Stationary waves forced by topography in a vertically sheared, stratified, rotating fulid

The effect of an isolated topographic bump in a two-layer fluid on a β-plane is investigated. An analytical solution is derived in terms of the appropriate Green's function for arbitrary topography of finite horizontal extent. It is found that the disturbances generated by the bump are composed of two fundamental modes which may be wave-like or evanescent. The wave-like modes are topographically induced Rossby waves which occur only when there is eastward flow in at least one of the layers. These waves are always confined to the downstream (eastward) side of the bump. Whereas previous studies of this type have concentrated on eastward flow over topography, the theory has been extended here to include a wide range of vertically sheared flows. Particularly important is the case of low level westward flow combined with upper level eastward flow, as it has direct application, for example, to the summertime atmospheric circulation over the sub-tropical regions of the continental land.masses. In this case a wave-like disturbance extends far downstream from the bump for sufficiently large shear, and is of smaller amplitude in the upper layer than in the lower layer because of the effects of the stratification. For small shears, the wave-like mode in the lower layer is small and the character of the disturbance is evanescent, confining it to the immediate neighbourhood of the bump. A stability analysis of the solutions shows that the disturbances may be baroclinically unstable for sufficiently large mean shear.