Nonlinear Singular Kelvin Modes in a Columnar Vortex

摘要

This paper considers the propagation of helical neutral modes within a cylindrical vortex and the subsequent formation of nonlinear critical layers around the radius where the mean-flow angular velocity and the mode frequency are comparable. Analogy can be done with the stratified critical layers. We formulate a steady-state theory valid when the analogous Richardson number is small at the critical radius. The apparent singularity is removed by retaining nonlinear terms in the critical-layer equations of motion. The result from the interaction is the emergence of multipolar vortices whose poles are located around the critical radius, spiral along the basic vortex axis and are embedded in a distorted mean flow caused by a slow diffusion of the three-dimensional vorticity field from the critical layer.