A Validated Study of a Modified Shallow Water Model for Strong Cyclonic Motions and Their Structures in a Rotating Tank

Abstract

A joint theoretical and numerical study was carried out to investigate the fluid dynamical aspect of the motion of a vortex generated in a rotating tank with a sloping bottom. This study aims at understanding the evolution of strong cyclonic motions on a β-plane in the Northern Hemisphere. The strong cyclonic vortices were characterized by four nondimensional parameters which were derived through a scale analysis of the depth variations of fluid. By simplifying the model flow field and the prototype flow field, respectively, through the conservation of potential vorticity, two sets of dynamic similarity conditions are derived. This study proposed a sophisticated modified shallow water model (MSWM) to investigate the flow features of such strong vortices. A detailed numerical calculation adopted by multidimensional positive definite advection transport algorithm (MPDATA) was carried out to validate those effects considered in the MSWM model, including sloping bottom, parabolic free surface deformation, and viscous dissipation. Close agreements were found between the experimental and numerical results, including the streamlines patterns and the vortex trajectory. Comprehensive simulations for strong cyclonic vortices over different sloping bottoms were investigated to understand the impact of planetary β effect on vortex. The results calculated by MSWM demonstrate a variety of flow features of interactions between the primary vortex and induced secondary Rossby wave wakes that were essential and prominent in environmental geophysical flows.