Baroclinic instability over wavy topography

Abstract

The occurrence of new unstable modes of quasigeostrophic baroclinic oscillation of rotating stratified shear flow over a wavy bottom is examined. To obtain a tractable mathematical problem, the bottom topography is considered as a perturbation modifying the oscillations. It is found that combinations of a top-intensified and a bottom-intensified Eady mode, each stable without topography, can be destabilized by topography if certain resonant conditions are met. These are that (i) the two modes possess the same wavefrequency, and (ii) topography possesses a wavenumber c bridging the gap between the wavenumbers of the modes a, b, i.e. c = a – b. Growth rate of this instability (called type A) is proportional to the amplitude of the topographic component. There are two special cases: (i) when one of the basic modes is a marginally neutral mode – according to the classical analysis without topography – the instability is stronger (type M) with growth rate proportional to the 2/3-power of topographic amplitude; (ii) when both modes are marginally neutral the instability is even stronger (type M2) with growth rate proportional to the square root of topographic amplitude.These topographic instabilities, like classical baroclinic instability, draw their energy from the available potential by transporting buoyancy down the mean gradient associated with the geostrophic shear flow.