The Meridional Scale of Baroclinic Waves

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Abstract
Further numerical and analytical solutions are obtained for unstable disturbances in a two-layer, hydrostatic, quasi-geostrophic model with both vertical and meridional shear in the basic zonal wind, the meridional shear being confined to the upper layer. Contrary to a suggestion of Stone, the meridional scale of the most unstable wave is not, in general, the radius of deformation. As in previous studies, when the meridional scale of the zonal flow is of the order of the radius of deformation, the fastest-growing disturbance is found to take a similar meridional scale. However, for zonal flows of greater meridional extent, numerical solutions show the most unstable wave to have a meridional scale larger than the radius of deformation, although less than that of the zonal flow. In this case the meridional scale of the wave is shown analytically to be given, in general, by the geometric mean of the radius of deformation and a length scale determined by the curvature of the flow profile at the position of maximum upper-level wind. When this curvature vanishes, the disturbance takes a meridional scale closer to that of the zonal flow, with a weaker dependence an the radius of deformation.

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