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abstract: 'Transverse dunes appear in regions of mainly unidirectional wind and high sand availability. A dune model is extended to two dimensional calculation of the shear stress. It is applied to simulate dynamics and morphology of transverse dunes which seem to reach translational invariance and do not stop growing. Hence, simulations of two dimensional dune fields have been performed. Characteristic laws were found for the time evolution of transverse dunes. Bagnold’s law of the dune velocity is modified and reproduced. The interaction between transverse dunes led to interesting results which conclude that small dunes can pass through bigger ones.'
author:
- 'Veit Schwämmle$^{(1)}$ and Hans J. Herrmann$^{(1)}$'
bibliography:
- 'dune.bib'
title: Modelling transverse dunes
---

Introduction
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Transverse dunes have been investigated with constant interest recently. Field measurements have been carried out in order to obtain more knowledge about airflow and sediment transport over transverse dunes [@Wilson72; @Lancaster82; @Lancaster83; @Mulligan88; @Burkinshaw93; @McKenna2000]. Several numerical models have been proposed to model dune formation [@Wippermann86; @zeman-jensen:88; @Fisher88; @Stam97; @NishimoriXX; @boxel-arens-van_dijk:99; @van_dijk-arens-boxel:99; @herrmann-sauermann:2000; @MomijiWarren2000; @SauermannKroy2001; @KroySauermann2002]. But still many questions are not answered and some efforts are needed to better understand dune morphology and dynamics or even to anticipate dune formation. The 