THE MUTUAL INTERACTION OF MULTIPLE VORTEXES AND ITS INFLUENCE ON BINARY AND SINGLE TROPICAL VORTEX SYSTEMS

Abstract

A two-layer discrete vortex model developed previously is applied to the study of short-term displacements of tropical vortexes due to their mutual interaction. The model treats the tropical cells as point-form vortexes and obtains analytic solutions for the stream functions in two layers in terms of Hankel functions of zero order. These solutions form a system of ordinary differential equations that governs the motion of the vortex filaments of finite strengths in the lower and upper layers. The model can handle a finite number of vortexes simultaneously. It also allows the influence of a basic flow to be considered. Initially, the model is applied to some analytical data in an attempt to study the patterns of motion for both binary and single tropical vortex systems. It is found that the individual vortexes exhibit a variety of complex trajectories depending upon their strengths and tilts, and upon stability parameters, µ21 and µ22. Of interest in this study is the ?self-interaction? concept according to which the upper level circulation of a sloping vortex interacts with the lower level circulation. It is shown that the observed short-period oscillations of the surface trajectory of a tropical cyclone can he explained to a reasonable extent using this concept. A case study is made involving multiple vortexes over the North Atlantic Ocean. The results illustrate how mutual interaction influences the motion of individual vortexes and further demonstrate the importance of the surrounding vortexes in modifying the well-known cyclonic rotation of a binary system. Preliminary calculations indicate that the model may provide a useful tool for predicting short-term displacements of tropical cyclones.