Numerical Study of Amplitude-Driven Flow Dynamics in Shocked Heavy-Fluid Layers

Mathematics, vol. 14, pp. 82

Abstract

In this study, a comprehensive numerical investigation of amplitude-driven flow dynamics in shocked heavy-fluid layers is presented to focus on the evolution of the Richtmyer–Meshkov instability (RMI). A high-order mixed local discontinuous Galerkin scheme is employed to resolve the complex interactions between shock waves and perturbed interfaces within a compressible viscous flow framework. Impacts of the initial interface amplitudes are systematically examined through a series of single-mode configurations with amplitude–wavelength ratios ranging from a0/λ=0.025 to 0.4. The simulations capture the complete transition from early linear growth to nonlinear roll-up and subsequent mixing. This investigation illustrates that increasing the initial perturbation amplitude enhances baroclinic vorticity generation, intensifies interfacial deformation, and accelerates the onset of secondary instabilities. Low-amplitude interfaces maintain nearly symmetric deformation with delayed nonlinear transition, whereas high-amplitude cases exhibit pronounced spike–bubble asymmetry, stronger curvature, and rapid Kelvin–Helmholtz roll-ups. Quantitative diagnostics of the circulation, enstrophy, and kinetic energy demonstrate that both baroclinic torque and mixing intensity scale directly with the initial perturbation amplitude. This study offers new physical insight into amplitude-dependent shock–interface interactions and elucidates the mechanisms governing vorticity amplification and energy redistribution in RMI flows.

Authors 2

1. Ahmed Hussein Msmali

   Jazan University

   Affiliation as printed

   Department of Mathematics, College of Science, Jazan University, Jazan 45142, Saudi Arabia

2. Satyvir Singh corresponding Aachen Institute for 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 for Applied and Computational Mathematics, RWTH Aachen University, 52062 Aachen, Germany