Decay rates of internal waves in a fluid near the liquid-vapor critical point

We study the damping of internal waves in a viscous fluid near the liquid-v apor critical point. Such a fluid becomes strongly stratified by gravity du e to its large compressibility. Using the variable-density incompressible N avier-Stokes equations, we model an infinite fluid layer with rigid horizon tal boundaries and periodic side boundary conditions. We present operator-t heoretic results that predict the existence of internal-wave modes with arb itrarily small damping rates. We also solve the eigenvalue problem numerica lly using a compound matrix shooting method and a second method based on a matched-asymptotic perturbation expansion for small viscosity. At temperatu res far above the critical point, the damping of the internal waves is subs tantially influenced by both boundary layer and volumetric effects. The bou ndary layer effect is caused by horizontal shearing layers near the two fix ed horizontal boundaries. As the temperature approaches the critical temper ature, an additional internal shearing layer develops as the density strati fication curve steepens on approach to the two-phase regime. Numerical calc ulations show that for some of the internal-wave modes this causes a dramat ic increase in the damping rate that dominates the boundary layer effects.