Form drag caused by topographically forced waves in a barotropic β channel:: Effect of higher mode resonance

The relationship between form drag and the zonal mean velocity of steady states is investigated in a very simple system; a barotropic quasi-geostrophic beta channel with sinusoidal topography. When a steady solution is calculated by the modified Marquardt method, keeping the zonal mean velocity constant as a parameter, the characteristic of the solution changes at a phase speed of a wave with a wavenumber higher than that of the bottom topography. For velocities smaller than this critical value, there exists a stable quasi-linear solution similar to the linear solution. For larger velocities, there exist three solutions whose form drag is very large. In addition, the resonant velocity of the mode, whose wavenumber is the same as the bottom topography, has no effect on these solutions. When the quiescent fluid is accelerated by a constant wind stress, acceleration stops around the critical velocity for a wide range of the wind stress. If the wind stress is too large for the acceleration to stop, the zonal current speed continues to increase infinitely. It is implied that the zonal velocity of equilibrium is mainly determined, not by the wind stress, but by the amplitude of the bottom topography and the viscosity coefficient.