THE EVOLUTION OF VORTICES IN VERTICAL SHEAR .1. INITIALLY BAROTROPIC VORTICES

The behaviour of initially-barotropic vortices in vertically-sheared environmental flows is investigated. The strength and structure of the vortices used are representative of tropical cyclones. The calculations are performed using a primitive-equation numerical model on an f-plane. It is found that the initial response of the vortex to the vertical shear is to tilt in the plane of the shear. As soon as a tilt is established, the upper- and lower-level centres begin to rotate cyclonically about the mid-level centre. This rotation can be understood in terms of upper- and lower-level potential-vorticity anomalies which are displaced in the horizontal relative to one another. The now associated with the vertical projection of each anomaly advects the other anomaly, leading to the observed cyclonic rotation. The rotation rate decreases with time, so that the direction of tilt becomes constant, but the magnitude of the tilt continues to increase. We argue that the observed rotation acts to oppose the destructive action of the vertical shear on the vortex, even in the absence of diabatic processes. The role of the vertical circulation is considered in detail. It is shown that the vertical circulation develops in a manner which is consistent with the model flow remaining balanced. It is found that the mesoscale nature of the vertical circulation leads to a distortion of the axisymmetric vortex. This results in the inner core having a smaller vertical tilt than the outer region. The vertical circulation does not act on a large enough scale to explain why the vortex is not destroyed by the vertical shear. The behaviour of the vortex is found to depend on various parameters. Results are presented where the vertical shear, the strength and size of the vortex, the Coriolis parameter, and the static stability are varied. With the exception of the vertical shear, altering any of these parameters alters the vertical penetration of a potential-vorticity anomaly. The results show that increasing the penetration depth leads to an increase in the rotation rate of the upper- and lower-level vortex centres about the mid-level centre, and to a reduction in the magnitude of the vertical tilt.