Columnar vortex stability in island wakes

grantor: University of TorontoThe motivation for this work derives from observations of a broken symmetry of the von Karman vortex streets that are often generated in the lee of oceanic islands. I consider the linear stability against three-dimensional perturbations of columnar vortices in a rotating environment and thereby seek to understand the dynamics of the processes through which such vertically oriented barotropic vortices may be destabilized. In the absence of rotational influence, it is shown that the nonlinear evolution of columnar vortices is most strongly controlled by one or the other of two mechanisms. One mechanism of instability is identifiable as a so-called elliptical instability, which promotes the initial bending of vortex tubes in a sinusoidal fashion, while the other is a hyperbolic mode, which is responsible for the development of streamwise vortex streaks in the "braids" between adjacent vortex core areas. In the rotating case, anticyclonic vortices are strongly destabilized by weak background rotation relative to the non-rotating case, while rapid rotation stabilizes both the cyclones and anticyclones. The anticyclones are themselves subject to two distinct forms of instability, namely a Coriolis force modified elliptical instability and an inertial (centrifugal) instability. The former instability is very similar to the non-rotating mode of elliptical instability as it promotes the initial bending of vortex tubes, while the latter type of instability grows on the edge of the vortex core and generates streaks of vorticity, which surround the vortex core itself. I also examine the three-dimensional, nonlinear evolution of columnar vortices in a rotating environment. As the initial vorticity distribution, a wavetrain of finite amplitude Kelvin-Helmholtz vortices in shear is employed. Through direct numerical simulation of the Navier-Stokes equations I seek to better understand the process of maturation of the various three-dimensional modes of instability to which such vortex flows are subject, especially those which exist as a consequence of the action of the Coriolis force. The results obtained from the earlier stages of nonlinear evolution are compared in detail with the results obtained on the basis of threedimensional linear stability analysis. These results of direct numerical simulation fully verify the results obtained on the basis of stability considerations.Ph.D