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Efficient perturbation methods for Richtmyer–Meshkov and Rayleigh–Taylor instabilities: Weakly nonlinear stage and beyond

Published online by Cambridge University Press:  03 March 2004

M. VANDENBOOMGAERDE
Affiliation:
Commissariat à l'Energie Atomique, Bruyères-Le-Châtel, France
C. CHERFILS
Affiliation:
Commissariat à l'Energie Atomique, Bruyères-Le-Châtel, France
D. GALMICHE
Affiliation:
Commissariat à l'Energie Atomique, Bruyères-Le-Châtel, France
S. GAUTHIER
Affiliation:
Commissariat à l'Energie Atomique, Bruyères-Le-Châtel, France
P.A. RAVIART
Affiliation:
Université Pierre et Marie Curie, Paris, France

Abstract

The simplified perturbation method of Vandenboomgaerde et al. (2002) is applied to both the Richtmyer–Meshkov and the Rayleigh–Taylor instabilities. This theory is devoted to the calculus of the growth rate of the perturbation of the interface in the weakly nonlinear stage. In the standard approach, expansions appear to be series in time. We build accurate approximations by retaining only the terms with the highest power in time. This simplifies and accelerates the solution. High order expressions are then easily reachable. For the Richtmyer–Meshkov instability, multimode configurations become tractable and the selection mode process can be studied. Inferences for the intermediate nonlinear regime are also proposed. In particular, a class of homothetic configurations is inferred; its validity is verified with numerical simulations even as vortex structures appear at the interface. This kind of method can also be used for the Rayleigh–Taylor instability. Some examples are presented.

Type
Research Article
Copyright
© 2003 Cambridge University Press

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