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-vapor critical point. Such a fluid becomes strongly stratified by gravity due to its large compressibility. Using the variable-density incompressible Navier-Stokes equations, we model an infinite fluid layer with rigid horizontal boundaries and periodic side boundary conditions. We present operator-theoretic results that predict the existence of internal-wave modes with arbitrarily small damping rates. We also solve the eigenvalue problem numerically using a compound matrix shooting method and a second method based on a matched-asymptotic perturbation expansion for small viscosity. At temperatures far above the critical point, the damping of the internal waves is substantially influenced by both boundary layer and volumetric effects. The boundary layer effect is caused by horizontal shearing layers near the two fixed horizontal boundaries. As the temperature approaches the critical temperature, an additional internal shearing layer develops as the density stratification curve steepens on approach to the two-phase regime. Numerical calculations show that for some of the internal-wave modes this causes a dramatic increase in the damping rate that dominates the boundary layer effects.