The proper scale decomposition in flows with significant density variations is not as straightforward as in incompressible flows, with many possible ways to define a 'length-scale.' A choice can be made according to the so-called inviscid criterion [1]. It is a kinematic requirement that a scale decomposition yield negligible viscous effects at large enough 'length-scales.' It has been proved [1] recently that a Favre decomposition satisfies the inviscid criterion, which is necessary to unravel inertial-range dynamics and the cascade. Here, we present numerical demonstrations of those results. We also show that two other commonly used decompositions can violate the inviscid criterion and, therefore, are not suitable to study inertial-range dynamics in variable-density and compressible turbulence. Our results have practical modeling implication in showing that viscous terms in Large Eddy Simulations do not need to be modeled and can be neglected. *

Growth of the single-fluid single-mode Rayleigh-Taylor instability (RTI) is revisited in 2D and 3D using fully compressible high-resolution simulations. We conduct a systematic analysis of the effects of perturbation Reynolds number (Re p ) and Atwood number (A) on RTI's late-time growth. Contrary to the common belief that single-mode RTI reaches a terminal bubble velocity, we show that the bubble re-accelerates when Re p is sufficiently large, consistent with [Ramaparabhu et al. 2006, Wei andLivescu 2012]. However, unlike in [Ramaparabhu et al. 2006], we find that for a sufficiently high Re p , the bubble's late-time acceleration is persistent and does not vanish. Analysis of vorticity dynamics shows a clear correlation between vortices inside the bubble and re-acceleration. Due to symmetry around the bubble and spike (vertical) axes, the self-propagation velocity of vortices points in the vertical direction. If viscosity is sufficiently small, the vortices persist long enough to enter the bubble tip and accelerate the bubble [Wei and Livescu 2012]. A similar effect has also been observed in ablative RTI [Betti and Sanz 2006]. As the spike growth increases relative to that of the bubble at higher A, vorticity production shifts downward, away from the centerline and toward the spike tip. We modify the Betti-Sanz model for bubble velocity by introducing a vorticity efficiency factor η = 0.45 to accurately account for re-acceleration caused by vorticity in the bubble tip. It had been previously suggested that vorticity generation and the associated bubble re-acceleration are suppressed at high A. However, we present evidence that if the large Re p limit is taken first, bubble re-acceleration is still possible. Our results also show that re-acceleration is much easier to occur in 3D than 2D, requiring smaller Re p thresholds.

scaling law with α b dependent on the initial conditions and ablation velocity. The value of α b is determined by the bubble competition theory, indicating that mass ablation reduces α b with respect to the classical value for the same initial perturbation amplitude. It is also shown that ablation-driven vorticity accelerates the bubble velocity and prevents the transition from the bubble competition to the bubble merger regime at large initial amplitudes leading to higher α b than in the classical case. Due to the dependence of α b on initial perturbation and vorticity generation, ablative stabilization of the nonlinear ARTI is not as effective as previously anticipated for large initial perturbations.