Pseudoinviscid Wake Formation by Mountains in Shallow-Water Flow with a Drifting Vortex

Ronald B. Smith Department of Geology and Geophysics, Yale University, New Haven, Connecticut

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David F. Smith Department of Geology and Geophysics, Yale University, New Haven, Connecticut

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Abstract

Numerical solutions to the shallow-water equations are used to examine the generation of wake vorticity as a cyclone drifts past a mountain. In cases with sufficient vortex strength. mountain height, and vortex-mountain proximity, the flow becomes supercritical over the mountain and hydraulic jumps generate wake vorticity. The dissipative vorticity transport in jumps modifies the usual vorticity integral constraints for inviscid shallow-water flow regarding potential enstrophy, vorticity centroid, and vortex size. The increase in vortex size during wake formation represents a weakening of the vortex. These changes, and the macroscopic flow patterns, are independent of the viscosity coefficient. The generation of vertical vorticity within a viscous jump, and the associated Bernoulli loss, arise from a shear stress induced at the sloping upper interface of the layer and transmitted down through the layer by a secondary flow. Applied to the problem of a typhoon drifting past Taiwan, the shallow-water equations capture many of the observed phenomena such as upstream blocking, downstream sheltering, corner winds, and foehn and secondary vortex formation.

Abstract

Numerical solutions to the shallow-water equations are used to examine the generation of wake vorticity as a cyclone drifts past a mountain. In cases with sufficient vortex strength. mountain height, and vortex-mountain proximity, the flow becomes supercritical over the mountain and hydraulic jumps generate wake vorticity. The dissipative vorticity transport in jumps modifies the usual vorticity integral constraints for inviscid shallow-water flow regarding potential enstrophy, vorticity centroid, and vortex size. The increase in vortex size during wake formation represents a weakening of the vortex. These changes, and the macroscopic flow patterns, are independent of the viscosity coefficient. The generation of vertical vorticity within a viscous jump, and the associated Bernoulli loss, arise from a shear stress induced at the sloping upper interface of the layer and transmitted down through the layer by a secondary flow. Applied to the problem of a typhoon drifting past Taiwan, the shallow-water equations capture many of the observed phenomena such as upstream blocking, downstream sheltering, corner winds, and foehn and secondary vortex formation.

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