Sand banks and sand waves are two types of sand structures that are commonly
observed on an off-shore sea bed. We describe the formation of these features 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.