Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-10T12:33:47.769Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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