A quasi-linear theory for rotating flow over topography. Part 1. Steady β-plane channel

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Abstract
Steady rotating flow over topography in a periodic channel is examined, with emphasis on the interaction of waves, topography and mean flow. A simple quasi-linear theory is presented that features an implicit equation relating the net zonal flow to the forcing and topography. A good description of the dynamics is obtained, even when resonant Rossby waves appear. Multiple solutions for given external parameters are predicted in some cases, and confirmed by comparison with a fully nonlinear numerical model.The nonlinear results also indicate that the zonally averaged shear can be important when topographic effects or Rossby numbers are large. With this factor taken into account the theory gives good agreement with the fully nonlinear model, as long as eddy–eddy interactions are minor.The theory is relevant to the dynamics of planetary waves in the atmosphere, and may also be applied to some oceanic problems.