Vortex methods are ideally suited for numerical integration of the Euler equations in two and three dimensions. In three dimensions, the vorticity of the flow is represented by a collection of vortex lines, each of which represents the axis of a vortex tube with a smooth vorticity distribution in its core. A spatially varying vorticity field can be represented by an appropriately distributed collection of such tubes. The vortex lines are advected by the velocity field, which itself is computed from the vorticity field as described by the lines.
In recent years the author has investigated the dynamics of vortices which are subjected to the stretching and radial inflow associated with a deformation field, analogous to those which maintain intense geophysical vortices such as tornadoes and hurricanes. In this investigation we use vortex methods to extend this analysis to fully nonlinear simulations of three-dimensional vortices. We first show how a strongly perturbed vortex transitions to three dimensional turbulence. An example is shown in the Figure below, which depicts the development of three dimensional turbulence in a perturbed vortex which is represented by 18 vortex lines and is periodic in the vertical direction. We then go on to show how this process is inhibited or even reversed when the vortex lies in a deformation field and is stretched along its axis. If the stretching is strong eneough, the vortex behaves much like a two-dimensional vortex, which allows for axisymmetrization and an upscale transfer of energy which enhances intensification.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics