Nonlinear Ekman effects in rotating barotropic flows

In the presence of background rotation, conventional two-dimensional models of geostrophic flow in a rotating system usually include Ekman friction – associated with the no-slip condition at the bottom – by adding a linear term in the vorticity evolution equation. This term is proportional to E1/2 (where E is the Ekman number), and arises from the linear Ekman theory, which yields an expression for the vertical velocity produced by the thin Ekman layer at the flat bottom. In this paper, a two- dimensional model with Ekman damping is proposed using again the linear Ekman theory, but now including nonlinear Ekman terms in the vorticity equation. These terms represent nonlinear advection of relative vorticity as well as stretching effects. It is shown that this modified two-dimensional model gives a better description of the spin-down of experimental barotropic vortices than conventional models. Therefore, it is proposed that these corrections should be included in studies of the evolution of quasi-two-dimensional flows, during times comparable to the Ekman period.