Inviscid Damping of Vortex Asymmetries by a Critical Layer Flux

Experiments and theory characterize a novel regime of near-inviscid 2D vortex symmetrization, wherein a weak flux through the critical layer causes algebraic (rather than exponential) damping of azimuthal asymmetries. This is distinct from exponential critical-layer damping (or spiral wind-up), where the damping may cease once the critical-layer vorticity is trapped in cats-eyes.\footnote{D.A. Schecter et al., Phys. Fluids {\bf 12}, 2397 (2000).} Here, weak viscosity causes slow vortex expansion and negligible direct azimuthal-shear damping; but when the weak expansion flux reaches the critical layer, previously un-damped Kelvin waves are rapidly damped to zero. Pure electron plasma experiments have quantitatively characterized this novel damping for $m_\theta=1$ and $m_\theta=2$ waves, obtaining wave amplitudes varying as $A(t) = A_0 - \gamma \, t$. A simple analysis of critical-layer dynamics agrees well with experiments for $m_\theta=1$ waves (with a bounding wall); but suggests a $\gamma \, t^{2/3}$ dependence for $m_\theta=2$ due to the critical-layer width scaling with wave amplitude. Simulations suggest that weak diffusion may obviate this discordant time exponent of 2/3.