Linear and nonlinear Rossby waves in basins both with and without a thin meridional barrier

Abstract

The linear and nonlinear Rossby wave solutions are examined in homogeneous square basins on the [beta]-plane both with and without a thin meridional barrier. In the presence of the meridional barrier the basin is almost partitioned into two; only two small gaps of equal width, d, to the north and south of the barrier allow communication between the eastern and western sub-basins. Solutions are forced by a steady periodic wind forcing applied over a meridional strip near the eastern side. Bottom friction is present to allow the solutions to reach equilibrium. The linear solution for the basin containing the barrier is determined analytically and the nonlinear solutions for both basins are found numerically. In the linear solution with the barrier present, particular attention was paid to the resonant solutions. We examined the effects of varying the symmetry of the forcing about the mid-latitude, the frequency of the periodic forcing and the strength of the bottom friction. For each solution we focus on how the no net circulation condition, which is central to any solution in a barrier basin, is satisfied. The nonlinear solutions were studied for both basin configurations. In each case the transition from the weakly nonlinear solution to the turbulent solution was examined, as the forcing frequency and forcing strength were varied. Only integer multiples of the forcing frequency are present in the weakly nonlinear solutions. The turbulent solutions were accompanied by the appearance of many other frequencies whose exact origins are unknown, but are probably the result of instabilities. A hysteresis was found for the turbulent solutions of both the barrier-free and barrier basins. In the weakly nonlinear solutions of the barrier basin it was predicted and confirmed that there is never a steady net flow from sub-basin to sub-basin. It was also shown that with a symmetric forcing all modes oscillating with an odd multiple of the forcing frequency are symmetric and all modes oscillating with even multiples of the forcing frequency are antisymmetric.