Breeding and solitary wave behavior of dunes

Abstract

Beautiful dune patterns can be found in deserts and along coasts due to the instability of a plain sheet of sand under the action of the wind. Barchan dunes are highly mobile aeolian dunes found in areas of low sand availability and unidirectional wind fields. Up to now modelization mainly focused on single dunes or dune patterns without regarding the mechanisms of dune interactions. We study the case when a small dune bumps into a bigger one. Recently Schwämmle and Herrmann [Nature (London) 426, 610 (2003)] and Katsuki [(e-print cond-mat 0403312)] have shown that under certain circumstances dunes can behave like solitary waves. This means that they can "cross" each other which has been questioned by many researchers before. In other cases we observe coalescence--i.e., both dunes merge into one--breeding--i.e., the creation of three baby dunes at the center and horns of a Barchan dune--or budding--i.e., the small dune, after "crossing" the big one, is unstable and splits into two new dunes.

The dune size distribution and scaling relations of barchan dune fields

“…We find that the relative standard deviation σ col / w col of such distribution, where w col is the mean size, is constant for different initial conditions (Fig. 4b) and its value is fixed by the parameters of the dune model, which were chosen to reproduce the morphology of Moroccan dunes [6,17], which in turn determine the dune morphology and thus the phenomenological collision rule [16]. The constant value of the relative standard deviation is consequence of the scale invariance of our collision dynamics that depends on the relative dune size instead of the absolute size.…”

“…For instance, barchans occur in areas with unidirectional wind and low sand availability. The influence of the geographical constrains and the external physical conditions [2][3][4], of the dune-dune interactions [5][6][7] and even of the emergence of vegetation covers [8] in the dynamics and morphology of single dunes were quite well-established with the help of dune models [1,8,9]. There are also a few studies of entire dune fields [10][11][12][13], but a simple theoretical understanding of the size selection process within dune fields has still not been achieved.…”

“…Since barchan dunes move over the field with velocities that strongly depend on the size (v ∝ 1/w) [1], collisions are ubiquitous in such fields, turning out to be another relevant process for dune size alterations [7,13]. Therefore, the dune size distribution should be determined by the competition between the balance of sand flux on a single dune and the collisions between neighboring dunes [6,7,11]. Recently a third size selection mechanism was discovered, that involves the calving of large dunes due to wind fluctuations [13,14].…”

Remote sensing and spatial analysis of aeolian sand dunes: A review and outlook

“…The importance of dune form evolution has emerged as a top research priority in light of recent progress in numerical modeling and flume experiments (e.g., Schwämmle and Herrmann, 2003;Endo et al, 2004;Hersen et al, 2004;Durán et al, 2005;Hersen, 2005;Hersen and Douady, 2005;Durán et al, 2011;Katsuki et al, 2011). These approaches afford insight into dune dynamics and interactions and can be used to supplement the paucity of field observations.…”

Vegetation and Induration as Sand Dunes Stabilizators

“…Effectively, it is like if the smaller dune were crossing over the larger one (Schwämmle and Herrmann 2003), as proposed recently by Besler (1997). A systematic study of dune interaction has been presented in Durán et al (2005). Many times, however, dunes meet obstacles and cannot evolve freely on bedrocks or sand sheets under the action of wind.…”