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.

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We highlight the differing roles of vorticity and strain in the transport of coarse-grained scalars at length-scales larger than by smaller scale (subscale) turbulence. We use the first term in a multiscale gradient expansion due to Eyink [1], which exhibits excellent correlation with the exact subscale physics when the partitioning length is any scale smaller than that of the spectral peak.We show that unlike subscale strain, which acts as an anisotropic diffusion/anti-diffusion tensor, subscale vorticity's contribution is solely a conservative advection of coarse-grained quantities by an eddy-induced non-divergent velocity, v * , that is proportional to the curl of vorticity. Therefore, material (Lagrangian) advection of coarse-grained quantities is accomplished not by the coarsegrained flow velocity, u , but by the effective velocity, u + v * , the physics of which may improve commonly used LES models.

We study energy scale transfer in Rayleigh–Taylor (RT) flows by coarse graining in physical space without Fourier transforms, allowing scale analysis along the vertical direction. Two processes are responsible for kinetic energy flux across scales: baropycnal work $\varLambda$ , due to large-scale pressure gradients acting on small scales of density and velocity; and deformation work $\varPi$ , due to multiscale velocity. Our coarse-graining analysis shows how these fluxes exhibit self-similar evolution that is quadratic-in-time, similar to the RT mixing layer. We find that $\varLambda$ is a conduit for potential energy, transferring energy non-locally from the largest scales to smaller scales in the inertial range where $\varPi$ takes over. In three dimensions, $\varPi$ continues a persistent cascade to smaller scales, whereas in two dimensions $\varPi$ rechannels the energy back to larger scales despite the lack of vorticity conservation in two-dimensional (2-D) variable density flows. This gives rise to a positive feedback loop in 2-D RT (absent in three dimensions) in which mixing layer growth and the associated potential energy release are enhanced relative to 3-D RT, explaining the oft-observed larger $\alpha$ values in 2-D simulations. Despite higher bulk kinetic energy levels in two dimensions, small inertial scales are weaker than in three dimensions. Moreover, the net upscale cascade in two dimensions tends to isotropize the large-scale flow, in stark contrast to three dimensions. Our findings indicate the absence of net upscale energy transfer in three-dimensional RT as is often claimed; growth of large-scale bubbles and spikes is not due to ‘mergers’ but solely due to baropycnal work $\varLambda$ .

The vibration of solid is ubiquitous in nature and industrial applications, and gives rise to alternative droplet dynamics during impact. Using many-body dissipative particle dynamics (MDPD), we investigate the impact of droplets on superhydrophobic solid surfaces vibrating in the vertical direction at a vibration period similar to the contact time. Specifically, we study the influence of the impact phase and vibration frequency. We evaluate the influence from the aspects of maximum spreading diameter, the solid-liquid contact time and area, and the momentum variation during the impact. To quantitatively evaluate the solid-liquid contact, we introduce the area-time integral, which is the integral of the contact area over the whole contact time. It is meaningful when the heat exchange between solid and liquid is considered. One characteristic phenomenon of droplets impacting vibrating substrate is that multiple contacts may occur before the final rebound. Unlike previous studies defining the contact time as the time span from the first impact to the final detachment, we define the contact time as the summation of each individual contact time. Using this definition, we show that the discontinuity at the critical impact phase disappears. Moreover, We show that the probability of impact phase is affected by the vibrating frequency, and use it to calculate the weighted averaged outcome when the impact phase is not controlled. This study not only offers insights into the physics of droplet impact on vibrating surfaces, but also can be used to guide the design of surfaces to achieve manageable wetting using vibration.

We investigate the dynamics of droplet impacts on a ring-decorated solid surface, which is reported to reduce the integral of contact area over contact time by up to 80%. By using many-body dissipative particle dynamics (MDPD), a particle-based simulation method, we measure the temporal evolution of the shape and the impact force of two specific types of phenomena, overrun and ejection. The numerical model is first validated with experimental data on a plain surface from literature. Then, it is used to extract the impacting force of the ring and substrate separately, showing the ring does not provide the majority of vertical force to redirect the horizontal spreading. The impacting pressure in different concentric rings is also present as a function of time, showing pressure waves traveling from ring to center. The effect of the ring's height and radius on the impacting force is also discussed. To the best of our knowledge, this is the first MDPD study on droplets impacting on a solid surface with a validated force analysis.