Nonlinear stationary vortices in gravitating fluid
The problem of nonlinear self-organization of perturbations in differentially rotating, nonuniform, gravitating systems is studied. Two types of stationary nonlinear solutions, in the form of tripolar vortices and vortex chains of gravitational potential and density, dependent on the spatial profiles of the basic state quantities, are found. They propagate with a constant velocity perpendicularly to the basic state gradients, and characteristic time scales for the creation of such vortical structures are shown to be much shorter than the corresponding intervals for gravitational contraction.
Tripolar vortex in plasma flow
Abstract Strongly nonlinear processes in a two-component plasma with sheared flow, in the low-frequency limit, in comparison with the ion gyro frequency Ωi, and for perturbations propagating perpendicularly to the ambient magnetic field are studied. In the linear domain such a system is prone to the development of instability of the Kelvin–Helmholtz type. In the nonlinear regime this instability can saturate into stationary travelling solutions of the form of vortex chains and tripolar vortices, which are found in this paper.
Laboratory experiments on the tripolar vortex in a rotating fluid
Within the framework of the study of coherent vortex structures as emerging in rotating, quasi-two-dimensional flows, the tripolar vortex is a relatively novel feature. It consists of a symmetric, linear arrangement of three patches of distributed vorticity of alternate signs, and the axis of this configuration rotates about the centre of the core vortex. This paper describes an experimental study of the formation of a tripole from an unstable axisymmetric vortex in a solidly rotating, homogeneous fluid. The flow is visualized by addition of dye, and is measured by streak photography of tracer particles. After digitization, the spatial distributions of the vorticity ω and the stream function ψ are calculated numerically, and 'scatter plots’ of ω versus ψ are presented for the various stages in the tripole formation process. Owing to viscous effects (spin-down by the bottom Ekman layer and lateral entrainment of ambient fluid) the tripole shows an exponential decay, both in its rotation speed and its internal, relative flow. The comparison of the observed flow characteristics with a simple point-vortex model shows reasonable quantitative agreement.