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Startup process in the Richtmyer-Meshkov instability

Lombardini, M. and Pullin, D. I. (2009) Startup process in the Richtmyer-Meshkov instability. Physics of Fluids, 21 (4). 044104. ISSN 1070-6631.

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An analytical model for the initial growth period of the planar Richtmyer–Meshkov instability is presented for the case of a reflected shock, which corresponds in general to light-to-heavy interactions. The model captures the main features of the interfacial perturbation growth before the regime with linear growth in time is attained. The analysis provides a characteristic time scale τ for the startup phase of the instability, expressed explicitly as a function of the perturbation wavenumber k, the algebraic transmitted and reflected shock speeds U_(S1) < 0 and U_(S2) > 0 (defined in the frame of the accelerated interface), and the postshock Atwood number A^+: τ=[(1-A^+)/U_(S2)+(1+A^+)/(-U_(s1))]/(2k). Results are compared with computations obtained from two-dimensional highly resolved numerical simulations over a wide range of incident shock strengths S and preshock Atwood ratios A. An interesting observation shows that, within this model, the amplitude of small perturbations across a light-to-heavy interface evolves quadratically in time (and not linearly) in the limit A→1^−.

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Additional Information:© 2009 American Institute of Physics. Received 2 October 2008; accepted 4 November 2008; published 14 April 2009. This work was supported by the Advanced Simulation and Computing ASC Program under Subcontract No. B341492 of DOE Contract No. W-7405-ENG-48. M.L. and D.I.P. would like to thank Dr. David J. Hill for numerous discussions and comments on the manuscript.
Funding AgencyGrant Number
Department of EnergyB341492
Department of EnergyW-7405-ENG-48
Subject Keywords:flow instability; flow simulation; interface phenomena; perturbation theory; shock wave effects; shock waves
Issue or Number:4
Record Number:CaltechAUTHORS:20090820-090629481
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:15180
Deposited By: Tony Diaz
Deposited On:20 Aug 2009 19:58
Last Modified:03 Oct 2019 00:55

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