×

Small amplitude theory of Richtmyer-Meshkov instability. (English) Zbl 0831.76040

When a shock wave collides with the interface between two different materials, small perturbations at this interface grow into nonlinear structures having the form of “bubbles” and “spikes”. The occurrence of this shock induced instability was predicted by Richtmyer and confirmed in subsequent experiments by Meshkov. This paper presents a new analysis of small amplitude Richtmeyr-Meshkov instability. The linear theory of reflected rarefaction waves is formulated and numerically treated. Additional results include the formulation of criteria determining the reflected wave type in terms of preshocked quantities, identification of parameter regimes corresponding to total transmission of the incident wave, discussion of an instability associated with a rarefaction wave, investigation of phase inversions and the related phenomenon of freeze-out, and the study of sensitivity of numerical solutions to initial conditions.

MSC:

76L05 Shock waves and blast waves in fluid mechanics
76E99 Hydrodynamic stability
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1002/cpa.3160130207 · doi:10.1002/cpa.3160130207
[2] Meshkov E. E., NASA Tech. Trans., NASA TT 13 pp 074– (1970)
[3] DOI: 10.1103/PhysRevLett.71.3473 · doi:10.1103/PhysRevLett.71.3473
[4] DOI: 10.1103/RevModPhys.61.75 · Zbl 1129.35439 · doi:10.1103/RevModPhys.61.75
[5] DOI: 10.1016/0021-9991(85)90146-9 · Zbl 0581.76079 · doi:10.1016/0021-9991(85)90146-9
[6] DOI: 10.1017/S0022112089000170 · Zbl 0662.76090 · doi:10.1017/S0022112089000170
[7] DOI: 10.1017/S0022112091001623 · doi:10.1017/S0022112091001623
[8] DOI: 10.1063/1.1693980 · doi:10.1063/1.1693980
[9] DOI: 10.1063/1.865722 · Zbl 0592.76091 · doi:10.1063/1.865722
[10] Samtaney R., Bull. Am. Phys. Soc. 37 (1992)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.