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 te rm in the vorticity evolution equation. This term is proportional to E-1/2 (where E is the Ekman number), and arises from the linear Ekman theory, whi ch yields an expression for the vertical velocity produced by the thin Ekma n layer at the flat bottom. In this paper, a two-dimensional model with Ekm an damping is proposed using again the linear Ekman theory, but now includi ng nonlinear Ekman terms in the vorticity equation. These terms represent n onlinear advection of relative vorticity as well as stretching effects. It is shown that this modified two-dimensional model gives a better descriptio n of the spin-down of experimental barotropic vortices than conventional mo dels. Therefore, it is proposed that these corrections should be included i n studies of the evolution of quasi-two-dimensional flows, during times com parable to the Ekman period.