Hydrodynamic modes and pulse propagation in a cylindrical Bose gas above the Bose-Einstein transition

We study hydrodynamic oscillations of a cylindrical Bose gas above the Bose-Einstein transition temperature using the hydrodynamic equations derived by Griffin, Wu, and Stringari. This extends recent studies of a cylindrical Bose-condensed gas at $T=0.$ Explicit normal mode solutions are obtained for non-propagating solutions. In the classical limit, the sound velocity is shown to be the same as a uniform classical gas. We use a variational formulation of the hydrodynamic equations to discuss the propagating modes in the degenerate Bose-gas limit and show there is little difference from the classical results. We discuss the propagation of sound pulses above and below TBEC.