Shallow-Water Flow past Isolated Topography. Part II: Transition to Vortex Shedding

Abstract

Abstract The formation of Karman vortex streets is studied within the framework of single-layer shallow-water dynamics and in absence of surface friction and background rotation. In the first part of this study, steady numerical solutions for flow past circular topography were obtained by imposing a symmetry condition that essentially suppressed vortex shedding. In the second part, this symmetry condition is relaxed in order to study the transition into the vortex-shedding regime. This transition is due to an instability of the symmetric wake pattern. The most unstable global normal mode of this instability is derived by a numerical method. Most of the features of this mode can be understood in terms of the absolute instability theory. The mode is essentially barotropic and relies on a positive feedback between the perturbations located on the two shearlines on either side of the wake. The classical shear modes centered on a single shearline are, on the other hand, shown to be absolutely stable even thoug...