Nonlinear dynamics of sand banks and sand waves

Sand banks and sand waves are two types of sand structures that are commonly observed on an off-shore sea bed. We described the formation of these featues using the equations of the fluid motion coupled with the mass conservation law for the sediment transport. The bottom features are a result of an instability due to tide-bottom interactions. There are at least two mechanisms responsible for the growth of sand banks and sand waves. One is linear instability, and the other is nonlinear coupling between long sand banks and short sand waves. One novel feature of this work is the suggestion that the latter is more important for the generation of sand banks. We derive nonlinear amplitude equations governing the coupled dynamics of sand waves and sand banks. Based on these equations, we estimate characteristic features for sand banks and find that the estimates are consistent with measurements.