Topographic Linear Instability on a Sphere for Various Ridge Orientations and Shapes

Abstract

The linear instability of a zonal flow passing over a large-scale mountain, having one of two orientations and two shapes, is considered via an eigenvalue/eigenvector problem using spherical coordinates in a quasi-geostrophic model. Topography enters only as slope flow in the bottom boundary condition. All variables are expressed using orthogonal functions in three dimensions. Realistic (variable) static stability is applied in the study. The topography reduces the growth rates primarily by reducing the baroclinic energy conversion. For the two mountain orientations investigated here, when the ridge is oriented east?west the growth rates are reduced more than when the orientation is north-south. The highs and lows (at the surface) are deflected northward by the topography which places them where the basic flow vertical shear is less for a longer time when the ridge is oriented east?west. The deflection effects the eddy heat fluxes by increasing the meridional velocity on the southeastern side of each eddy. This increases the meridional heat fluxes, making the baroclinic conversion (from zonal mean to eddy available potential energy) largest on the upslope side. The eddy vertical velocities are also enhanced on the upslope (west) side of the ridge. This means that the conversion from eddy available potential to eddy kinetic energy is also larger there. On the downslope side the heat fluxes are usually reduced. In most cases the topography deflects the storm track more in the lower troposphere than in the upper troposphere. In a few cases, the topography causes the upper and lower level eddies to move at different rates and to be deflected in different directions; the phase relationship between temperature and pressure is altered such that negative baroclinic conversion occurs on the downslope side of the mountain. Accurate solutions require even higher horizontal resolution than anticipated by earlier studies. But, much economy is gained by adopting a ?parallelogramic? truncation, which uses more meridional than zonal wave-numbers.