Observation of the whole process of interaction between barchans by flume experiments



[1] Through laboratory experiments generating unidirectional water flows, we examine the process of interaction between two moving barchans (sandy bed configurations in a crescentic plan-shape), which may take dozens of years for barchan dunes in the nature. Three types of the interaction were observed. The first type was absorption of two barchans into one. The second was that the upstream fast barchan rode on the downstream slow barchan and simultaneously a newly born barchan was ejected from the lee side of the slow barchan. The third was that the downstream slow barchan was split into two before the upstream fast barchan touched the downstream. The type of the interaction was determined by both relative and absolute size of two barchans.

1. Introduction

[2] Barchans are bedforms (sand dunes or sandy ripple marks) in a crescentic shape generated by wind in desert on Earth [Bagnold, 1941; Lancaster, 1995] and on Mars [Breed et al., 1979] or by water flows on the ocean floor [Newell and Rigby, 1957; Allen, 1968] and on the river bottom [McCullogh and Janda, 1964], where sand is sparse. Some barchans exceed 30 m in height and 300 m in width and length. Barchans move downstream pointing their crescent tips in the direction of their migration. Erosion on the stoss-side (upstream) slope and sedimentation on the lee-side (downstream) slope are virtually balanced, so a barchan moves nearly maintaining the size and shape. Barchans in one dune field, subject to the same wind condition, migrate at a speed reciprocally proportional to their size [Bagnold, 1941], which can reach several tens of meters per year.

[3] A smaller barchan migrates faster than a larger one and the collision between the two necessarily occurs if they exist on the same path. In the field, some barchans are observed to coalesce with others into complex topographies on Earth [Breed et al., 1979; Besler, 2002] and on Mars [Breed et al., 1979], which suggest the midterm stage of a collision process. The dynamics of dunes have been discussed in theoretical studies to explain the pattern of dune fields [Werner, 1995; Nishimori et al., 1998; Lima et al., 2002]. A recent model study [Schwämmle and Hermann, 2003] paid attention on the interaction purely between two barchans and solved the equations of motion to interpret small barchans existing downwind of bigger barchans. Interaction between barchans is an important elementary process in dune dynamics, because it causes the change of the size and space distributions of barchans. Understanding the whole process of the interaction is significant for comprehending complex topographies found in the nature and for tracing the history of and predicting the future of dune fields. However it is difficult to watch the process from beginning to end in the nature, because it takes very long time (probably several decades).

[4] Laboratory study can downsize the time and space scale of the phenomena. Niño and Barahona [1997], Hersen et al. [2002] and Endo et al. [2004] reproduced barchan fields in a flume, where many barchans occurred ubiquitously. Experimental study focusing on interaction between two barchans has not been conducted. The present study is aimed at observing interaction processes between barchans under steady unidirectional flows through flume experiments and providing information useful for understanding dune dynamics.

2. Methods

[5] To reproduce barchans in the laboratory, we conducted experiments using a recirculating flume (10 m long, 20 cm wide and 50 cm deep), which can generate a steady unidirectional water flow. Water depth (13 cm) and flow velocity (35 cm/s; depth-averaged) were kept constant in all runs. At the beginning of each run, flow was gradually accelerated to the objective velocity not to generate water waves, taking about 2 minutes. Sand with diameter of 100 μ was used. While the conventional experimental studies for barchans adopted a thin sand sheet as the initial condition, in this study to control the position and size of two barchans we placed two sand mounds in cone morphology initially; a bigger mound was located downstream of a smaller one with a space of about 10 cm. A sand cone changes into a barchan automatically by water flows (Figure 1). Fourteen cases were carried out by combining weight of two sand mounds (10 g or 20 g for a larger one, and 0.5 g–1.7 g, every 0.2 g, for a smaller one). The width of barchans of 20 g, 10 g, 1.7 g and 0.5 g are about 9 cm, 7 cm, 3.5 cm and 2.5 cm, respectively. The height of barchans in the laboratory is about one-tenth of the width, which accords with the previous field study [Hesp and Hastings, 1998]. The duration of each run was about 30–40 minutes, depending on the speeds of migration and/or interaction of barchans.

Figure 1.

Photo sequence displaying the formation of a barchan from a sand cone. Time flows from left to right. The leftmost panel shows a sand cone when the water just began to move. The flow velocity attained to a given value (35 cm/s) at about 2 minutes after the flow started. Numbers below arrows represent time intervals. Height of each panel corresponds to 10 cm. The weight of sand was 20 g. A sand cone of lesser weight is transformed into a barchan more quickly.

3. Results and Discussion

[6] The present experiments well controlling the size and position of barchans enabled the systematic observation on the whole process of interactions between barchans; three distinct processes were recognized (Figure 2). The first type of process was that the small fast barchan was completely absorbed into the large slow barchan (Figure 2a), which is hereafter referred to as “absorption.” In “absorption” process, the small barchan caught up to and rode on the back of the large one. The superimposed barchan vanished due to smoothing of the upstream slope of the larger barchan by the flow. The previous simulation studies [Nishimori et al., 1998; Momiji et al., 2000; Schwämmle and Hermann, 2003; Hersen et al., 2004] have reproduced “absorption” of sand dunes into a larger one. Momiji et al. [2000] suggested that non-linear speedup of the flow velocity with height was a key factor for the smoothing of the bed surface. Although assessing the flow around the barchans quantitatively is useful to understand the mechanics of the smoothing, the measurement is the future work because there are some problems due to the limitation of the equipment. In this study, “absorption” occurred when an upstream barchan was much smaller than the other barchan (Figure 3).

Figure 2.

Photo sequences showing three types of interaction between two barchans. Time flows from left to right. Time intervals between neighbouring panels are denoted below arrows. Height of each panel corresponds to 12 cm. (a) “Absorption” type. Initially, the upstream barchan was of 0.5 g and the downstream was of 20 g. (b) “Ejection” type. The upstream, 1.1 g; downstream, 20 g. (c) “Split” type. The upstream, 1.7 g; downstream, 10 g.

Figure 3.

Type of interaction between two barchans, depending on combination of weights. A: “absorption”; E:“ejection”; S: “split.”

[7] The second type was that the upstream barchan caught up with the downstream large barchan and a new barchan was born out of the lee side of the large barchan (Figure 2b), which is here referred to as “ejection.” Although the larger barchan was deformed and looked to be braking, the stoss slope of it was smoothed and it kept being one form to the end of the run for seven minutes (but did not recover to a complete barchan shape). The “ejection” process seemed as if the small barchan passed through the large one, but actually the previous small barchan was superimposed on and merged into the large barchan and the ejected barchan was the completely new one. In “ejection” process, erosion occurred on the back of the large barchan, which was caused by vortices generated near the lee side face of the superimposed barchan. The eroded back of the large barchan resulted in the new barchan. Occurrence of “ejection” processes needed a small barchan to ride on the back of a large one as “absorption” process, but required difference in size between two barchans to be less than the case of “absorption” (Figure 3). In each case of “ejection”, the ejected barchan was smaller than the initially upstream barchan. It is not sure that continuous vortices observed here occur in subaerial environments. However, what is significant for the interaction between barchans is promotion of erosion on the back of a downstream barchan rather than occurrence of a vortex itself. A strong wind will cause separation of the flow at the crest of a barchan. When the separated flow reattaches on the back of a downstream dune, the erosional rate will increase. It is thought that substantially the same phenomenon occurs both in subaerial and subaqueous environments. The “ejection” process is similar to “solitary wave behavior” suggested by previous studies [Besler, 2002; Schwämmle and Hermann, 2003], and further investigation for the comparison between these is necessary.

[8] The third type was not contact between two barchans in the strict sense, but was that the downstream barchan was split into two by approach of the upstream one before touch (Figure 2c). Here we call this process “split.” During the “split” process, the vortex produced at the lee side of the upstream barchan swept away sand particles at the rim of the stoss side of the downstream barchan even when the distance between the two was not short (i.e., before they contacted). So, the edge (tail) of the downstream barchan kept away from the chasing upstream barchan and the upstream one could not catch up with and hence could not ride on the downstream one. This phenomenon necessarily gave rise to deformation of the downstream barchan. Further approach of the upstream barchan caused a thorough split of the downstream barchan, which results in three barchans ideally, although the situation of entirely isolated three barchans was seldom realized because of coalescence between barchans due to imperfection in symmetry of the barchan shape. “Split” occurred when an upstream barchan was larger than a certain value that depends on the size of a downstream barchan (Figure 3). The downstream-protruding part to be split (the fourth panel of Figure 2c) is reminiscent of a parabolic topography of a Peruvian dune interpreted as collision features [Breed et al., 1979].

[9] The critical value of initial size-ratio of two barchans between one type of interaction and other was not constant (Figure 3); threshold between “absorption” and “ejection” was 0.09 (0.9/10) for a 10 g larger barchan but 0.06 (1.1/20) for a 20 g larger barchan, and threshold between “ejection” and “split” was 0.11 for a 10 g larger barchan but 0.08 for a 20 g larger barchan. Thus, interaction type was determined by both relative and absolute size of two barchans at a constant flow velocity. Type of interaction depends on the balance between rates of erosion on the back of the downstream barchan and burying with sand by the upstream barchan itself, both of which are governed by the barchan size. The drift speed of the erosion surface of the downstream barchan depends positively on the height of the upstream barchan responsible for the strength of the vortex and negatively on the height of the erosion surface. On the other hand, the migration speed of each barchan is reciprocally proportional to the each height. If the relative speed between two barchans does not exceed the drift speed of the erosion surface, the upstream barchan never catch up with the eroded area and “split” occurs. Although the type of interaction process and its size effect must be associated to fluid conditions and therefore more investigations are needed, findings obtained here would help to understand the time-evolution of dune fields in relation to elementary processes.


[10] We thank H. Nishimori for discussions. This work was supported by JSPS to N. E.