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Nonlinear behaviour of convergent Richtmyer–Meshkov instability

Published online by Cambridge University Press:  19 August 2019

Xisheng Luo
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
Ming Li
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
Juchun Ding*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
Zhigang Zhai
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
Ting Si
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
*
Email address for correspondence: djc@ustc.edu.cn

Abstract

A novel shock tube is designed to investigate the nonlinear feature of convergent Richtmyer–Meshkov instability on a single-mode interface formed by a soap film technique. The shock tube employs a concave–oblique–convex wall profile which first transforms a planar shock into a cylindrical arc, then gradually strengthens the cylindrical shock along the oblique wall, and finally converts it back into a planar one. Therefore, the new facility can realize analysis on compressibility and nonlinearity of convergent Richtmyer–Meshkov instability by eliminating the interface deceleration and reshock. Five sinusoidal $\text{air}{-}\text{SF}_{6}$ interfaces with different amplitudes and wavelengths are considered. For all cases, the perturbation amplitude experiences a linear growth much longer than that in the planar geometry. A compressible linear model is derived by considering a constant uniform fluid compression, which shows a slight difference to the incompressible theory. However, both the linear models overestimate the perturbation growth from a very early stage due to the presence of strong nonlinearity. The nonlinear model of Wang et al. (Phys. Plasmas, vol. 22, 2015, 082702) is demonstrated to predict well the amplitude growth up to a normalized time of 1.0. The prolongation of the linear increment is mainly ascribed to the counteraction between the promotion by geometric convergence and the suppression by nonlinearity. Growths of the first three harmonics, obtained by a Fourier analysis of the interface contour, provide a first thorough validation of the nonlinear theory.

Type
JFM Papers
Copyright
© 2019 Cambridge University Press 

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