On the dynamics of inviscid relaxation in 2D fluids and nonneutral plasmas

Two-dimensional (2D) flows in atmospheres, oceans and plasmas can rapidly relax to metastable patterns before viscosity affects the dynamics. This dissertation is on the mechanics of inviscid relaxation. Three topics are covered: vortex motion driven by a background vorticity gradient, the inviscid damping (Landau damping) of asymmetries on a circular vortex, and vortex crystal formation.; All topics were motivated by experiments with magnetized electron columns, where the (r, theta) flow of electrons is approximately governed by the 2D Euler equations. These equations also govern 2D inviscid incompressible uniform-density fluids.; In one experiment, a turbulent flow relaxed through the migration of vortices to extrema in the background vorticity. In Chapter 2, a theory describing this vortex motion is developed. Generally, the vortex speed is proportional to the background vorticity gradient; however, a vortex that is prograde with respect to the background shear moves slower than a retrograde vortex of equal strength. Separate theories are given for the motion of prograde and retrograde vortices. Both theories compare favorably to simulations and the experiment.; In Chapter 3, the rate at which a perturbed vortex relaxes toward an axisymmetric equilibrium is examined using linear perturbation theory. The initial perturbation is created by the brief application of an external flow field, modelling recent experiments. In the core of the vortex, the perturbation typically behaves like an exponentially damped normal mode. An eigenmode analysis shows that this "quasi-mode" is actually a wave-packet of neutral continuum modes that decays through interference as the continuum modes disperse. Physically, a quasi-mode decays to conserve total angular momentum as vorticity is mixed in an outer resonance layer. Theoretical decay rates are found to agree with the experiments.; In Chapter 4, vortex-in-cell simulations of 2D Euler flow are compared directly to electron plasma experiments in which turbulent flows relax to vortex crystals. A vortex crystal is an array of intense vortices that rotates rigidly in a lower vorticity background. The simulations and the experiments relax to vortex crystals at the same rate, proving that vortex crystal formation in electron plasmas does not require physics beyond the 2D Euler equations. Vortex crystals are formed due to the mixing of background vorticity by the intense vortices, which has a cooling effect on the chaotic vortex motion.