Multipolar spherical and cylindrical vortices

Multipolar vortices and algebraic curves

This paper demonstrates that analytical solutions to the steady two-dimensional Euler equations possessing all the qualitative properties of multipolar vortices observed experimentally and numerically can be constructed using the theory of algebraic curves and quadrature domains. The solutions consist of a finite set of line vortices superposed on finite-area patches of uniform vorticity. By wa...

A class of exact multipolar vortices

A class of exact solutions to the steady Euler equations representing finite area patches of nonuniform vorticity is presented. It is demonstrated that the solutions constitute a special class of steady multipolar vortical structures and have many qualitative similarities with the multipolar equilibria observed in two-dimensional flows at high Reynolds numbers. The results provide insights into...

On the dynamics of nonreducible cylindrical vortices

This work is a natural companion of [10], where the dynamics of cocycles of isometries of R over a minimal dynamics (semigroup action) is studied. While [10] is mostly devoted to the case in which the orbits of the fibered (skew) dynamics are bounded (a condition that turns out to be equivalent to the existence of a continuous invariant section), here we concentrate on the opposite (i.e. non-re...

Steady Multipolar Planar Vortices with Nonlinear Critical Layers

This article considers a family of steady multipolar planar vortices which are the superposition of an axisymmetric mean flow, and an azimuthal disturbance in the context of inviscid, incompressible flow. This configuration leads to strongly nonlinear critical layers when the angular velocities of the mean flow and the disturbance are comparable. The poles located on the same critical radius po...

Section 13.7 Cylindrical and Spherical Coordinates