Non-linear process based modelling of offshore sand waves

Sand waves are more or less parallel ridges, making bed patterns in shallow seas. Due to their dimensions and migration rate, they can have a considerable effect on offshore human activities. In relation to such activities especially the variation in the sand wave characteristics (wave length, height and migration) are of importance. Due to the large spatial scale of sand waves and the different time scales involved for the tidal flow (hours) and the bed pattern changes (years to decades), modelling the sand wave behaviour from its initial stage up to its final equilibrium shape is a challenge, let alone to include the spatial variation within a sand wave field. In this paper a numerical solver is presented that describes sand waves from their initial state up to their final equilibrium. It is a 2DV idealized model, based on non-linear stability analysis. Both the model equations and the numerical setup are described and the model is validated against linear stability analysis. To investigate variations in a field of sand waves and the interaction between individual waves, simulations on large domains are presented and show that this solver is able to describe the development of a realistic sand wave field, with variations, from an initially flat sand bed with small random disturbances. The solver shows to be a promising tool, it is computational fast due to the efficient numerical algorithms and is easy to extend with other physical processes. Results show good agreement with analytical results in the linear regime and with field data.