A Di use - Interface Description ofInternal Waves in a Near - Critical FluidD

We present a diiuse-interface treatment of the internal gravity waves which have been observed experimentally by Berg et al. in xenon near its thermodynamic critical point. The results are compared with theoretical predictions by Berg et al. that were obtained using separate models above and below the critical temperature T c. The diiuse-interface model applies both above and below T c , and is formulated by using the density as an order parameter. The diiuse interface is represented as a transition zone of rapid but smooth density variation in the model, and density gradients appear in a capillary tensor, or Korteweg stress term, in the momentum equation. We obtain static density prooles, compute internal wave frequencies and compare with the experimental data and theoretical results of Berg et al. both above and below the critical temperature. The results reveal a singularity in the diiuse-interface model in the limit of incompressible perturbations.