Smith, Roger K., Ulrich, Wolfgang, and Sneddon, Graeme (2000) On the dynamics of hurricane-like vortices in vertical-shear flows. Quarterly Journal of the Royal Meteorological Society, 126 (569). pp. 2653-2670.

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Abstract

A simple two-layer analogue model is used to elucidate aspects of vortex motion in a vertically sheared zonal flow. The model is based on the idea that a vortex can be considered as the sum of a pair of barotropic vortices, one whose vorticity, or potential vorticity, resides in the upper layer and the other whose vorticity resides in the lower layer. Each vortex has an associated tangential velocity distribution in the other layer, which advects the vortex in that layer. The strength of this velocity distribution is characterized by a coupling parameter, which, in the case of quasi-geostrophic vortices, is related to the Rossby depth scale. Besides their mutual advection, the component vortices are differentially advected by vertical shear. The model leads to a set of coupled ordinary differential equations for the motion of each component vortex, which may be solved analytically in certain circumstances. The calculations indicate two types of flow behaviour according to the strength of the component vortices, the degree of vertical coupling and the strength of the shear. For weak shear and/or strong vortices and strong coupling, the vortices rotate around each other as their mean centre translates with a fraction of the mean zonal flow. For Strong shear and/or weak vortices and weak coupling, the vortices undergo a partial rotation while they are in proximity, but become progressively separated by the shear. The calculations are an aid to understanding the range of behaviour of vortices in shear in numerical calculations by other authors, and it is reasonable to presume that the processes represented by the model are fundamental processes in tropical cyclones also.

The analogue model is evaluated in the context of quasi-geostrophic theory, where the breakdown into the component vortices can be accomplished and where the complete problem can be solved numerically without approximation. The results of the quasi-geostrophic model are contrasted with those of other recent studies of baroclinic vortices in the absence of vertical shear.

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