Dunes

Of the several geomorphological patterns which occur in rivers, fluvial dunes represent one of the simplest to observe, but the theory to describe their formation is less easy. This chapter discusses models of dune formation in both fluvial and aeolian contexts, and in particular gives detailed discussion of two models based on descriptions of turbulent flow with either a constant eddy viscosity, or one derived from mixing length theory. The former leads to Benjamin’s theory for flow over a bump, the latter leads to the Jackson–Hunt theory. Both produce instability, but the Jackson–Hunt theory has formulation problems. The issue of separation renders the problem difficult. It can be treated using complex variables methods, as described here, but practical models require something more direct, as described in the notes.