Vortex waves and evolution in sharp vorticity gradient vortices - Terwey, Wesley D., author; Montgomery, Michael T., author (Colorado State University. Libraries, 2003)
Intense geophysical vortices are observed to be strongly axisymmetric and frequently possess steep gradients of vorticity around their cores. Such vortices are often surrounded by asymmetric disturbances that act to deform the mean vortex. The evolution of such intense vortices in response to these small-amplitude forcings is an important and interesting study and the topic of this work. Previous studies investigated the interactions between vorticity perturbations on two, concentric, sharp vorticity gradients and detailed a classic exponential instability. We per- £ rm here a general and complete linearized analysis of a similar, but unrestricted, three region vortex initial value problem (IVP) in a two-dimensional, non-divergent model, including initial disturbances both on and in the vicinity of the pair of steep vortex gradients. Using this more general model, we complete the exponential instability analysis, noting the existence of a wavenumber-2 instability in cases previously not studied. After constructing the solution to the linear IVP, we show that the addition of sheared disturbances does not change the long-time stability properties of the main vortex. The mean flow changes due to the momentum fluxes of these sheared disturbances, however, are altered considerably by the perturbation flow associated with the deformed vortex core. Mean flow changes are particularly large in magnitude for sheared disturbances located near critical radii in the mean flow. Perturbations near these radii resonantly force and deform the main vortex, leading o the breakdown of linear theory and the significance of nonlinear mixing processes around these radii. The nonlinear effects on the mean vortex in these resonant cases can lead to resonant damping of the deformed vortex which is not possible in the strictly linear IVP. Finally, we demonstrate the importance of nonlinearities in evolution of sharp gradient vortices and point out the usefulness and limitations of linear theory.
April 2003.
Also issued as Wesley D. Terwey's thesis (M.S.) -- Colorado State University, 2003.
Keywords: Tornadoes -- Mathematical models; Vortex-motion