Shock Mach Number Effect on Instability Evolution at a Light–Heavy Fluid Interface: A Numerical Investigation

Axioms, vol. 14, pp. 813

Abstract

Shock–accelerated interfaces between fluids of different densities are prone to Richtmyer–Meshkov-type instabilities, whose evolution is strongly influenced by the incident shock Mach number. In this study, we present a systematic numerical investigation of the Mach number effect on the instability growth at a light–heavy fluid layer. The governing dynamics are modeled using the compressible multi-species Euler equations, and the simulations are performed with a high-order modal discontinuous Galerkin method. This approach provides accurate resolution of sharp interfaces, shock waves, and small-scale vortical structures. A series of two-dimensional simulations is carried out for a range of shock Mach numbers impinging on a sinusoidally perturbed light–heavy fluid interface. The results highlight the distinct stages of instability evolution, from shock–interface interaction and baroclinic vorticity deposition to nonlinear roll-up and interface deformation. Quantitative diagnostics—including circulation, enstrophy, vorticity extrema, and mixing width—are employed to characterize the instability dynamics and to isolate the role of Mach number in enhancing or suppressing growth. Particular attention is given to the mechanisms of vorticity generation through baroclinic torque and compressibility effects. Moreover, the analysis of controlling parameters, including Atwood number, layer thickness, and initial perturbation amplitude, broadens the parametric understanding of shock-driven instabilities. The results reveal that increasing shock Mach number markedly enhances vorticity generation and accelerates interface growth, while the resulting nonlinear morphology remains strongly sensitive to variations in Atwood number and perturbation amplitude.

Authors 3

1. Salman Saud Alsaeed

   Jouf University

   Affiliation as printed

   Department of Mathematics, College of Science, Jouf University, P.O. Box 2014, Sakaka 72388, Saudi Arabia

2. Satyvir Singh corresponding Aachen Institute of Applied and Computational Mathematics

   RWTH Aachen University · Graphic Era University

   Affiliation as printed

   Department of Mathematics, Graphic Era Deemed to be University, Dehradun 248002, India

   Institute of Applied and Computational Mathematics, RWTH Aachen University, 52062 Aachen, Germany

3. Nahar Fehaid Alshammari

   Jouf University

   Affiliation as printed

   Department of Electrical Engineering, College of Engineering, Jouf University, P.O. Box 2014, Sakaka 72388, Saudi Arabia