{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T20:06:32Z","timestamp":1762200392651,"version":"build-2065373602"},"reference-count":54,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T00:00:00Z","timestamp":1761868800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Graduate Studies and Scientific Research at Jouf University","award":["DGSSR-2025-FC-01034"],"award-info":[{"award-number":["DGSSR-2025-FC-01034"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Shock\u2013accelerated interfaces between fluids of different densities are prone to Richtmyer\u2013Meshkov-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\u2013heavy 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\u2013heavy fluid interface. The results highlight the distinct stages of instability evolution, from shock\u2013interface interaction and baroclinic vorticity deposition to nonlinear roll-up and interface deformation. Quantitative diagnostics\u2014including circulation, enstrophy, vorticity extrema, and mixing width\u2014are 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.<\/jats:p>","DOI":"10.3390\/axioms14110813","type":"journal-article","created":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T19:30:27Z","timestamp":1762198227000},"page":"813","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Shock Mach Number Effect on Instability Evolution at a Light\u2013Heavy Fluid Interface: A Numerical Investigation"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7391-8627","authenticated-orcid":false,"given":"Salman Saud","family":"Alsaeed","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, Jouf University, P.O. Box 2014, Sakaka 72388, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6669-5296","authenticated-orcid":false,"given":"Satyvir","family":"Singh","sequence":"additional","affiliation":[{"name":"Institute of Applied and Computational Mathematics, RWTH Aachen University, 52062 Aachen, Germany"},{"name":"Department of Mathematics, Graphic Era Deemed to be University, Dehradun 248002, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7650-6978","authenticated-orcid":false,"given":"Nahar F.","family":"Alshammari","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, College of Engineering, Jouf University, P.O. Box 2014, Sakaka 72388, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1146\/annurev.fluid.34.090101.162238","article-title":"The Richtmyer-Meshkov instability","volume":"34","author":"Brouillette","year":"2002","journal-title":"Annu. Rev. Fluid Mech."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1002\/cpa.3160130207","article-title":"Taylor instability in shock acceleration of compressible fluids","volume":"13","author":"Richtmyer","year":"1960","journal-title":"Commun. Pure Appl. Math."},{"key":"ref_3","first-page":"101","article-title":"Instability of the interface of two gases accelerated by a shock wave","volume":"4","author":"Meshkov","year":"1969","journal-title":"Commun. Pure Appl. 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