A Numerical Investigation of Hydrodynamic Instability and Energy Conversions in the Quasi-Geostrophic Atmosphere: Part I

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Abstract
The hydrodynamic instability characteristics of planetary zonal flows are investigated through use of a quasi-geostrophic numerical model of high spatial resolution. An initial-value technique is employed to obtain solutions of the linear problem. Certain zonal flows containing both vertical and lateral shears, which are representative of those observed in the earth's atmosphere, are found to be unstable with respect to the large-scale quasi-geostrophic disturbances. Westerly currents, each characterized by a latitudinally symmetric jet containing absolute vorticity extrema at various latitudes, amplify perturbations of some scales through a dominating baroclinic mechanism, and amplify perturbations of other scales through a dominating barotropic mechanism. For these flows, the unstable perturbations of relatively short zonal wavelength convert zonal available potential energy into perturbation energy and simultaneously strengthen the zonal kinetic energy of the basic flow. On the other hand, the unstable perturbations of relatively long zonal wavelength reduce both the zonal kinetic and available potential energies of the basic flow, with the former reduction dominating. For certain flows, these combinations produce two distinct wavelengths of maximum instability. Flows which are similar but contain no vanishing meridional gradient of absolute vorticity are found to produce baroclinically unstable perturbations with a tendency toward barotropic damping.

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