An analytic theory of tropical‐cyclone motion in a barotropic shear flow

The recent analytic theory for the barotropic motion of an initially symmetric vortex on a beta plane at rest presented by Smith and Ulrich is extended to the case of a horizontal shear flow, enabling the precise effects of shear on vortex motion to be isolated. These effects are characterized by the contribution of the shear‐related terms in the vorticity equation to the evolution and structure of the wave‐number‐1 component of the vortex asymmetry. The analysis proceeds on the assumption that a general shear flow may be adequately approximated by the first three terms of a double Taylor‐series expansion about the initial vortex centre. The manner in which the linear and quadratic terms of this expansion affect the asymmetries is illustrated in detail for a zonal shear flow with a linear or quadratic variation in the meridional direction. For tropical‐cyclone‐scale vortices, the theory shows excellent agreement with equivalent numerical calculations for a period of one or two days. As well as providing insight into the effects of horizontal shear on tropical‐cyclone motion, the calculations have the potential to assist in the design of ‘bogus’ vortices for the initialization of dynamically based tropical‐cyclone forecast models.