The basic mechanism for normal sand ripples formation is a screening instability (Andreotti et al, 2006). When the saltation high energy grains collide with the bed, they eject grains of smaller energy, termed as reptons (Andreotti et al, 2006). The windward slope of a small bump is submitted to more impacts than the lee slope, so that the flux of reptons is higher uphill than downhill and makes the bump amplify. Although normal ripples were extensively studied and there are mathematical models which capture the instability mechanism (Yizhaq et al., 2004; Manukyan and Prigozhin, 2009), there are still open questions regarding their formation. The most challenging one is the dependence of the wavelength on the wind speed. It was shown that the mean reptation length does not depend on the wind shear velocity, which means that according to the current mathematical models, the ripple wavelength will be almost the unchanged for different wind velocities. Field and wind tunnel experiments (Anderotti et al, 2006) showed that both the initial and final wavelengths, as well as the drifting speed of the ripples are linear functions of the wind velocity. These results indicted that something is missing in the current models of sand ripples and in our understanding of sand transport in general.

Megaripple formation is much less understood than formation of normal sand ripples as it involved different grains sizes. A simple mathematical model of aeolian megaripples introduced by Yizhaq (2005) is also based on the Anderson reptation model but is written for bi-modal sand. It is assumed that the “fine fraction impact ripples” mechanism takes into account the spatial variation of saltation flux caused by the developing sand surface undulations. Linear stability analysis of this model indicates the presence of two maxima in the growth rate of the unstable modes: one corresponds to the standard ripples and the other, with the wavelength several times longer, is attributed to megaripples. This model, however, does not account for sand sorting. Manukyan and Prigozhin (2009) presented a continuous model capable of demonstrating some salient features of aeolian sand ripples: the realistic asymmetric ripple shape, coarsening of the ripple field at the nonlinear stage of ripple growth, saturation of ripple growth for homogeneous sand, typical size segregation of sand, and formation of armoring layers of coarse particles on ripple crests and windward slopes for inhomogeneous sand. However, they didn't simulate the formation of mature megaripples. Some researchers assume that the large wavelength of megaripples reflects an inherent length scale of saltation trajectories.

The basic mechanism for normal sand ripples formation is a screening instability (Andreotti et al, 2006). When the saltation high energy grains collide with the bed, they eject grains of smaller energy, termed as reptons (Andreotti et al, 2006). The windward slope of a small bump is submitted to more impacts than the lee slope, so that the flux of reptons is higher uphill than downhill and makes the bump amplify. Although normal ripples were extensively studied and there are mathematical models which capture the instability mechanism (Yizhaq et al., 2004; Manukyan and Prigozhin, 2009), there are still open questions regarding their formation. The most challenging one is the dependence of the wavelength on the wind speed. It was shown that the mean reptation length does not depend on the wind shear velocity, which means that according to the current mathematical models, the ripple wavelength will be almost the unchanged for different wind velocities. Field and wind tunnel experiments (Anderotti et al, 2006) showed that both the initial and final wavelengths, as well as the drifting speed of the ripples are linear functions of the wind velocity. These results indicted that something is missing in the current models of sand ripples and in our understanding of sand transport in general.

Megaripple formation is much less understood than formation of normal sand ripples as it involved different grains sizes. A simple mathematical model of aeolian megaripples introduced by Yizhaq (2005) is also based on the Anderson reptation model but is written for bi-modal sand. It is assumed that the “fine fraction impact ripples” mechanism takes into account the spatial variation of saltation flux caused by the developing sand surface undulations. Linear stability analysis of this model indicates the presence of two maxima in the growth rate of the unstable modes: one corresponds to the standard ripples and the other, with the wavelength several times longer, is attributed to megaripples. This model, however, does not account for sand sorting. Manukyan and Prigozhin (2009) presented a continuous model capable of demonstrating some salient features of aeolian sand ripples: the realistic asymmetric ripple shape, coarsening of the ripple field at the nonlinear stage of ripple growth, saturation of ripple growth for homogeneous sand, typical size segregation of sand, and formation of armoring layers of coarse particles on ripple crests and windward slopes for inhomogeneous sand. However, they didn't simulate the formation of mature megaripples. Some researchers assume that the large wavelength of megaripples reflects an inherent length scale of saltation trajectories.