Spatio-temporal pulse propagation during highly-resolved onset of Rayleigh-Taylor and Kelvin-Helmholtz Rayleigh-Taylor instabilities

TL;DR

This study uses high-resolution simulations to analyze the initial development of Rayleigh-Taylor and Kelvin-Helmholtz Rayleigh-Taylor instabilities, revealing acoustic triggers and energy contributions, serving as a benchmark for various fluid dynamics applications.

Contribution

It introduces a novel parallel algorithm for compressible Navier-Stokes equations and provides detailed insights into the onset mechanisms of RTI and KHRTI through comprehensive analysis.

Findings

Acoustic pressure disturbances trigger instabilities.

Energy budget analysis highlights pressure and kinetic contributions.

Spatio-temporal features differentiate RTI and KHRTI onset mechanisms.

Abstract

The present study explores the onset of the Rayleigh-Taylor instability (RTI) and Kelvin-Helmholtz Rayleigh-Taylor instability (KHRTI) with highly-resolved direct numerical simulations of two setups which consider air at different temperatures (or densities) and/or velocities in two halves of three-dimensional cuboidal domains. The compressible Navier-Stokes equations are solved using a novel parallel algorithm which does not involve overlapping points at sub-domain boundaries. 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. The relative contributions of pressure, kinetic energy and rotational energy to the overall energy budget is explored for both instabilities, revealing acoustic trigger to be the incipient mechanism 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 the 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.