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Richtmyer–Meshkov instability on two-dimensional multi-mode interfaces

Published online by Cambridge University Press:  15 October 2021

Yu Liang
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei230026, PR China NYUAD Research Institute, New York University Abu Dhabi, Abu Dhabi129188, UAE
Lili Liu
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei230026, PR China
Zhigang Zhai*
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei230026, PR China
Juchun Ding
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei230026, PR China
Ting Si
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei230026, PR China
Xisheng Luo*
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei230026, PR China
*
Email addresses for correspondence: sanjing@ustc.edu.cn, xluo@ustc.edu.cn
Email addresses for correspondence: sanjing@ustc.edu.cn, xluo@ustc.edu.cn

Abstract

Shock-tube experiments on eight kinds of two-dimensional multi-mode air–SF$_6$ interface with controllable initial conditions are performed to examine the dependence of perturbation growth on initial spectra. We deduce and demonstrate experimentally that the amplitude development of each mode is influenced by the mode-competition effect from quasi-linear stages. It is confirmed that the mode-competition effect is closely related to initial spectra, including the wavenumber, the phase and the initial amplitude of constituent modes. By considering both the mode-competition effect and the high-order harmonics effect, a nonlinear model is established based on initial spectra to predict the amplitude growth of each individual mode. The nonlinear model is validated by the present experiments and data in the literature by considering diverse initial spectra, shock intensities and density ratios. Moreover, the nonlinear model is successfully extended based on the superposition principle to predict the growths of the total perturbation width and the bubble/spike width from quasi-linear to nonlinear stages.

Type
JFM Papers
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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