Inviscid damping of asymmetries on a two-dimensional vortex

The inviscid damping of an asymmetric perturbation on a two-dimensional cir cular vortex is examined theoretically, and with an electron plasma experim ent. In the experiment, an elliptical perturbation is created by an externa l impulse. After the impulse, the ellipticity (quadrupole moment) of the vo rtex exhibits an early stage of exponential decay. The measured decay rate is in good agreement with theory, in which the perturbation is governed by the linearized Euler equations. Often, the exponential decay of ellipticity is slow compared to a vortex rotation period, due to the excitation of a q uasimode. A quasimode is a vorticity perturbation that behaves like a singl e azimuthally propagating wave, which is weakly damped by a resonant intera ction with corotating fluid. Analytically, the quasimode appears as a wave packet of undamped continuum modes, with a sharply peaked frequency spectru m, and it decays through interference as the modes disperse. When the expon ential decay rate of ellipticity is comparable to the vortex rotation frequ ency, the vorticity perturbation does not resemble a quasimode; rather, it is rapidly dominated by spiral filaments. Over longer times, linear theory predicts algebraic decay of ellipticity; however, nonlinear oscillations of ellipticity emerge in the experiment before a transition to algebraic deca y would occur. (C) 2000 American Institute of Physics. [S1070-6631(00)01110 -7].