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Shock-tube studies of single- and quasi-single-mode perturbation growth in Richtmyer–Meshkov flows with reshock

Published online by Cambridge University Press:  10 May 2022

Xu Guo Open the ORCID record for Xu Guo [Opens in a new window] ,
Zhouyang Cong ,
Ting Si Open the ORCID record for Ting Si [Opens in a new window]  and
Xisheng Luo Open the ORCID record for Xisheng Luo [Opens in a new window]
Xu Guo
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Zhouyang Cong
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Ting Si*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Xisheng Luo
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
*
†Email address for correspondence: tsi@ustc.edu.cn
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Abstract

The Richtmyer–Meshkov instability of heavy/light single-mode (SM), trapezoid (TR) and sawtooth (ST) interfaces is studied experimentally by considering the reshock. The TR and ST interfaces can be expanded into Fourier series with a dominant fundamental mode and more high-order modes, recognized as quasi-single-mode ones. In experiments, the distorted interfaces at the time of first reshock arrival develop in the weakly nonlinear stage, ensuring an approximate single-scale function of evolving interface. The results show an evident memory of initial interface shapes: the bubbles and spikes of ST interface after reshock mainly develop in the streamwise direction with sharp heads, while the counterparts of TR interface tend to grow in the spanwise direction. The influences of high-order modes are amplified by the reshock, resulting in significant interface shape dependence of mixing width growths. The amplitude superposition of major odd-order modes promotes the growth rates of mixing widths for the SM and ST cases, different from the TR one. The ST interface has larger mixing width growth rates in comparison with the SM interface, since high-order modes play a great role in promoting the increase of ST amplitudes, while the TR interface has a relatively small one. The linear and nonlinear mixing width growths of SM, TR and ST interfaces before and after reshock are further analysed theoretically, indicating that the fundamental mode still has a predominant influence on the interface evolution after reshock, and the growth behaviours exhibit strong similarities to those for the singly shocked cases.

JFM classification

Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 941 , 25 June 2022 , A65
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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