Comparing the highly-resolved onset of Rayleigh–Taylor and Kelvin–Helmholtz Rayleigh–Taylor instabilities

Abstract

The present study explores onset of Rayleigh–Taylor instability (RTI) and Kelvin–Helmholtz Rayleigh–Taylor instability (KHRTI) with highly-resolved direct numerical simulations of two setups considering air at different temperatures (or densities) and/or velocities in two halves of three-dimensional (3D) cuboidal domains. The RTI and KHRTI are simulated with 4.2 billion and 480 million mesh points, respectively. Here, we do not impose any external perturbation similar to the unforced experiments of RTI and KHRTI. The compressible Navier–Stokes equations are solved using a novel parallel algorithm which does not involve overlapping points at sub-domain boundaries. This removes the errors at sub-domain boundaries and provides same level of accuracy as sequential computing. The pressure disturbance field is compared during onset of RTI and KHRTI and corresponding convection- and advection-dominated mechanisms are highlighted by instantaneous features, spectra, and proper orthogonal decomposition. Relative contributions of pressure energy, kinetic energy and rotational energy to overall energy budget are explored, revealing acoustics to play a central role in initial perturbation for both RTI and KHRTI. The nonlinear, spatio-temporal nature of the instability is further explored by application of a transport equation for enstrophy of compressible flows. This provides insights into the similarities and differences between onset mechanisms of RTI and KHRTI, serving as a benchmark data set for shear and buoyancy-driven instabilities across diverse applications in geophysics, nuclear energy and atmospheric fluid dynamics.