Linear baroclinic instability of a nonzonal flow with special regard to thermal internal forcing

The linear baroclinic instabilities of a basic geostrophic shear flow in a stratified, thermally active ocean are considered, including the β-effect. It is shown that the internal heat production, even if it introduces only minor changes into the geostrophic balance, may deeply modify the stability properties of the stationary solutions. If density, geostrophic basic flow, and heat production are all regarded as arbitrary functions of depth only, and if a linear nonzonal assumption is made about the geostrophic pressure field, it can be shown how the geostrophic equilibrium is altered and how the internal heating affects both the directions of propagation and the growth rates of quasi-geostrophic disturbances. A semicircle theorem valid for every direction of propagation is proved, by generalizing well-known results obtained for adiabatic geostrophic flows.Finally, it is found that the modified instability can be described adequately by a directional Richardson number related to the perturbed stationary geostrophic flow.