A numerical study of tropical cyclone motion using a barotropic model. I: The role of vortex asymmetries

Abstract

The motion of an initially symmetric vortex on a beta plane and the motion of initially asymmetric vortices on a beta planes are studied using a nondivergent. barotropic model. It is assumed that there is no basic flow, the effects of a basic flow will be addressed in part II. Parameter values such as vortex size and strength and computational domain size are chosen for their relevance to tropical cyclones. the simultaneous evolution of the asymmetric vorticity and streamfunction fields is investigated in terms of a partitioning of the flow introduced by Kasahara and Platzman in which all asymmetries are regarded as part of the vortex environment. It is shown that in this partitioning the asymmetric streamflow provides a 'steering current' for the vortex to a very close approximation. For early times, typically 24 h for the parameters chosen, the development of the asymmetries in the vortices studied can be largely understood in terms of a simple analytical theory in which the vortex centre is fixed and the initial absolute vorticity distribution is rearranged by advection by the (initial) symmetric circulation. The shearing effect of this mechanism alone would appear to preclude the establishment of a true steady state in the flows considered. the numerical calculation for the initially symmetric vortex on a beta plane is used to assess averaging procedures for computing the environmental wind field of a tropical cyclone from observed wind data. the results show that the averaging regions that have been commonly employed in observational studies are too large to properly characterize the environmental flow at the cyclone centre and they suggest caution in making inferences from these studies in relation to physical mechanisms such as beta drift. The calculations for initially asymmetric vortices on an f plane show that the effects of the asymmetry on motion depend strongly on the scale of the asymmetry compared with that of the vortex. When the scale of the asymmetry is relatively small, the asymmetry is rapidly degraded by tangential shear and its effect on motion is not sustained. In contrast, larger asymmetries have a more persistent effect on motion. When the motion takes place on a beta plane, asymmetries induced by the advection of planetary vorticity ultimately dominate those present initially and, irrespective of the scale of the initial asymmetry, the vortex track finally turns to the north-west as in the case of the initially symmetric vortex. Finally, as a case of extreme asymmetry we study the mutual interaction of a strong vortex and a weak one. the behaviour is similar to that just described, the weak vortex merging with the stronger one. the analytical theory also proves useful in understanding the evolution of initial vortex asymmetries. The interpretations of the calculations add insight into the dynamics of tropical cyclone motion, complementing the findings of recent studies by Chan and Williams and Fiorino and Elsberry.