sediments in the confluence, bringing mostly silt and clay with a particle size D < 25 µm and 9% of organic matter [Flumen Group, 2009]. Assuming that SG ∼ 2.65 (as in Chen et al. [2006]), the contribution of SS to density was always at least 1 order of magnitude lower than those caused by salinity and temperature differences. In February, for example, with the lowest temperatures (8°C) and the smallest differences in specific conductance (80 μS cm−1, Table 2), the salinity driven-density contrast between the sources was O(10−2) kg m−3. Differences in turbidity of 10 nephelometric turbidity units (ntu) (Table 2), in turn, introduced density differences of O(10−3) kg m−3.

4. Results and Discussion

4.1. Density Differences Between Sources

[13] Specific conductance versus temperature for all records collected at all depths and spatial locations during the days of experiments for the three field campaigns are plotted in Figure 3. Density estimates are shown as isolines on these plots. Note that the records tend to form straight lines between two points representing the characteristics of the E- and S-rivers (end members), which is indicative of all water parcels in the confluence being the result of mixing between these two rivers.

Figure 3.

Distribution of specific conductance versus water temperature (dots) observed at different points in the confluence between Ebro and Segre rivers in Ribarroja reservoir. Colored lines in the background are lines with equal densities, calculated as in Chen and Millero [1986] (see Pawlowicz [2008]). (a) February experiment. Dot color represents (1) red: day 49, (2) black: morning on day 50, (3) cyan: afternoon on day 50 and (4) blue: day 51; (b) July experiment; and (c) November experiment. The gray straight-dashed line in Figure 3c shows the curvature of lines of equal density.

[14] Temperature differences between rivers in February were as much as 1°C. E-temperatures were nearly constant (≈ 8°C). S-temperatures, in turn, experienced diurnal oscillations with amplitudes that exceeded the average temperature differences between the two sources (Figures 3a and 4). As a result of those changes, the records in the confluence also exhibited diurnal oscillations, forming straight lines between the end members. Conductivity differences between sources at this time of the year were of O(10) µS cm−1, with the lower conductivities (718 μS cm−1) observed in S-River. Relative density differences Δρ/ρ0, driven both by differences in temperature and salinity between sources were of O(10−5). As a result of the daily temperature variations, S-water could be lighter or have similar density to E-water. Maximum density differences Δρ/ρ0 occurred during the afternoon on day 50 with values of O(10−4) (Figure 3a).

Figure 4.

Temperature data from thermistor chains (triangles in Figure 1) located at (a) the Ebro River (chain-E), (b) the Segre River (chain-S), and (c) downstream of the confluence (chain-C), and differences between depth-averaged temperature ΔT for Segre and Ebro rivers, ΔT = TS − TE. White lines indicate 0000 h, 1200 h, and 2400 h on day 50 [Time (h) = 0 at 0:00 h on day 49]. Shaded areas show time for CTD casts on days 49 and 50. CTD profiles on day 51 were collected between 1100 and 1330 h.

[15] In contrast to the data from February, the data from July and November cluster along a unique straight line between the two end members (Figures 3b–3c). This is partly due to the large temperature and conductivity differences between sources at those times of the year, compared to the diurnal oscillations. In July, for example, temperature differences of up to 6°C (warmer in S-River) were observed between the sources. Conductivity differences at this time were, in turn, weak, and approximately six times smaller than those observed in November. Hence, density differences between sources at this time were largely driven by temperature differences, and the isopycnals in Figure 3b appear as steep lines compared to the other two periods. In November, in turn, temperature differences between sources were of up to 5°C and the differences in conductivity were ∼900 μS cm−1. Inflow buoyancy was, at that time, controlled both by differences in temperature and salinity, and E-water was, for example, denser than inflows from S-River, despite being warmer. Note that all points tend to accumulate along two different lines, each one corresponding to data from the 2 days of the experiment (Figure 3c). While the water properties from E-River were nearly constant during the experiment, S-water was colder on the second day. Note also that water parcels formed by mixing between the two sources on the second day of the experiment should be denser than the end members, as a consequence of the curvature of the lines of equal density in Figure 3c. This interpretation, however, largely depends on the values of scaling factor used in equation (1). For 0.63 < λ < 0.8 mg L−1 (μS cm−1)−1, mixed water is denser than both E- and S-water. For λ > 0.8 mg L−1 (μS cm−1)−1, in turn, the larger the fraction of E-water in the mixed parcel, the larger is its density. Experimentally derived values of λ (see methods) includes a range of ±0.2 mg L−1 (μS cm−1)−1 around λ = 0.8; hence, both conditions are possible.

4.2. Experiment I

[16] The experiment was conducted shortly after a major rainfall event. Inflow rates from E-River were approximately 700 m3 s−1 on day 50, almost seven times larger than S-inflows (Table 2). These differences in flow rates are typically observed in winter time, as reported, for example, by Prats et al. [2010]. The weather during the field campaign was cold, cloudy at night, and calm most of the time. The internal Froude number Fi, estimated using cross-sectional average velocities and temperature differences (Table 2 and Figure 3a), varied from O(1) to O(10), and was always >4, which suggests that flows and circulation patterns near the confluence are dominated by inertial forces. Hence, temperature variations were assumed to be unimportant from a dynamic standpoint.

4.2.1. Spatial Arrangement of Inflows Under Weakly Stratified Conditions

[17] Given the marked contrast in the specific conductivity SC25 between E- and S-water (∼80 µS cm−1), SC25 was taken as a tracer of the source of water in the confluence [Gaudet and Roy, 1995; Laraque et al., 2009; Rueda and MacIntyre, 2010], and the dilution of E-water at any given site i was calculated as follows:

display math(4)

[18] Here SC25i is the specific conductivity of the mixture at site i, and SC25E and SC25S denote the conductivity of the end members (Figure 3a and Table 2). The conductivity plots on Figure 3a and the spatial distribution of dilution rates (Figure 5a) suggest that S-water flowed attached to the left side of the confluence with a nearly vertical interface. Assuming (1) that vertically well mixed conditions prevail at and downstream the confluence, (2) that mixing is not affected by the small density differences encountered in the field, and (3) that hydraulic forcing remains steady, the transverse mixing coefficient εt between E- and S-water masses downstream of the confluence can be estimated by fitting the steady-state depth-integrated diffusion equation for SC25 [Bouchez et al., 2010]

display math(5)

to the observations. Here, C (=[SC25i]int/SC25E) is the ratio between the depth-integrated specific conductance of a given site and the specific conductance of E-water; Y (= y/b) is the transverse distance y divided by the river width b, assumed constant over the whole reach (=400 m); and Λ (= εt t/b2) is the nondimensional elapsed time, where the time t = x/us, x being the distance downstream and us the average streamwise velocity (= 0.4 m s−1). To solve equation (5), the fluxes through the banks are assumed negligible, i.e., ∂C/∂Λ = 0 at Y = 0 and Y = 1. S-water (C = 0.89) was initially assumed to occupy 22.5% of the cross section; the remaining was filled with E-water (C = 1). This initial distribution of S- and E-water arise from the assumption of uniform velocities at cross section A (Figure 1), with the observed inflow rates QE and QS on day 50 (Table 2). Equation (5) was calibrated against measured SC25 profiles collected at (1) sites a and b 250 m downstream of the confluence; (2) site d, 5.7 km downstream of the confluence; and (3) sites e and f, 13.8 km downstream of the confluence (Figure 1). The best agreement between equation (5) and observed SC25 (Table 3) was found for εt = 1.7 ± 0.1 m2 s−1 (RMSE = 1.5 µS cm−1). This is consistent with values of εt reported for large river conflueces. For example, Bouchez et al. [2010] found εt to be 1.8 m2 s−1 at the confluence between the Solimões and the Purús rivers, and Lane et al. [2008] found εt to vary between 5.6 m2 s−1 and 266.0 m2 s−1 at the confluence between the Paraná and Paraguay rivers. If we assume that complete mixing occurs when cross-stream conductivity gradients become <1 µS cm−1, and if we ignore the effect of the dam, the mixing length L needed for E- and S-water to become fully mixed is L = 16.3 ± 1 km (or 40.75 ± 2.5 channel widths). These estimates of L of O(10–102) times the channel widths agree with mixing lengths encountered at large river confluences during periods of weak density differences [e.g., Lane et al., 2008, and references therein], and, suggest that E- and S-masses would mix before reaching the dam (located ∼27 km downstream of the confluence).

Table 3. Measured—CTD Profiles a, b, d, e, and f in Figure 1— and Modeled [equation (5)] Depth-Integrated Specific Conductance SC25 (µS cm−1)a
CTD Profilexb (m)YcMeasured SC25 (µS cm−1)Modeled SC25 (µS cm−1)
  1. a

    Modeled values correspond to a tranverse mixing coefficient εt =1.7 m2 s−1.

  2. b

    x, distance downstream of the confluence.

  3. c

    Y = y/b, nondimensional transverse distance, where y is the transverse distance from the left bank and b is the channel width.

a2500.067719.6720.9
b2500.916801.0801.0
d57000.513780.5782.2
e138000.990780.3781.7
f138000.635779.5781.6

4.2.2. Transverse Circulation

[19] The CTD profiles collected downstream of the confluence only exhibit some stratification toward the left bank with lower conductivity values and slightly larger temperatures toward the surface (Figure 6). This pattern is indicative of S-water overflowing southward, though slowly, on top of E-water, transversely to the streamwise direction as it is carried downstream. The slow transverse circulation can be the result of (1) momentum of S-water, flowing southward in a shallow channel and into the reservoir; (2) secondary circulation occurring in the main channel as a result of its meandering planform; and (3) S-water being positively buoyant. All processes should lead to horizontal motions of similar magnitude of order O(10−2) m s−1. For example, the average southward speed of water in the S-River upstream of the confluence, estimated from the ADCP transect, was O(10−1) m s−1 (Table 2). Once in the reservoir, S- and E-waters moving in different directions mix and given the different flow rates of both rivers, the transverse velocity of the mixture should be at least seven times smaller and become O(10−2) m s−1. The maximum transverse velocity un,c that develops in flows in curved or meandering channels, as a result of the centrifugal acceleration, can be estimated following Johannesson and Parker [1988] [see also Geyer, 1993] as follows

display math(6)

where Rs is the radius of curvature. For a curved channel, with Rs = 750 m (see Figure 1), and the flow conditions prevailing in this scenario (h = 10 m, us = 0.4 m s−1), the secondary currents should be approximately 3 × 10−2 m s−1. Finally, the velocity magnitude that develops in a channel of depth h in response to a change in temperature inline image can be estimated as [Fischer et al., 1979]

display math(7)
Figure 5.

Dilution rates (%) from linearly-interpolated specific conductance collected from CTD casts on days (a) 50–51, (b) 329, and (c) 330 at the confluence. Dots account for locations of CTD casts. Red and blue arrows show the direction of the flow. North direction is shown.

[20] Here inline image(T) is the thermal expansion coefficient, which depends on temperature. For h = 10, inline image = 1°C, and α = 6 × 10−5 °C−1 (value of α for T = 8°C) density-driven transverse velocities un,b should be O(10−2) m s−1. Hence, neglecting frictional effects, one would expect S-water to move southward with a speed un,b-Segre = 10−2 m s−1. At that speed, the water on one side of a 400 m wide channel can reach the other bank in ∼5–10 h. For us = 0.4 m s−1, as observed in Ribarroja, the water would have travelled 7–14 km downstream before reaching the right margin. Note, however, that 6 h is also the length of time that the temperature in S-River takes to increase 1°C above the temperature of E-River (Figure 4). Hence, our calculations, being based on steady-state equations, are only approximate. In any case, they suggest that for a significant portion of the length of Ribarroja, S- and E-waters flow side by side. This is consistent with the results of Cook et al. [2006] in the study of the confluence of the Clearwater and Snake rivers, with similar length scales to those of the confluence of the E- and S-rivers (width ∼ 500 m and maximum channel depths of ∼16 m). They presented Multispectral Thermal Images (MTIs) of the confluence taken under nonstratified conditions that demonstrate that both rivers meet and flow parallel to each other for several kilometers downstream. The lateral extent occupied by S-waters in Ribarroja reservoir will likely depend on the inflow southward momentum of S-water, the relative flow rates and the buoyancy differences, which in this period of time, should be small but not negligible. All these factors will change, especially the relative flow rates (as seen, for example, in Figure 2).

Figure 6.

Temperature (°C), specific conductivity (µS cm−1), and turbidity (ntu) profiles collected on day 50. CTD profile c in Figure 1.

4.2.3. Horizontal Circulation

[21] Horizontal recirculation patterns, or gyres, were only observed in a reach far downstream of the confluence where the channel widens, leaving a shallow region to the left (transects F22–24 in Figure 1). The recirculation cell in this reach is approximately 1 km long, occupying the shallowest regions of the channel and attached to the left bank (Figure 1). Upstream velocities with depth-averaged values of ∼10−2 m s−1 were observed in a fringe of ∼300 m from the left bank (Figure 7a). This recirculation was also observed in summer (Figure 7b). Recirculation and flow separation, however, were not observed immediately downstream of the confluence, on the left margin of E-River, as expected according to laboratory and numerical experiments of 90° confluences [e.g., Gurram et al., 1997; Weber et al., 2001]. The absence of recirculation downstream of a confluence, though, has also been reported in other studies of natural junctions [Roy et al., 1988; Roy and Bergeron, 1990; Biron et al., 1993; De Serres et al., 1999]. The presence of a deposition bar just downstream of the confluence at the bank closer to the tributary and the differences in channel bottom depth between the mainstream and the side channel (bed discordance) have been proposed in the literature as possible causes to explain the absence of flow separation [De Serres et al., 1999]. Both conditions apply in our study site (Figure 1, and Bladé i Castellet et al. [2010, Figure 5]). In fact, S-water flows into the reservoir through two channels (Figure 1), with depths of 4 and 2 m depth, respectively, which are shallower than the E-channel (∼10 m). The fact that S-channel is curved and not a straight channel (Figure 1) [Biron et al., 1993] as well as the smoothly curving geometry of the downstream junction corner [Rhoads and Kenworthy, 1995] could also explain the absence of recirculation and flow detachment.

Figure 7.

Depth-averaged E-W velocities (m s−1) from (a) ADCP transects F22 and F24 on day 50 and F23 on day 51 and (b) ADCP transects J19-J21 on day 203.

4.3. Experiment II

[22] The weather during the experiment was dry with high temperatures and strong winds (Table 2) from the southeast. Average water temperatures were ∼22°C, but S-water was, in general, warmer (ΔT ≈ 4–6°C), more turbid, and less salty than E-water (Figure 3b and Table 2). Water releases from Mequinenza followed the same schedule in both days of the experiment. Releases started at 0800 h and completed at 2200 h. Flow rates increased from ∼150 m3 s−1 at 0800 h to ∼250–280 m3 s−1 from 1400 h to 1600 h, to supply electricity at peak demand. This schedule is typical of a summer day. These changes in flow rates are translated downstream at a velocity scale us,b characterizing the propagation of perturbations in a density-stratified fluid, which can be estimated as in equation (7). For α = 2.25 × 10−4 °C−1, ΔT ≈ 4°–6°C and h ≈ 10 m, us,b is ∼ 0.3 m s−1 and the changes in release rates at the dam would propagate to the confluence in 2–3 h. Hence, our observations, collected in the confluence from ∼16 to 18 h, largely represent the hydrodynamic conditions for maximum or near-maximum flow rates.

4.3.1. Spatial Arrangement of Inflows Under Strongly Stratified Conditions

[23] Turbidity records from our CTD casts collected at the confluence were used to recreate the spatial distribution of S- and E-waters in the confluence. This approach was considered valid given that the differences in turbidity between the sources were large (at least 1 order of magnitude, see Table 2) and, hence, it can be used to trace the source of water in the confluence. This assumption is reasonable as long as the time needed to settle for a sediment particle is much larger than the travel time needed by a particle to flow through the confluence, so that it behaves as a conservative tracer in the region of interest. The flow time scales Tf can be calculated as the time to transverse the O(103) m reach that includes the confluence region at a speed of 0.1 m s−1, as observed in our velocity profiles. That time scale Tf is ∼2 h. The time scales of deposition Td, in turn, can be estimated by dividing the depth of the reservoir h ≈ 10 m by a velocity scale representing the settling velocity w0 of the particles, which can be estimated from Stokes law [van Rijn, 1987]. For particle diameters D ≤ 25 µm [Flumen Group, 2009] and SG ≈ 2.65, w0 is of O(10−4) m s−1 and Td is ≥ 5 h. Hence, given that Tf < Td, our approach to trace source water from turbidity values appears to be justified. In general, the minimum values of turbidity, indicative of Mequinenza water, appear in the deepest areas of the confluence (Figure 8). Two plumes, with large turbidity values, characteristic of S-water, appear near the surface both at the northeastern and western ends of the confluence as shown by the longitudinal transect in Figure 8. These two plumes correspond to the two inflow channels from the S-River. Minimum turbidity values appear along the center of the E-channel, upstream of the westernmost plume due to the entrance of low turbidity water from the E-River. Turbidity also peaks along the northern and southern shore of E-River, which is either (1) water that existed there early in the morning before the start of discharge operations in Mequinenza or (2) water from the most upstream plume formed by the S-River flowing upstream along the E-River. Photographs taken on day 202, one day before the CTD profiles were collected, support our interpretation of the distribution of waters in the confluence (Figure 8).

Figure 8.

Linearly interpolated turbidity values (ntu) from CTD casts collected on day 203 and picture taken on day 202 at 1528 P.M. from location shown in Figure 1 (star). July experiment. Dots account for locations of CTD casts. Red and blue arrows show the direction of the flow. North direction is shown.

4.3.2. Inertial, Buoyancy, and Wind Forcing

[24] Average flow velocities were 0.1–0.2 m s−1, and the internal Froude number Fi for these velocities was O(10−1). For the maximum velocities of 0.3 m s−1 observed near the center of E-channel, though, Fi was close to O(1), which suggests that even though buoyancy may be the dominant force driving motion, inertial forces cannot be ignored in our analysis. The sheared velocity profiles encountered along the E-River, with the largest downstream velocities occurring near the bottom, in fact, appear to be controlled by an inertial-buoyancy balance (Figure 9). The buoyancy forces work to arrest the downstream flow near the surface and make the warmer water flow upstream over the cold Mequinenza water. The latter, in turn, will tend to flow downstream driven both by the inertial and buoyancy forces. Upstream of the confluence, water flowed mostly downstream with the largest velocities (0.2 m s−1) occurring near the bottom and nearly stagnant water near the top (Figure 9, J4). Downstream, the inertial forces diminish as a consequence of (1) mixing and (2) friction with the bottom and lateral boundaries, and buoyancy forces drive the top of the water column flow upstream (Figure 9). Given that streamwise velocity maxima occur near the channel bed (Figure 9), and that Fi ∼ 1, E-flows likely behave as density currents below the S-waters [e.g., Kneller et al., 1999].

Figure 9.

Laterally averaged E-W velocities for transects J4–8 (Figure 1) across Ebro channel on day 203.

[25] Wind forcing could have also contributed to the balance of forces in the confluence and need to be taken into account to interpret the field observations. For example, water in the S-channel appeared to flow upstream along the shallowest sections (Figure 10), probably as a result of strong southeasterly winds. The low turbidity values existing between the two inflow channels of the S-River in Figure 8 could be the result of the wind-driven upstream flow of low turbidity E-water. Also as a result of the strong wind forcing, turbidity and temperatures varied laterally in the S-channel. Temperatures, for example, varied from 24°C to 25°C in most of the profiles, reaching values of up to 28°C near the right bank. This distribution could be interpreted as the result of the strong wind forcing accumulation of warm surface water in the westernmost boundaries of the reservoir and tilting of the isotherms.

Figure 10.

Temperature (°C) and turbidity (ntu) from CTD casts, and N-S velocity (m s−1) from ADCP transect at the Segre River (transect J1 in Figure 1) on day 202. Dots account for locations of CTD casts at right. W, western (rigth) bank, E, eastern (left) bank.

[26] The CTD casts collected along transect J4 in the E-channel also reveal a stratified water column with tilted isotherms (Figure 11). Near the center of the channel, a sharp interface at a depth of 2 m separates the cold water (19°C–20°C) at the bottom from warmer (23°C) at the surface. At the left bank, in turn, the surface water is warmer (24°C) and the temperature gradients are smoother. The tilting of the isotherms, in this case, could be attributed to the strong southeasterly winds acting on the stratified water column. The southeasterly winds will tend to elevate and widen the isotherms near the southern shore. Assuming a two-layer stratification with an upper mixed layer of thickness H, the displacement of the isotherms Δh driven by wind forcing can be estimated in terms of the Wedderburn number, W, as Δh = 0.5H/W [Shintani et al., 2010]. Wedderburn numbers, W, expressing the balance between wind and baroclinic forcing was calculated in the cross-stream direction as follows:

display math(8)

where inline image is the shear velocity of air ( inline image = ρa0 CdwU102) calculated from the air density ρa, wind drag coefficient Cdw (≈ 10−3, Fischer et al. [1979]), and wind speeds U10 measured at 10 m above the free surface. For H = 2 m and average wind speeds of U10 of ∼7 m s−1, as measured on day 203, ua* = 8 × 10−3 m s−1, W ∼ 2, and the isotherm displacements Δh could be up to 0.5 m, lower than observed in the field (Figure 11). The tilting of the isotherms upstream of the confluence can also be interpreted as the result of the lateral circulation that develops due to the curved shape of the E-riverbed upstream of the confluence (Figure 1). Similar observations have been reported for density currents flowing in sinuous subaqueous channels [Cossu and Wells, 2010], estuarine flows through curved channels [Seim and Gregg, 1997; Lacy and Monismith, 2001], and turbulent buoyant flows in curved open channels [Shen et al., 2003]. The isotherm displacement Δh driven by secondary flows in a curved channel can be estimated if we assume a steady-state balance between centrifugal acceleration and cross-channel baroclinic pressure gradients in the channel. The timescale Tb to reach steady state is determined by the cross-channel baroclinic adjustment time and can be estimated as [Lacy and Monismith, 2001] Tb = b/(g′H)1/2. For a channel width in the E-inflow channel bE = 300 m and H = 2 m (mean depth of the S-River at this section and time), Tb ∼ 0.5 h. This is lower than the advective time for the flow to pass around the bend (2–3 h for a distance of 3 km), which suggests that the isotherms rapidly adjust to any changes in the flow field driven by perturbations in inflow rates, and, hence, that the steady-state assumption for the cross-channel flow in Ribarroja is reasonable. Under steady-state conditions, in a two-layer flow in a curved channel, in which only the bottom layer flows as a gravity current, the isotherm displacement Δh can be calculated as follows [Komar, 1969]

display math(9)
Figure 11.

Linearly interpolated temperature (°C) from CTD casts in transect J4 (Figure 1) on day 203. Dots show the locations of CTD profiles at right. N, northern (left) bank; S, southern (right) bank.

[27] For Rs = 1 km (as is the case of E-channel, upstream of the confluence, Figure 1), us = 0.3 m s−1, and Δρ/ρ0 =10−3 as observed in transects J4–5, the expected displacement of the isotherms Δh = 2.5 m, in agreement with the observations (Figure 11). The tilting of the isotherms shown in Figure 11 suggests the existence of secondary circulation, with water in the upper layers flowing toward the inner bank, which is opposite in sign to the classical circulation in open-channel flow through bends [Rozovskii, 1961]. This type of reversed secondary circulation has been observed under nonlogarithmic streamwise velocity profiles in curved estuarine channels [Seim and Gregg, 1997; Lacy and Monismith, 2001], and it is a common feature in density currents flowing in sinuous subaqueous channels [e.g., Corney et al., 2006; Keevil et al., 2006, 2007; Cossu and Wells, 2010; Parsons et al., 2010]. Corney et al. [2006, 2008] suggested that the sign of the secondary circulation in stratified sinuous channels is largely controlled by the height above the channel bed where the streamwise velocity is maximal. Reversed secondary circulation will develop for streamwise velocity profiles exhibiting peak values below ∼40%–45% of the channel depth, as is the case of Ribarroja (see Figure 9). Driven by either centrifugal and/or wind forcings, isotherm tilting could be important to understand mixing between the two sources in the confluence, given that the area of the mixing interface increases as a result of the tilt, and water parcels are allowed to mix horizontally, at faster rates than vertical mixing under stratified conditions [e.g., Imboden and Wüest, 1995].

4.3.3. Mixing at the Confluence

[28] Using laterally averaged velocity profiles and CTD profiles at the deepest points along transects J8 and J9 (near the confluence), gradient Richardson numbers Rig were estimated as follows:

display math(10)

[29] These calculations suggest that indeed there is a shear mixing-layer between 4 and 5 m of depth, where Rig < 0.25 (Figure 12), indicative of active mixing [Rohr et al., 1988]. The thickness of the shear layer encountered in the confluence agrees with the scaling proposed by Sherman et al. [1978]. A shear layer forming as a result of billowing in stratified flows should have a thickness at equilibrium δB of the form

display math(11)
Figure 12.

Laterally averaged E-W velocities from ADCP transects, temperature profiles from CTD casts, and estimated Rig for transects (a) J8, (b) J9 and (c) N10 in Figure 1. Dashed lines account for Rig = 0.25.

[30] For α = 2.25 × 10−4°C−1, ΔT = 4°C–5°C, and a velocity difference Δu = 0.2 m s−1 (the laterally averaged speed in E-River upstream of the confluence, at the time of maximum discharge), equation (11) predicts a shear layer of approximately 1 m. This is indicative of strong mixing at the confluence tending to form a diffused interface between E- and S-waters. Immediately below the shear-layer (deeper than 5 m), there exists an interface (thermocline) where the temperature changes from 25°C to 20°C and gradient Richardson numbers are well above 0.25. Vertical diffusivities at the thermocline were calculated from our estimates of Rig as in Latif et al. [1994]

display math(12)

[31] For Rig of O(1), equation (12) predicts values of O(10−5) m2 s−1 for the thermocline at the confluence (transect J9). These values are consistent with those calculated using a three-dimensional hydrodynamic model of the confluence for the same period of time, as reported by Ramón [2011]. Assuming that E-water flows as a layer of 2 m (the average thickness of the hypolimnion, based on temperature profiles in Figures 12a and 12b), below the water from S-River, in a channel of constant depth h equal to the depth of the E-channel at the confluence (10 m), and assuming that mixing rate is constant in time, both layers would need ∼37 h to mix. With average downstream speeds of 0.2 m s−1 as measured in the field, these two layers would be mixed ∼27 km downstream of the confluence. These calculations suggest stratification near the dam being largely inherited from the difference in properties between E- and S-waters.

4.4. Experiment III

[32] During experiment III, the weather was cold, foggy during the morning, and sunny from noon to sunset. Wind was weak at all times (Table 2). Average discharge rates from Mequinenza estimated from ADCP transects varied from 240 to 266 m3 s−1 on day 329 and from 144 to 200 m3 s−1 on day 330. Measured discharges at the inflow section of the S-river were 12 and 69 m3 s−1 on day 329 and 330, respectively. This order of magnitude for the inflows from the E- and S-rivers agrees with inflows at the confluence in 1998 (Figure 2) and 2004 and 2005 during this month [Prats et al., 2010]. Average water velocities were O(10−1) m s−1 in the E-River and O(10−2) m s−1 in the S-River upstream of the confluence (Table 2). The internal Froude number Fi was O(1), which suggest that an equilibrium between inertial and buoyancy forces exists at the confluence. S-water was, in general, colder and more turbid but had lower specific conductance values than E-water (Table 2).

4.4.1. Spatial Arrangement of Inflows

[33] Given the strong differences in the conductivity of the sources (∼900 µS cm−1), SC25 was used to trace the source of the water in the confluence. The conductivity was taken here to be 837 and 1755 μS cm−1, for S- and E-waters, respectively (Table 2). Dilution rates were estimated from SC25 data as in equation (4). All profiles were collected from 1100 h to 1400 h in the vicinity of the confluence of the S- and E-rivers. Hence, they represent a synoptic view of the flow field and the distribution of E- and S-waters as they flow into the reservoir. On day 329, with a discharge ratio Rq = QS /QE = 0.047, the water column in the reservoir appeared unstratified upstream of the confluence but stratified downstream, with S-water occupying the shallower layers. At the confluence, the S-plume appeared confined to the left margin, but, further downstream it moved toward the right margin. The lateral extension of the plume was limited and only reached the right margin of the channel very close to the surface (Figure 5b). On day 330, with S-inflow rates almost six times those recorded on day 329 (Rq = 0.4), the S-water reached the right bank at the confluence and mixing between the sources appears to be stronger (Figure 5c). Immediately downstream of the confluence (transect N12 in Figure 1), E-water accumulated near the right bank (Figure 5c). The interpolated conductivity plots show two local maxima, which can also be interpreted as a result of two plumes. One, formed near the upstream end of the confluence where the deepest channel of the S-River discharged into the reservoir, corresponds to the southernmost maximum. The second formed at the downstream end of the confluence as a result of the discharge of the shallowest (easternmost) channel of the S-River. Farther downstream (transect N18 in Figure 1), the low conductivity water from S-River appeared attached to the right margin, while the high conductivity water from Mequinenza accumulated near the left margin (Figure 5c). These observations are suggestive of a strong lateral circulation set up as a result of the inertia of the side inflow being of similar magnitude to the longitudinal inertia of the main-stream inflows. This braided circulation is consistent with field data and results of three-dimensional simulations of the confluence between the Snake and Clearwater rivers [Cook et al., 2006] for Rq = 0.87 and Δρ/ρ0 of O(10−3). It seems plausible that E-water might have been preferably flowing near the right margin, and we could have missed it in our CTD casts.

4.4.2. Mixing at the Confluence

[34] On day 330, the fraction of E-water in the lower layer in transect N18 (Figure 1), estimated from conductivity values as in equation (4), was only 53%, which is indicative of very strong mixing between E- and S-waters. Large mixing rates could have occurred as a consequence of (1) high shear near the bottom in a weakly stratified water column, or alternatively, (2) as a result of the development of weakly unstable density profiles during mixing of E- and S-waters. Whether shear mixing or density-driven instabilities are responsible for the strong mixing that appears to occur downstream of the confluence is beyond the scope of this manuscript. In any case, shear could be strong enough to reduce the density gradients across a large fraction of the water column. Assuming a stably stratified water column on day 330 with density differences of ∼0.05 kg m−3 and longitudinal velocity differences of 0.1 m s−1 between E- and S-water in the main channel (Figure 12c), one would expect a shear layer of thickness δB ∼ 6 m, which is similar in magnitude to the depth of the channel h. The gradient Richardson number is < 0.25 at all depths, indicative of active mixing. For Rig of O(10−1) m2 s−1, as encountered at the thermocline, vertical diffusivities were of O(10−4) m2 s−1. Assuming a constant mixing rate, and that E-River flows as a layer of ∼7 m thick (thickness of the hypolimnion based on the temperature profiles, Figure 12c) below the S-water in a channel of constant depth h = 10 m (depth of the E-channel at the confluence region), both layers would need ∼35 h to mix. With average observed velocities of 0.1 m s−1, both rivers would appear mixed after 13 km downstream of the confluence.

4.5. Parameterization of Flows at River Confluences

[35] Our results from Experiments I–III suggest that the spatial arrangement of two rivers at a large asymmetrical river confluence with a junction angle of nearly 90° is largely controlled not only by the inflow velocities of the tributary Ut and the mainstream Um but also by the density differences between the two rivers. The velocity ratio Rv (= Ut/Um) represents the ratio of inertial forces between the side inflow and the mainstream, and for a given geometry is determined by the discharge ratio of tributary to mainstream inflows Rq (= Qt/Qm). The ratio of the buoyancy of the side stream, parameterized in terms of the celerity of the internal perturbations (g'h)1/2, and the magnitude of the inertial forces, characterized by the streamwise velocities along the main channel, is the inverse of the internal Froude number Fi for the confluence. For Fi >> 1, the effect of density differences can be neglected, and the mixing interface between the confluent rivers remains largely vertical (Figures 13a and 13b). The location of the mixing layer, in this case, is largely controlled by the magnitude of Rv. For Rv << 1, the mixing interface will be close to the tributary bank. This was the case of Experiment I in Ribarroja conducted under weakly stratified conditions. For Rv >> 1, in turn, the interface gets closer to the opposite bank (Figure 13b). Earlier work conducted under nearly neutrally buoyant conditions conducted in the laboratory [Best, 1987] or in small river confluences [Biron et al., 1993; Rhoads and Kenworthy, 1995, 1998; De Serres et al., 1999] are consistent with our results and suggest that the location of the mixing interface largely depends on the momentum flux ratio M (= UtQt/UmQm) and the junction angle. The confluent rivers flow side by side (Figures 13a and 13b), mixing laterally at a rate controlled by shear-driven horizontal turbulence and the existence of secondary circulation. In general, under weakly buoyant conditions, mixing rates will be small, unless the mixing interface becomes distorted due to channel-scale secondary circulation [Rhoads and Kenworthy, 1995, 1998] or under the influence of topographic forcings such as the presence of bed discordance [Gaudet and Roy, 1995].

Figure 13.

Conceptual model for the near surface (gray lines) and near bottom (black dashed lines) velocity streamlines and for the location of the mixing interface at the surface plane (black straight lines) for different velocity ratios (Rv=Ut/Um) between the tributary t and the main stream m and internal Froude numbers Fi (= Um/(g′h)1/2) at an asymmetrical confluence with a 90° junction angle. (a) Rv = 0.25 and Fi >>1, (b) Rv = 2 and Fi >>1, (c) Fi << 1, (d) Rv = 2 and Fi ≤ 1, and (e) Rv = 1 and Fi >1.

[36] Vertical stratification will develop at the confluence if Fi < 1, and even upstream of the confluence if Fi << 1, as a result of the nonneutrally buoyant side-inflow moving upstream along the mainstream (Figure 13c). Under those conditions, the mixing interface will tilt and become horizontal at or immediately downstream of the confluence if Rv < 1. Mixing rates will decrease as a result of vertical stratification and the two rivers may remain unmixed long distances downstream of the confluence. This was the case of Experiment II in Ribarroja, where stratification, as observed near the dam, is largely determined by the differences in buoyancy between S- and E-waters. If Rv > 1, in turn, the mixing interface may become tilted across the mainstream as a result of the large lateral inertia of the side inflow in comparison with the stability of the water column, and the negatively buoyant flow may even upwell downstream of the confluence at the tributary bank (Figure 13d; Experiment III). For intermediate values of Fi of O(1), the distance downstream needed for the tributary water to reach its opposite bank will depend both on Fi and Rv (Figure 13e). This distance will decrease in response to increases in Fi−1 and Rv.

[37] The dependence of large river confluences on Fi is consistent with field observations at large river confluences. For example, vertical stratification develops for nonneutrally buoyant side flows (Fi ≤ 1) at the confluence between the Snake and Clearwater rivers [Cook et al., 2006]. Near vertical mixing interfaces were, in turn, reported for weakly buoyant side flows, Fi >> 1. Laraque et al. [2009] also report observations collected at the confluence between the Negros and Solimões rivers, with widths of O(1) km downstream of the confluence, and suggest that under weakly buoyant side flows, with Fi > 1, the mixing interface between the confluent rivers was significantly distorted. Note, however, that in our analysis we have ignored other important effects, such as, those of the centrifugal forces, wind forcing or topographic forcing (such as the presence of bed discordance). For example, secondary circulations driven by the curvature of the streamlines at the confluence and/or the planform curvature of the confluence could lead to a higher distortion of the mixing interface than expected from baroclinic effects alone [e.g., Rhoads and Kenworthy, 1995; Rhoads and Sukhodolov, 2001].

5. Conclusions

[38] The spatial arrangement of inflows and their mixing rates in large asymmetrical river confluences are largely controlled by the ratio between forces driving the cross-stream motion of the side inflow (inertia, buoyancy, and centrifugal forces associated to the meandering form of the main stream) and the inertial forces in the mainstream. The behavior of the confluent streams can be parameterized in terms of an internal Froude number and the velocity ratio between the confluent streams. For Fi >> 1, buoyancy forces are negligible compared with inertia and the mixing interface remains vertical. For Fi < 1 the confluence becomes vertically stratified. For intermediate values of Fi, the distance downstream needed for the tributary water to reach its opposite bank will depend on the velocity ratio. For higher velocity ratios, the mixing interface would locate farther from the tributary bank, and these distances become shorter. The influence in a specific location of other forces such as centrifugal forces, topographic forcing, and/or wind forcing will increase or decrease this length scale. A more quantitative and exact relationship between these controlling factors and the lateral extension of the tributary waters should be further explored with the aid of three-dimensional modeling tools.

Notation
A

area, m2.

b

channel width, m.

C

nondimensional SC25.

C0

conductivity values, µS cm−1.

Cdw

wind drag coefficient.

D

particle size, m.

Fi

internal Froude number.

g

gravitational acceleration, m s−2.

g'

reduced gravity, m s−2

h

depth of the channel, m.

H

depth of the upper layer in a two-layer system, m.

Δh

vertical displacement of the interface between rivers, m.

Kv

vertical diffusivity, m2 s−1.

L

mixing length, m.

Q

discharge, m3 s−1.

Rig

gradient Richardson number.

Rq

discharge ratio.

Rs

radius of curvature, m.

Rv

velocity ratio.

SC25

specific conductance (T = 25°C), µS cm−1.

SG

specific gravity of suspended solids.

SS

suspended solid concentration, mg L−1.

t

time, s.

T

temperature, °C.

ΔT

magnitude of temperature differences, °C.

Td

time scales of deposition, s.

Tf

flow time scales, s.

Tb

baroclinic adjustment time, s.

TDS

total dissolved solids concentration, mg L−1.

Turb

turbidity, ntu.

U

inflow velocity, m s−1.

U10

wind velocity at 10 m height, m s−1.

u

local streamwise current velocity, m s−1.

inline image

shear velocity of air, m s−1.

un,c

maximum transverse velocity as a result of the centrifugal acceleration, m s−1.

un,b

lateral velocity magnitude due to buoyancy forces, m s−1.

us

average streamwise velocity, m s−1.

us,b

streamwise velocity magnitude due to buoyancy forces, m s−1.

V

volume, m3.

W

Wedderburn number.

w0

settling velocity, m s−1.

x,y,z

streamwise, lateral, and vertical (positive upward) coordinates, m.

Y

nondimensional cross-stream distance.

Greek letters

α

thermal expansion coefficient, °C−1.

Γ

dilution rate, %.

δB

shear layer thickness, m.

εt

transverse mixing coefficient, m2 s−1.

λ

scaling factor to transform conductivity into salinity, mg L−1(μS cm−1)−1.

Δρ

density differences between rivers, kg m−3.

ρ

density of water, kg m−3.

ΔρSS

density contribution due to suspended solids, kg m−3.

Λ

nondimensional elapsed time.

Subscripts

0

reference value.

E

Ebro.

S

Segre.

m

main stream.

t

tributary.

Acknowledgments

[39] This work was funded through a collaborative agreement between the University of Barcelona and the University of Granada to work jointly in the project “Gestión hidráulica y técnicas de detección remota aplicada al control de poblaciones mejillón cebra: el caso del embalse de Ribarroja y el tramo inferior del río Ebro,” funded by the Spanish Ministry of the Environment. We thank all the people that participated and helped in the data collection campaigns: Javier Vidal (University of Granada), Karla Gleichauf (Stanford University), Gonzalo González (University of Barcelona), Ángel David Gutiérrez Barceló, Ana Silió, and Raúl Medina (Instituto de Hidráulica Ambiental IH Cantabria). We are also in debt with the scientific personnel from ENDESA-Medio Ambiente, for their invaluable help facilitating our access to the reservoir, sending us samples when we needed them, and supplying hydrological information in a timely manner.