A simple model for a transverse dune field

We present a simple one-dimensional model to describe the evolution of a transverse dune field. The model is characterized by the distances between the dunes and their heights, which determine the inter-dune sand flux. The model reproduces the observation that the dunes in a given field have approximately all the same height. We find that this result is independent on the initial configuration of the field, as well as on coalescence effects between migrating dunes. The time for the final state to be reached is studied as a function of the relevant phenomenological parameters.