| We study the Rayleigh-Taylor (RT) instability in both the moderately compressible and weakly compressible regimes. Rayleigh-Taylor mixing is an acceleration driven instability of a layer separating two fluids of distinct densities. For the two dimensional single mode case, we find that the dimensionless terminal velocities (and associated Froude numbers) are nearly constant over most of this region of parameter space, as the thermodynamic parameters describing the equation of state are varied. The phenomenological drag coefficient which occurs in the single mode buoyancy-drag equation is directly related to the terminal velocities and has a similar behavior. Pressure differences and interface shape, however, display significant dependence on the EOS parameters even for the weakly compressible flows. For three dimensional multimode mixing, we expect that density stratification rather than drag will provide the leading compressibility effect. We develop an analytical model to account for density stratification effects in multimode self-similar mixing. Our, theory is consistent with and extends numerically based conclusions developed earlier which also identify density stratification as the dominant compressibility effect for multimode three dimensional mixing.; New simulations with Locally Grid Based Front Tracking Method compare Rayleigh-Taylor mixing rates for ideal fluids and for real fluids with experimental values for surface tension or mass diffusion. The simulated real fluid mixing rates agree with those measured experimentally. Comparison to theoretical predictions relating the mixing rate, the bubble width and the bubble height fluctuations based on bubble merger models shows similar agreement with experiment. The ideal fluid mixing rate is some 50% larger, providing an example of the sensitivity of the mixing rate to physical scale breaking interfacial phenomena; we also observe sensitivity to numerical scale breaking artifacts.; Key Words: Rayleigh-Taylor instability, front racking method, surface tension, mass diffusion. |
