Three-Dimensional Dune Skeleton Model as a Coupled Dynamical System of Two-Dimensional Cross Sections

To theoretically analyze the stability of the shape and the migration process of transverse dunes and barchans, we propose a skeleton model of three-dimensional (3D) dunes described by the coupled dynamics of 2D cross sections. First, the 2D cross sections of a 3D dune parallel to the wind direction are extracted as elements of a skeleton of the 3D dune; hence, the dynamics of each cross section and the interaction between them is considered. This model simply describes the essential dynamics of 3D dunes as a system of coupled ordinary differential equations. Using the model, we study the stability of the shape of 3D transverse dunes and their deformation to barchans depending on the amount of available sand in the dune field, and on sand flow parallel and perpendicular to wind direction.