2-FLUID HYDRODYNAMICS FOR A TRAPPED WEAKLY INTERACTING BOSE-GAS

We derive coupled, equations of motion for the condensate (superfluid) and noncondensate (normal fluid) degrees of freedom in a trapped Bose gas at finite temperatures. Our results are based on the Hartree-Fock -Popov approximation for the time-dependent condensate wave function, and thermodynamic local equilibrium for the noncondensate atoms. In th e special case of a uniform weakly interacting gas, our hydrodynamic e quations are shown to be consistent with the two-fluid equations of La ndau. The collective modes in a parabolically trapped Bose gas include the analog of the out-of-phase second-sound mode in superfluid He-4.