Development and steady states of transverse dunes: A numerical analysis of dune pattern coarsening and giant dunes

We investigate the development and steady states of transverse dunes for ranges of flow depths and velocities using a cellular automaton dune model. Subsequent to the initial bed instability, dune pattern coarsening is driven by bed form interactions. Collisions lead to two types of coalescence associated with upstream or downstream dominant dunes. In addition, a single collision-ejection mechanism enhances the exchange of mass between two adjacent bed forms (throughpassing dunes). The power law increases in wavelength and amplitude exhibit the same exponents, which are independent of flow properties. Contrary to the wavelength, dune height is limited not only by flow depth but also by the strength of the flow. Superimposed bed forms may propagate and continuously destabilize the largest dunes. We identify three classes of steady state transverse dune fields according to the periodicity in crest-to-crest spacing and the mechanism of size limitation. In all cases, the steady state is reached and maintained through the dynamic equilibrium between flow strength and dune aspect ratio. In the limit of low flow strength, where it becomes the primary factor of size limitation, the bed shear stress in the dune trough regions is close to its critical value for motion inception. Comparisons with natural dune fields suggest that many of them may have reached a steady state. Finally, we infer that the sedimentary patterns in the model may be used to bring new constraints on the development of modern and ancient dune fields.