Hydrodynamic modes in a trapped bose gas above the Bose-Einstein transition

We discuss the collective modes of a trapped Bose gas in the hydrodynamic regime where atomic collisions ensure local thermal equilibrium for the distribution function. Starting from the conservation laws, in the linearized limit we derive a closed equation for the velocity fluctuations in a trapped Bose gas above the Bose-Einstein transition temperature. Explicit solutions for a parabolic trap are given. We find that the surface modes above the transition have the same dispersion relation as the one recently obtained by Stringari for the oscillations of the condensate at T = 0 within the Thomas-Fermi approximation. Results are also given for the monopole ''breathing'' mode as well as for the m = 0 excitations which result from the coupling of the monopole and quadrupole modes in an anisotropic parabolic well.