Vortex crystals from 2D Euler flow: Experiment and simulation

Abstract

Vortex-in-cell simulations that numerically integrate the 2D Euler equations are compared directly to experiments on magnetized electron columns ͓K. S. Fine, A. C. Cass, W. G. Flynn, and C. F. Driscoll, ''Relaxation of 2D turbulence to vortex crystals,'' Phys. Rev. Lett. 75, 3277 ͑1995͔͒, where turbulent flows relax to metastable vortex crystals. A vortex crystal is a lattice of intense small diameter vortices that rotates rigidly in a lower vorticity background. The simulations and experiments relax at the same rates to vortex crystals with similar vorticity distributions. The relaxation is caused by mixing of the background by the intense vortices: the relaxation rate is peaked when the background circulation is 0.2-0.4 times the total circulation. Close quantitative agreement between experiment and simulation provides strong evidence that vortex crystals can be explained without incorporating physics beyond 2D Euler theory, despite small differences between a magnetized electron column and an ideal 2D fluid.

Motion of extended vortices in an inhomogeneous pure electron plasma

“…In Ref. 19 this procedure is considered to represent well the real coarse graining that is implicit in an experimental plasma density measurement.…”

Vortex dynamics of 2D electron plasmas

“…In this approximation, the ðr; hÞ flow of the electrons is described by the 2D drift-Poisson equations [1], which can be written in terms of the vorticity fðr; h; tÞ ð4pec=BÞn and the scaled electrostatic potential wðr; h; tÞ ðc=BÞ/ as Physica C 369 (2002) [21][22][23][24][25][26][27] www.elsevier.com/locate/physc…”

Polygonal N-vortex arrays: A Stuart model

“…Beyond hydrodynamics, the fact that vortex lattices also emerge as self-organized structures in non-neutral plasmas has added further momentum to the study of such problems. 7,8 By far, the problem of N-polygonal arrays of line vortices has received the most attention. Since the early work of Thomson,3 numerous investigations have been carried out.…”