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Nonlinear analytic growth rate of a single-mode Richtmyer–Meshkov instability

Published online by Cambridge University Press:  03 March 2004

M. VANDENBOOMGAERDE
M. VANDENBOOMGAERDE
Affiliation:
Commissariat à l'Energie Atomique, Bruyères-Le-Châtel, France
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Abstract

A perturbation method in which only the most secular terms are retained gives simple results for the weakly nonlinear growth of a single-mode shock-accelerated interface (Vandenboomgaerde et al., 2002). This result can be written as a series in integer powers of time. It can be considered as the Taylor expansion of an analytic function. We believe that an approximation of such a function has been identified; it described the evolution of the instability from linear to intermediate nonlinear regime. Furthermore, this function has no singularity. The relevance of this analytic formula is checked against two-dimensional simulations and experimental data.

Keywords

InstabilityNonlinearRichtmyer–MeshkovTheory

Information

Type
Research Article
Information
Laser and Particle Beams , Volume 21 , Issue 3 , July 2003 , pp. 317 - 319
Copyright
© 2003 Cambridge University Press

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References

REFERENCES

Holyer, J.Y. (1979). Large amplitude progressive interfacial waves. J. Fluid Mech. 93, 433–448.CrossRefGoogle Scholar
Jacobs, J.W., & Krivets, V.V. (2001). PLIF flow visualization of the nonlinear development and transition to turbulence of the Richtmyer–Meshkov instability. Proc. 23th Int. Symp. Shock Wave, 22–27 July 2001, Fort Worth, TX, USA.
Mügler, C., & Gauthier, S. (2000). Two-dimensional Navier–Stokes simulations of gaseous mixtures induced by Richtmyer–Meshkov instability. Phys. Fluids 12, 1783.Google Scholar
Mügler, C., Hallo, L., Gauthier, S., & Aubert, S. (1996). Validation of an ALE Godunov algorithm for solutions of the two-species Navier–Stokes equations. Proc. 27th Fluid Dyn. Conf., New Orleans, LA, 17–20 June (1996), AIAA Paper 96-2068: American Institute for Aeronautics and Astronautics.
Prasad, J.K., Rasheed, A., Kumar, S., & Sturtevant B. (2000). The late-time development of the Richtmyer–Meshkov instability. Phys. Fluids 12, 2108–2115.CrossRefGoogle Scholar
Vandenboomgaerde, M., Gauthier, S., & Mugler, C. (2002). Nonlinear regime of a multimode Richtmyer–Meshkov instability: A simplified perturbation theory. Phys. Fluids 14, 1111–1122.CrossRefGoogle Scholar
Zhang, Q., & Sohn, S.-I. (1997). Nonlinear theory of unstable fluid mixing driven by shock wave. Phys. Fluids 9, 1106–1124.CrossRefGoogle Scholar