Shock Waves

, Volume 29, Issue 2, pp 263–271 | Cite as

Richtmyer–Meshkov instability of a sinusoidal interface driven by a cylindrical shock

  • L. Liu
  • J. DingEmail author
  • Z. Zhai
  • X. Luo
Original Article


Evolution of a single-mode interface triggered by a cylindrically converging shock in a V-shaped geometry is investigated numerically using an adaptive multi-phase solver. Several physical mechanisms, including the Bell–Plesset (BP) effect, the Rayleigh–Taylor (RT) effect, the nonlinearity, and the compressibility are found to be pronounced in the converging environment. Generally, the BP and nonlinear effects play an important role at early stages, while the RT effect and the compressibility dominate the late-stage evolution. Four sinusoidal interfaces with different initial amplitudes (\(a_\mathrm {0}\)) and wavelengths (\(\lambda \)) are found to evolve differently in the converging geometry. For the very small \(a_\mathrm {0}\)/\(\lambda \) interfaces, nonlinearity is negligible at the early stages and the sole presence of the BP effect results in an increasing growth rate, confining the linear growth of the instability to a relatively small amount of time. For the moderately small \(a_\mathrm {0}\)/\(\lambda \) cases, the BP and nonlinear effects, which, respectively, promote and inhibit the perturbation development, coexist in the early stage. The counterbalancing effects between them produce a very long period of growth that is linear in time, even to a moment when the amplitude over wavelength ratio approaches 0.6. The RT stabilization effect at late stages due to the interface deceleration significantly inhibits the perturbation growth, which can be reasonably predicted by a modified Bell model.


Richtmyer–Meshkov instability Cylindrical shock wave Single-mode interface Convergence effect 



This work was supported by the China Postdoctoral Science Foundation (Grant No. 2016M602026), National Natural Science Foundation of China (Grant Nos. 11625211, 11621202, and NSAF U1530103) and the Fundamental Research Funds for the Central Universities.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Advanced Propulsion Laboratory, Department of Modern MechanicsUniversity of Science and Technology of ChinaHefeiChina

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