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Startup process in the Richtmyer–Meshkov instability

Authors

Abstract

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 τ for the startup phase of the instability, expressed explicitly as a function of the perturbation wavenumber k k , the algebraic transmitted and reflected shock speeds U S 1 <0 U S 1 < 0 and U S 2 >0 U S 2 > 0 (defined in the frame of the accelerated interface), and the postshock Atwood number A + A + : τ = (1− A + )/ U S 2 +(1+ A + )/(− U S 1 )/(2 k ) τ = ( 1 − A + ) ∕ U S 2 + ( 1 + A + ) ∕ ( − U S 1 ) ∕ ( 2 k ) . Results are compared with computations obtained from two-dimensional highly resolved numerical simulations over a wide range of incident shock strengths S S and preshock Atwood ratios A 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 − A → 1 − .

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Journal

Physics of FluidsAmerican Institute of Physics

Published: Apr 1, 2009

Keywords: flow instability; flow simulation; interface phenomena; perturbation theory; shock wave effects; shock waves

DOI: 10.1063/1.3091943

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