Amplitude and Mean Drift Equations for the Oceanic Ekman Layer

We derive the coefficients of the amplitude and mean drift equations describing the marginally unstable oceanic Ekman layer. This generic system consists of the anisotropic two-dimensional complex Ginzburg-Landau equation for the amplitude coupled to a Poisson equation for the mean drift. We simulate these equations numerically with coefficients corresponding to selected latitudes and wind directions and find chaotic behavior of the solutions. Although always chaotic, there is a qualitative difference between solutions for different wind directions at the same latitude. The main distinguishing factor is the presence or absence of spirals.