On the structure of supercritical western boundary currents

The structure of supercritical western boundary currents is investigated using a quasi-geostrophic numerical model. The basic how is of meridional Munk balance, and the input boundary is per turbed by the most unstable wave solution obtained from linear spatial instability calculations. Self-preserving (or equilibrium) solutions are obtained for the model runs at Re = 30, 60, 90, and 120, and their energy and vorticity budgets are analyzed. In an analogy with the laboratory turbulence of wall boundary layers, the western boundary layer is divided into inner and outer layers. In the inner layer, the mean energy is dissipated via direct viscous dissipation. while in the outer layer it is converted to the eddy energy via turbulence production. The main scenario is that the mean energy is produced in the inner layer via ageostrophic pressure work divergence, and it is partly removed due to viscous action within a narrow region near the wall, defined here as viscous sub-layer. The remaining portion is converted to the eddy energy via turbulence production in the outer layer, which is in turn transported to the inner layer, then again to the viscous sub-layer where it is ultimately dissipated. In the near-wall side, the vorticity balance of the mean flow is maintained by viscous effect and Reynolds Aux divergence, while in the offshore side it is maintained by beta effect and Reynolds flux divergence. The length scale of the supercritical boundary current is roughly similar to0.2 root ReLM, where L-M is the Munk length, as observed from a dimensional analysis. (C) 2001 Elsevier Science B.V. All rights reserved.