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Small-amplitude perturbations in the three-dimensional cylindrical Richtmyer–Meshkov instability

Lombardini, M. and Pullin, D. I. (2009) Small-amplitude perturbations in the three-dimensional cylindrical Richtmyer–Meshkov instability. Physics of Fluids, 21 (11). Art. No. 114103. ISSN 1070-6631.

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We first study the linear stability of an interface between two fluids following the passage of an imploding or exploding shock wave. Assuming incompressible flow between the refracted waves following shock impact, we derive an expression for the asymptotic growth rate for a three-dimensional combination of azimuthal and axial perturbations as a function of the Atwood ratio, the axial and azimuthal wave numbers, the initial radial position and perturbation amplitude of the interface, and the interface velocity gain due to the shock interaction. From the linearized theory, a unified expression for the impulsive asymptotic growth rate in plane, cylindrical, and spherical geometries is obtained which clearly delineates the effects of perturbation growth due to both geometry and baroclinic vorticity deposition. Several different limit cases are investigated, allowing recovery of Mikaelian's purely azimuthal theory and Richtmyer's plane model. We discuss the existence of three-dimensional perturbations with zero growth, typical of curvilinear geometries, as first observed by Mikaelian. The effect of shock proximity on the interface growth rate is studied in the case of a reflected shock. Analytical predictions of the effect of the incident shock strength and the perturbation wave numbers are then compared with results obtained from highly resolved numerical simulations of cylindrical imploding Richtmyer–Meshkov instability for ideal gases. A parallel is made with the instability growth in spherical and plane geometry. In particular, we propose a representation of the perturbation growth by considering the volume of the perturbed layer. This volume is found to grow faster in the plane case than in the imploding cylindrical geometry, among other results.

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Additional Information:© 2009 American Institute of Physics. Received 13 May 2009; accepted 8 September 2009; published 6 November 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).
Funding AgencyGrant Number
Department of EnergyB341492
Department of EnergyW-7405-ENG-48
Subject Keywords:flow instability, shock waves
Issue or Number:11
Classification Code:PACS: 47.20.-k; 47.40.Nm.
Record Number:CaltechAUTHORS:20100120-131115012
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Official Citation:Small-amplitude perturbations in the three-dimensional cylindrical Richtmyer--Meshkov instability M. Lombardini and D. I. Pullin, Phys. Fluids 21, 114103 (2009), DOI:10.1063/1.3258668
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:17246
Deposited By: Tony Diaz
Deposited On:29 Jan 2010 00:04
Last Modified:03 Oct 2019 01:25

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