Numerical Investigation of Atwood Number Effects on Shock-Driven Single-Mode Stratified Heavy Fluid Layers

Salman Saud Alsaeed, Satyvir Singh () and Nouf A. Alrubea
Additional contact information
Salman Saud Alsaeed: Department of Mathematics, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia
Satyvir Singh: Applied and Computational Mathematics, RWTH Aachen University, 52062 Aachen, Germany
Nouf A. Alrubea: Department of Mathematics, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia

Mathematics, 2025, vol. 13, issue 18, 1-26

Abstract: This work presents a numerical investigation of Richtmyer–Meshkov instability (RMI) in shock-driven single-mode stratified heavy fluid layers, with emphasis on the influence of the Atwood number. High-order modal discontinuous Galerkin simulations are carried out for Atwood numbers ranging from A = 0.30 to 0.72 , allowing a systematic study of interface evolution, vorticity dynamics, and mixing. The analysis considers diagnostic quantities such as interface trajectories, normalized interface length and amplitude, vorticity extrema, circulation, enstrophy, and kinetic energy. The results demonstrate that the Atwood number plays a central role in instability development. At low A , interface deformation remains smooth and coherent, with weaker vorticity deposition and delayed nonlinear roll-up. As A increases, baroclinic torque intensifies, leading to rapid perturbation growth, stronger vortex roll-ups, and earlier onset of secondary instabilities such as Kelvin–Helmholtz vortices. Enstrophy, circulation, and interface measures show systematic amplification with increasing density contrast, while the total kinetic energy exhibits relatively weak sensitivity to A . Overall, the study highlights how the Atwood number governs the transition from linear to nonlinear dynamics, controlling both large-scale interface morphology and the formation of small-scale vortical structures. These findings provide physical insight into shock–interface interactions and contribute to predictive modeling of instability-driven mixing in multicomponent flows.

Keywords: Richtmyer–Meshkov instability; shock–interface interaction; Atwood number; stratified heavy fluid layer; vorticity dynamics; discontinuous Galerkin (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/18/3032/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/18/3032/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:18:p:3032-:d:1753560

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().