Damping and Trapping in 2D Inviscid Fluids

We demonstrate collisionless decay due to phase mixing of a disturbance in an inviscid 2D fluid with sheared flow. Experiments performed on a cylindrical pure electron plasma, which behaves as a 2D inviscid fluid, show that a small amplitude quadrupole excitation ($m=2$, $k=0$ mode) decays exponentially. At larger amplitudes, the exponential decay is modulated by bounce motion of fluid elements trapped in the azimuthally traveling wave field, with the bounce frequency proportional to the square root of the excitation amplitude. We also show that the linear decay rate is decreased by the addition of external dissipation. We describe a calculation of the linearized response function.