The Stability of Internal Baroclinic Jets: Some Analytical Results

Abstract

The stability of internal baroclinic jets to quasi-geostrophic, normal mode perturbations is studied. Some important aspects are clarified by considering a jet which consists of a baroclinic layer sandwiched between two barotropic layers of finite depth on an f-plane. Even when the total available potential energy is kept constant (by appropriately changing the velocity difference across the baroclinic layer) the maximum unstable mode growth rate increases as the depth of the baroclinic layer is decreased. Certain primitive equation instability calculations reported by James and Hoskins (1985) show qualitatively different behavior, and hence require reinterpretation; it is suggested that the tendency of a ?-effect to stabilize internal baroclinic jets is important in these cases. Examination of continuous sinusoidal internal jets establishes the existence of short-wave cutoffS to instability (SWCs) for such flows. A similar result for a more general class of internal jets is stated. It is found that the parametric location of the SWC is in some cases sensitively dependent on the degree and form of the lateral shear present in the basic flow. Implications for the theoretical interpretation of the upper axisymmetric flow transition in rotating annulus experiments are discussed. Some sinusoidal internal jet stability problems are solved numerically and it is found that, so long as the ?-effect is weak, the results are well reproduced analytically by coarsely truncated spectral representations which exploit the internal jet character of the basic flow and the perturbations. Phase diagrams of the f-plane stability properties according to these spectral representations are constructed. Via a three-dimensional anticascade argument, the spectral representations also provide useful interpretations of the location of the SWC in the sinusoidal internal jet flows.