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

Scott A. Wieland, Peter E. Hamlington, Scott J. Reckinger, and Daniel Livescu

Phys. Rev. Fluids 4, 093905 – Published 26 September 2019

Abstract

The effects of isothermal initial stratification on the dynamics of the vorticity 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 initial stratification strengths, corresponding to Mach numbers from 0.3 (weakly stratified) to 1.2 (strongly stratified), and for three different Reynolds numbers, from 25 500 to 102 000. Here, the Mach number is based on the Atwood-independent gravity wave speed and characterizes the strength of the initial stratification. All simulations use adaptive wavelet-based mesh refinement to achieve very fine spatial resolutions at relatively low computational cost. For all stratifications, the RTI 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 reacceleration, 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.

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Received 11 December 2018

DOI:https://doi.org/10.1103/PhysRevFluids.4.093905

Physics Subject Headings (PhySH)

Compressible flows Flow instability Rayleigh-Taylor instability

Fluid Dynamics

Authors & Affiliations

Scott A. Wieland^1,*, Peter E. Hamlington^1,†, Scott J. Reckinger^2,‡, and Daniel Livescu^3,§

¹Department of Mechanical Engineering, University of Colorado, Boulder, Colorado, USA
²Department of Mechanical and Industrial Engineering, University of Illinois, Chicago, Illinois, USA
³Los Alamos National Laboratory, Los Alamos, New Mexico, USA