ar X iv : c on d - m at / 9 71 10 36 v 2 5 D ec 1 99 7 Hydrodynamic damping in trapped Bose gases

Griffin, Wu and Stringari have derived the hydrodynamic equations of a trapped dilute Bose gas above the Bose-Einstein transition temperature. We give the extension which includes hydrodynamic damping, following the classic work of Uehling and Uhlenbeck based on the Chapman-Enskog procedure. Our final result is a closed equation for the velocity fluctuations δv which includes the hydrodynamic damping due to the shear viscosity η and the thermal conductivity κ. Explicit expressions are given for η and κ, which are position-dependent through dependence on the local fugacity when one includes the effect of quantum degeneracy of the trapped gas. For certain normal mode solutions (with ∇·δv =const), an unusual negative contribution to the damping arises from the gradient of the shear viscosity. We also discuss a trapped Bose-condensed gas, generalizing the work of Zaremba, Griffin and Nikuni to include hydrodynamic damping due to the (non-condensate) normal fluid.