Abstract
A multi-layer hydrostatic shallow-water model was developed in the present study. The layer-integrated hydrostatic nonlinear shallow-water was solved with θ time integration and the least-squares finite element method. Since the least-squares formulation was employed, the resulting system of equations was symmetric and positive–definite; therefore, it could be solved efficiently by the preconditioned conjugate gradient method. The model was first applied to simulate the von Karman vortex shedding. A well-organized von Karman vortex street was reproduced. The model was then applied to simulate the Kuroshio current-induced Green Island vortex street. A swirling recirculation was formed and followed by several pairs of alternating counter-rotating vortices. The size of the recirculation, as well as the temporal and spatial scale of the vortex shedding, were found to be consistent with ADCP-CDT measurements, X-band radar measurements, and analysis of the satellite images. It was also revealed that Green Island vortices were affected by the upstream Orchid Island vortices.
Highlights
Von Karman vortex shedding, which is induced by a steady incoming flow past a circular cylinder at low Reynolds numbers (Re = UL/ν, where U is the characteristic velocity, L is the characteristic length, and ν is the kinematic viscosity, respectively) is one of the most classic fluid mechanics problems
The developed model was first applied to the von Karman vortex street simulation, and to the Green Island vortex shedding simulation due to the passing of Kuroshio
Von Karman vortex shedding with pairs of periodic counter-rotating vortices downstream of an obstacle, generated by the flow past an obstacle, is a classic flow mechanic problem with many engineering applications [1,2,3,4,5]
Summary
Many theoretical and numerical approaches have been proposed to fix parts of the problem, mainly in three categories: Boussinesq-type models [41,42,43], non-hydrostatic shallow-water models [44,45,46,47,48,49,50,51,52,53,54], and multilayer models [55,56,57] They all exhibit some advantages and disadvantages, depending on the problems considered, the acceptance and requirements of the predictions (accuracy and efficiency), as well as the theory and programming complexity of the models.
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