  To analyze theoretically the stability of the shape and the migration process
of transverse dunes and barchans, we propose a {\it skeleton model} of 3D dunes
described with coupled dynamics of 2D cross-sections. First, 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 and 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 transversal dunes and their
deformation to barchans depending on the amount of available sand in the dune
field, sand flow in parallel and perpendicular to wind direction.
