A semi-implicit multiple-nested grid model for simulation of flow in a tropical storm

Abstract

ABSTRACT .A three-layer three-dimensional, triply-nested primitive equation model. suitable to simulate tropical storm, has been designed. A grid telescopic technique has been used with a fine grid mesh of 18 km grid length in the centre which is surrounded by a medium mesh of 54 km grid length; this is again surrounded by a course grid mesh of 162 km grid length. Each mesh consists of 32 X 32 array of momentum points enclosing 31 X 31 array of mass points. The variables are staggered in space which reduces the amount of averaging to a minimum and hence improves accuracy. To suppress non-linear instability an improved finite difference scheme has been applied. A two-way interaction method has been adopt to match the solutions between grids of different lengths. To increase the time step for integration, a semi-implicit scheme has been used. The speed of the solution of the system of Helmholtz equations arising out of semi-implicit scheme has been appreciably increased by devising an iterative method. To examine the role of surface friction as postulated by Yamasaki (1977) and forced subsidence as hypothesized by Arnold (1977), Gray (1977) and Yanai (1961) at the initial stage of development of a tropical storm. numerical experiments have been accomplished with this model varying coefficient of surface drag. and specifying heat around the centre of the to disturbance which is considered as the effect of forced subsidence through an analytical function similar to one used by Harrison (1973). The integration was started from a weak barotropic vortex in &r8dient balance en and continued for 48 hours in two cases and 60 hours in one case. It is observed that surface friction may not be an essential factor at the initial stage of development of tropical storm when the vortex is weak. On the  other  hand, initial development could be initiated by forced subsidence. But in the subsequent stage, surface friction plays an important role to induce mass convergence in the boundary layer and to reduce horizontal of the disturbance. This preliminary experiment has yielded smooth and encouraging results.