# An Idealized 3D Model of Interfacial Instability of Aeolian Bedform
###### Abstract  
An idealized morphodynamic model is constructed for formation of the aeolian sand ripples from small bottom perturbations of a two-dimensional sand bed. The main goal of the analysis is to evaluate the influence of the gravity flow (including \"impact-induced gravity flow\" in the reptation flux and \"topography-induced gravity flow\" in the creep flux) on the formation of the aeolian sand ripples and to clarify the relative contribution of various factors to the bed instability. A 3D linear stability analysis reveals that gravity flow appreciably affects the dynamics behaviors of aeolian sand ripples, which decreases the growth rate of sand ripples, tends to stabilize the sand bed, and leads to longer wavelength. We found that the competition between the destabilizing effect of reptation flow and the stabilizing effects of gravity flow leads to pattern selection. The along-crest diffusion of topography driven by impact and gravity is beneficial to the transverse stability of sand ripples, producing sand ripples with straighter and more continuous crests. For moderate values of \(D\), the most unstable mode has zero value of the transverse wavenumber (\(k_{y}=0\)), thus corresponding to aeolian ripples with crests perpendicular to the wind. Moreover, when the impact angle is 9-16\({}^{\circ}\), it has little effect on the characteristics of sand ripples for the initial stage of ripple development. For every increase of the impact angle by 1\({}^{\circ}\), the initial wavelength only increases by about 1.5%. In conclusion, the influence of the gravity flow on the dynamics of sand ripples formation stage cannot be neglected. ao 2021 26 August 2021 23 September 2021 26 September 2021 2021 2021 2021 2021 2021 2021 2021 2021 2021 2  
then screened from the most energetic impacts, which makes the spatial differences of the reptation flux. [PERSON] and [PERSON] [7] further considered grain rolling or avalanching under gravity. [PERSON] et al. [9] extended the continuous model to 3D structures on the sand surface, refined the reptation flux model, and predicted a saturation of ripples wavelength long term. Recently, based on direct numerical simulations, an instability mechanism leading to the formation of aeolian sand ripples was first suggested by [PERSON] et al. [10]: resonant grain trajectories, whose length is close to the initial wavelength and whose splash causes the mass transport to the ripple crests. However, this study did not involve the later stage of ripples development. [PERSON] [14] suggested that the wavelength depends on the height of the sand ripples and on the impact angle of the saltation particles. When the impact angle is smaller, the shadow zone length becomes larger, producing longer sand ripples. With wind tunnel experiment and numerical simulation, [PERSON] et al. [11] found that the shadow zone mechanism was more dominant in the subsequent nonlinear stage in which successive merging increased aeolian ripples. However, its relationship with the initial wavelength was not clearly demonstrated. The gravity flow includes impact-induced gravity flow and topography-induced gravity flow, which affect the transverse instability of aeolian megapirpples [15]. The impact of the topography-induced gravity flow on the contribution of aeolian bedforms has been reported by [PERSON] and [PERSON] [7], while the impact-induced gravity flow reduces the flux upslope and increases the flux downslope [15]. According to wind tunnel experiments and field observations, researchers gradually clarified the influence of wind speed and other factors on the formation and evolution of sand ripples [16; 17; 18; 4; 13; 14]. The grain size distributions play an important role in determining the size of the bedform, which has been the subject of considerable investigations [13; 14; 16; 17; 19; 20; 21; 22; 23; 24; 25]. Although significant progress has been made both in the prediction of sand ripples formation and geometric characteristics, much remains to be done.