A diffuse-interface description of internal waves in a near-critical fluid

Abstract

We present a diffuse-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 diffuse-interface model applies both above and below $T_c,$ and is formulated by using the density as an order parameter. The diffuse 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 profiles, 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 diffuse-interface model in the limit of incompressible perturbations.