## 1. Introduction

[2] Barchans are aeolian, crescentic sand dunes that are shaped by a unidirectional wind on firm ground. Their crescentic shapes as well as their high migration rates have motivated many investigations, starting with the far-reaching work of *Bagnold* [1941]. From then on, geologists, and more recently physicists, have considerably improved our description of aeolian bedforms and in particular of barchans by using field investigations [*Bagnold*, 1941; *Pye and Tsoar*, 1990; *Cooke et al.*, 1993; *Finkel*, 1959; *Hastenrath*, 1967; *Parker*, 1999; *Kocurek et al.*, 1992; *Sauermann et al.*, 2000], theoretical and numerical tools [*Werner*, 1995; *Werner and Kocurek*, 1997; *Nishimori et al.*, 1997; *Kroy et al.*, 2002; *Andreotti et al.*, 2002; *Hersen*, 2004], and laboratory experiments [*Mantz*, 1978; *Hersen et al.*, 2002; *Endo et al.*, 2004a; *Hersen*, 2005]. These studies have produced a fairly accurate description of solitary barchans. Here, we combine this knowledge with a new analysis to understand the long-time behavior of assemblies of barchans that are often found on the field: the corridors of barchans (see Figure 1). Such corridors are formed by many barchans of roughly uniform sizes and can extend several tens of kilometers downwind. As a matter of fact, trying to understand basic properties of these corridors from what is known about barchan dynamics leads to surprising conclusions.

[3] The speed of barchan, *c* is inversely proportional to its height, *h*, through the relation: *c* ∼ *q*/*h*, where *q* is the sand flux [*Bagnold*, 1941; *Andreotti et al.*, 2002], so that smaller barchans migrate faster. This implies that from an initial corridor of heterogenous barchans, size segregation should occur with time due to the relative differences in migration rate. This separation of dunes with respect to their sizes should keep increasing with time. It has also been shown that barchans are unstable towards sand flux variations [*Hersen et al.*, 2004]. This instability can be understood as follows: sand escapes the dunes only from the horns' tips, where no slip-face can trap sand grains. As the slip face appears only if the local slope is too steep, its formation in the lee side depends mainly on the local height rather than the height of the dune, *h*. This means that the total width of the horns, *w*_{h}, does not change significantly with *h* and thus with the total width, *w*. Moreover, in the wake of the horns, the output flux is concentrated such that it is close to the carrying capacity of the wind, i.e., it is nearly saturated [*Sauermann et al.*, 2000]. Therefore, the total output flux, Φ_{out} = *q*_{s}*w*_{h}, does not depends strongly on the size of a barchan. This qualitative argument is supported by numerical simulations of *Hersen et al.* [2004], which show that Φ_{out} = *q*_{s}*w*_{h} = *q*_{s}(α*w* + Δ), with α ∼ 0.05 ≪ 1, Δ ∼ 4.6 m and *q*_{s} the saturated sand flux. Consequently, if a barchan at equilibrium slightly increases its width, the total influx Φ_{in}, becomes larger than the total output flux Φ_{out} = *q*_{s}*w*_{h} and, as a result, the dune grows. This instability suggests that barchans in a corridor should either grow into mega barchans or shrink and disappear.

[4] Both conclusions are in obvious contradiction with basic field observation as shown on Figure 1. This paradox comes from the incorrect assumption that barchans in a corridor behave like solitary barchans. In particular, the density and the distribution of sizes of barchans in the corridor of Figure 1 suggest that collisions of dunes occur frequently. In fact, collisions should play a role in both the mass balance dynamics of barchans (and therefore their natural unstable behavior) and the spatial distribution of barchans with respect to their sizes since small barchans might merge with larger dunes. To make progress in understanding the stability of barchan corridors, it is helpful to first study a simple collision of two barchans. A typical collision event is depicted in Figure 1b but because of the size and speed of the involved barchans (between ∼30 m and ∼150 m and a difference of speed of a few meters a year) the whole process will take several decades.