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Nonlinear evolution of the Richtmyer–Meshkov instability

Published online by Cambridge University Press:  10 October 2008

MARCUS HERRMANN ,
PARVIZ MOIN  and
SNEZHANA I. ABARZHI
MARCUS HERRMANN
Affiliation:
Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ, USA
PARVIZ MOIN
Affiliation:
Center for Turbulence Research, Stanford, CA, USA
SNEZHANA I. ABARZHI*
Affiliation:
The University of Chicago and Illinois Institute of Technology, Chicago, IL, USA
*
†Author to whom correspondence should be addressed: [email protected]
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Abstract

We report analytical and numerical results describing the dynamics of the two-dimensional coherent structure of bubbles and spikes in the Richtmyer–Meshkov instability for fluids with a finite density ratio. The theory accounts for the non-local properties of the interface evolution, and the simulations treat the interface as a discontinuity. Good agreement between the analytical and numerical results is achieved. To quantify accurately the interface dynamics in the simulations, new diagnostics and scalings are suggested. The velocity at which the interface would move if it were ideally planar is used to set the flow time scale as well as the reference point for the bubble (spike) position. The data sampling has high temporal resolution and captures the velocity oscillations caused by sound waves. The bubble velocity and curvature are both monitored, and the bubble curvature is shown to be the relevant diagnostic parameter. According to the results obtained, in the nonlinear regime of the Richtmyer–Meshkov instability the bubbles flatten and decelerate, and the flattening of the bubble front indicates the multiscale character of the coherent dynamics.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 612 , 10 October 2008 , pp. 311 - 338
Copyright
Copyright © Cambridge University Press 2008

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References

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