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.
Highlights
A joint theoretical and numerical study is used to investigate the fluid dynamical aspect of the motion of a vortex generated in a rotating tank with a sloping bottom. is study is motivated by getting an insight of the evolution of a strong barotropic cyclone on a β-plane in the Northern Hemisphere. e dynamics of barotropic vortices on a β-plane have been studied intensively over the past several decades through analytical, numerical, and laboratory investigations [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22]
A joint theoretical and numerical study is used to investigate the flow features of a strong cyclonic vortex generated in a rotating tank with a sloping bottom. is study clarifies the idea of the dynamical similarity between the prototypical and model flow fields by satisfying the similarity conditions (14) and (15)
Calculations by the proposed modified shallow water model for the strong and intense cyclonic motions show a close agreement with the experimental results in a rotating tank. e present study proposed a modified shallow water model incorporating a gradient-wind-balance (GWB) vortex model for investigating the hurricane-like cyclonic motions on a β-plane in the Northern Hemisphere and their structures in a rotating tank with a gently sloping bottom
Summary
A joint theoretical and numerical study is used to investigate the fluid dynamical aspect of the motion of a vortex generated in a rotating tank with a sloping bottom. is study is motivated by getting an insight of the evolution of a strong barotropic cyclone on a β-plane in the Northern Hemisphere. e dynamics of barotropic vortices on a β-plane have been studied intensively over the past several decades through analytical, numerical, and laboratory investigations [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22]. A joint theoretical and numerical study is used to investigate the fluid dynamical aspect of the motion of a vortex generated in a rotating tank with a sloping bottom. Chen et al [22] generated a strong barotropic vortex of large vortex Rossby number Rov ∼ O(1) in a rotating tank with a gentle sloping bottom (sy ≈ 0.0538) to simulate the movement of a hurricane-like vortex on a β-plane.
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