A dynamic model for the analysis of surge in a tropical storm

Abstract

We obtain an analytic representation for the pro le of the surge wave in the sea, due to a tropical storm at a low latitude. The results reproduce the known experimental data adequately. In the calculations we take i n to account the in uence of Rossby's second parameter and we analyse its contribution to the surge wave, which is proved to be su ciently small to be neglected in higher latitudes. The obtained analytical solution allows us to study in detail the surge wave formation in the presence of such a storm. To solve the problem, Laplace method and Green functions are used. This allows us to improve previous results obtained by Evsa in 1989. I IntroductionIn the last years the interest of studying non-periodic oscillations of sea level has grown. In particular, it is of interest the study of those oscillations excited by pressure elds and strong winds in the tropical storm. It is possible to nd previous information about this theme in the work of Jelesniansky 1 and more recently, Johns et al. 2 , Fandry et al. 3 , Jerome et al. 4 , Signorini 5 , Davies et al. 6 and Lardner et al. 7 and 8 . The majority of these papers employ n umerical methods or qualitative analysis of the solution of the mathematical model. In the present paper we obtain an analytic solution of the problem, similar to the one formulated by Evsa 9 . In this work, there is an incorrect expresion for the Green function of the problem. Therefore, for the analytic solution, Evsa does not take account of the multi-valuated character of the complex variable function in the path integrations. In the present paper we make correct use of the Green function method and the integral transform techniques. We also analyze the inuence of Rossby's second parameter, which is usually neglected at high latitudes by other authors because of its smallness with respect to Rossby's rst parameter and because it allows to simplify the calculation. We check that Rossby's second parameter is small enough to be neglected at low latitudes. II Formulation of the problemLet us consider a tropical cyclone TC which causes a perturbation of the sea surface in an ocean region distant from any coast. The interaction region has a characteristic deepness less than the storm horizontal size by t wo orders of magnitude. Therefore, we can use the shalow w ater approximation. We also consider a quasistationary regime for the storm, in order to keep a xed coordinate center. Due to the axial symmetry of this problem, we use a cylindrical system of coordinates with center on the axis of the cyclone. The Navier-Stokes equations in the cilindrical system of coordinates including the Coriolis terms are given by c