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Shock tube experiments and numerical simulation of the single-mode, three-dimensional Richtmyer–Meshkov instability
A vertical shock tube is used to perform experiments in which an interface is formed using opposed flows of air and SF6. A three-dimensional single-mode perturbation is created by the periodic vertica...

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

Phys. Fluids 21, 114103 (2009); doi:10.1063/1.3258668

Published 6 November 2009

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M. Lombardini and D. I. Pullin
Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, California 91125, USA
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. ©2009 American Institute of Physics
History: Received 13 May 2009; accepted 8 September 2009; published 6 November 2009
Permalink: http://link.aip.org/link/?PHFLE6/21/114103/1
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KEYWORDS and PACS

Keywords
PACS
  • 47.20.-k
    Flow instabilities
  • 47.40.Nm
    Shock-wave interactions and shock effects
  • YEAR: 2009

PUBLICATION DATA

ISSN:
1070-6631 (print)   1089-7666 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (32)
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