Momentum balance in zonal flows and resonance of baroclinic Rossby waves

Wind-driven flow in a baroclinic quasigeostrophic channel with simple bottom topography is studied in a model with reduced physics and degrees of freedom as an analogy to the Antarctic Circumpolar Current. For a sinusoidal topography an approximate analytical solution is found using a low-order spectral model. Resonance of baroclinic Rossby waves can lead to different flow regimes of which one is a blocked state, where most of the momentum, imparted to the fluid by the wind stress, is transferred to the earth by bottom form stress. For some parameter values there are both resonant and nonresonant solutions to the model equations. It is shown that these results of the low-order model apply also to a more complicated spectral model with sinusoidal but also with Gaussian ridge topography. The steady states of these models are found numerically using a continuation algorithm. In the case of the ridge topography, the resonant and nonresonant steady states coexist over a wide range of topography heights.