Stability of transverse dunes against perturbations: A theoretical study using dune skeleton model

The dune skeleton model is a reduced model to describe the formation process and dynamics of characteristic types of dunes emerging under unidirectional steady wind. Using this model, we study the dependency of the morphodynamics of transverse dunes on the initial random perturbations and the lateral field size. It was found that (i) an increase of the lateral field size destabilizes the transverse dune to cause deformation of a barchan, (ii) the initial random perturbations decay with time by the power function until a certain time; thereafter, the dune shapes change into three phases according to the amount of sand and sand diffusion coefficient, and (iii) the duration time, until the transverse dune is broken, increases exponentially with increasing the amount of sand and sand diffusion coefficient. Moreover, under the condition without the sand supply from windward ground, the destabilization of transverse dune in this model qualitatively corresponds to the subaqueous dunes in water tank experiments.