A simple model for a transverse dune field

TL;DR

This paper introduces a simple one-dimensional model for transverse dune fields that captures dune height uniformity and analyzes the time evolution towards a steady state based on key parameters.

Contribution

The model is novel in its simplicity and ability to reproduce uniform dune heights regardless of initial conditions or coalescence effects.

Findings

Dunes tend to reach a uniform height in the model.

The time to reach equilibrium depends on model parameters.

The model's results are robust to initial configurations.

Abstract

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 of the initial configuration of the field, as well as of coalescence effects between migrating dunes. The time for the final state to be reached is studied as a function of the relevant phenomenological parameters.