Collision Dynamics of Two Barchan Dunes Simulated Using a Simple Model

Abstract

The collision processes of two crescentic dunes called barchans are systematically studied using a simple computer simulation model. The simulated processes, coalescence, ejection and reorganization, qualitatively correspond to those observed in a water tank experiment. Moreover we found the realized types of collision depend both on the mass ratio and on the lateral distance between barchans under initial conditions. A simple set of differential equations to describe the collision of one-dimensional (1D) dunes is introduced.

How do bedform patterns arise? New views on the role of bedform interactions within a set of boundary conditions

“…A specifi c type of merging that causes bedform instability is off-center collision among barchans, as observed in fl ume experiments with subaqueous ripples (Endo and Taniguchi, 2004;Hersen, 2005;Hersen and Douady, 2005), CA models ('reorganization' in Katsuki et al, 2005a), and fi eld observations (Gay, 1999;Elbelrhiti et al, 2005Elbelrhiti et al, , 2008Hersen and Douady, 2005) (Figures 1A, 2, 3, 5). The off-center collision of a small dune with a larger dune fosters the shedding (calving, breeding) of one or more smaller bedforms from the horn of the impacted bedform (Elbelrhiti et al, 2005;Hersen, 2005).…”

“…Merging may be most common in the early stages of fi eld development where bedforms are small, diverse in size and randomly spaced (Kocurek et al, 1992), but merging can be observed elsewhere when a small dunes overtakes a larger dune (Figures 2-5). Models, fl ume experiments, and fi eld observations indicate that merging is successful only where the approaching dune is signifi cantly smaller than the target dune (Schwammle and Herrmann, 2003;Endo and Taniguchi, 2004;Katsuki et al, 2005a;Herrmann, 2006;Elbelrhiti et al, 2008;Ewing and Kocurek, in review). With bedforms more equal in size, more complex interactions occur (see below).…”

“…The off-center collision of a small dune with a larger dune fosters the shedding (calving, breeding) of one or more smaller bedforms from the horn of the impacted bedform (Elbelrhiti et al, 2005;Hersen, 2005). Off-center collision between dunes more equal in size results in a reorganization in which the two dunes merge, but with a new dune ejected from the impacted bedform (Katsuki et al, 2005a;Elbelrhiti et al, 2008). In both cases, collision introduces considerable dynamics into the system, but mitigates the constructive merging process or may even be regenerative by increasing dune number and decreasing the size of the impacted dune (Elbelrthiti et al, 2005;Hersen and Douady, 2005).…”

“…The concept originated from CA models of wind ripples (Landry and Werner, 1994), but has been independently proposed for aeolian dunes (soliton model of Schwammle and Herrmann, 2003; 'ejection' of Katsuki et al, 2005a). The exact dynamics of the dune models are doubtful because the downwind dune must emerge from within the separation cell of the upwind dune (Livingstone et al, 2005).…”

“…lee deposition, angle-of-repose limit to grain stacking). Subsequent efforts included models that yield more realistic aeolian dune shapes (Nishimori et al, 1998;Momiji et al, 2000;Bishop et al, 2002), models that address specifi c processes such as bedform merging (Katsuki et al, 2005a), and analytical models that address defect dynamics (Werner and Kocurek, 1997) and bedform spacing (Werner and Kocurek, 1999) as observed in CA models. Initial incorporation of vegetation into the model (de Castro, 1995) has been followed by a more sophisticated treatment that allows interactions between vegetation and sand in transport (Baas, 2007;Nield and Baas, 2008).…”