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Published June 11, 2010 | Published
Journal Article Open

Linearized Richtmyer-Meshkov flow analysis for impulsively accelerated incompressible solids


We present an analytical study of the linearized impulsive Richtmyer-Meshkov flow for incompressible elastic solids. Seminumerical prior investigations of a related shock-driven compressible elastic problem suggest that the interface amplitude remains bounded in time, in contrast to the unstable behavior found for gases. Our approach considers a base unperturbed flow and a linearization of the conservation equations around the base solution. The resulting initial and boundary value problem is solved using Laplace transform techniques. Analysis of the singularities of the resultant function in the Laplace domain allows us to perform a parametric study of the behavior of the interface in time. We identify two differentiated long-term patterns for the interface, which depends on the material properties: standing wave and oscillating decay. Finally, we present results for the vorticity distribution, which show that the shear stiffness of the solids is responsible both for the stabilization of the interface, and also for the period of the interface oscillations. Comparisons with previous results are discussed.

Additional Information

© 2010 The American Physical Society. Received 10 March 2010; published 11 June 2010. We want to acknowledge M. Lombardini for his valuable comments on this paper. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award No. DE-FC52-08NA28613.

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Published - Ortega2010p10523Phys_Rev_E.pdf


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