Effects of isothermal stratification strength on vorticity dynamics for single-mode compressible Rayleigh-Taylor instability

Abstract

The effects of isothermal stratification strength on vorticity dynamics for single-mode Rayleigh-Taylor instability (RTI) are examined using two dimensional fully compressible wavelet-based direct numerical simulations. The simulations model low Atwood number (A = 0.04) RTI development for four different stratification strengths, corresponding to Mach numbers from 0.3 (weakly stratified) to 1.2 (strongly stratified), and for three different perturbation Reynolds numbers, from 5,000 to 20,000. All simulations use adaptive wavelet-based mesh refinement to achieve very fine spatial resolutions at relatively low computational cost. For all stratifications, the bubble and spike go through the exponential growth regime, followed by a slowing of the RTI evolution. For the weakest stratification, this slow-down is then followed by a re-acceleration, while for stronger stratifications the suppression of RTI growth continues. Bubble and spike asymmetries are observed for weak stratifications, with bubble and spike growth rates becoming increasingly similar as the stratification strength increases. For the range of cases studied, there is relatively little effect of Reynolds number on bubble and spike heights, although the formation of secondary vortices becomes more pronounced as Reynolds number increases. The underlying dynamics are analyzed in detail through an examination of the vorticity transport equation, revealing that incompressible baroclinicity drives RTI growth for small and moderate stratifications, but increasingly leads to the suppression of vorticity production and RTI growth for stronger stratifications. These variations in baroclinicity are used to explain the suppression of RTI growth for strong stratifications, as well as the anomalous asymmetry in bubble and spike growth rates for weak stratifications.

Revisiting the late-time growth of single-mode Rayleigh–Taylor instability and the role of vorticity

“…The generation mechanism of acoustic waves in two-fluid miscible RTI [44,45] is different. In the latter case, it is the enthalpy diffusion term in the energy equation leading to non-zero time derivative and the generation of acoustic waves,…”

“…(3) Are there fundamental differences in RTI bubble growth between 2D and 3D? Previous studies of late-time bubble growth were either restricted to 2D [38,44,45] or included 3D but were numerically under-resolved [35,37]. The absence of vortex stretching in 2D RTI makes the underlying vortex dynamics significantly different from 3D RTI.…”

“…(4) Will the dynamics of re-acceleration and chaotic development shown in [38] using incompressible fluid simulations be similar when using the fully compressible dynamics? Compressible effects such as background stratification, finite acoustic speed, non-zero velocity divergence, and the fluid's equation of state can have non-trivial effects on the RTI development [46,47,48,45]. Ref.…”

Kinetic energy and enstrophy transfer in compressible Rayleigh–Taylor turbulence

“…Wieland et al. (2019) found that the dilatation effects also have an important influence on the evolution of vorticity for the compressible RTI, such as total baroclinic effects. They also revealed that bubble and spike asymmetries in RTI growth were formed as a consequence of the dilatation and stratification contributions to the baroclinic torque based on the analysis of the vorticity transport equation.…”

Experiments and Simulations on the Turbulent, Rarefaction Wave Driven Rayleigh–Taylor Instability

“…Due to the very large accelerations in these experiments, one might question comparison with results from other incompressible experiments and simulations. To test the incompressible assumption, we calculated the static Mach number as defined by Wieland et al [36] and find it to exceed 0.3 only at the largest acceleration levels and only in the SF 6 gas where it achieves a value of 0.35. In addition, the static Mach number is generally well below 0.3.…”