Shallow flows with bottom topography

ABSTRACT: This paper discusses laboratory experiments and numerical simulations of dipolar vortex flows in a shallow fluid layer with bottom topography. Two cases are considered: a step topography and a linearly sloping bottom. It is found that viscous effects – i.e., no-slip conditions at the non-horizontal parts of the bottom – play an important role in shallow flows with bottom topography. The combination of these viscous effects and the 3D nature of the bottom topography gives rise to generation of vorticity (with a vertical component), which may significantly influence the flow evolution. Obviously, such shallow flows cannot be described simply by the two-dimensional Navier-Stokes equation with an additional ‘bottom friction’ term.