The microscopic-scale Richtmyer-Meshkov (RM) instability of a single-mode Cu-He interface subjected to a cylindrically converging shock is studied through the classical molecular dynamics simulation. An unperturbed interface is first considered to examine the flow features in the convergent geometry, and notable distortions at the circular inhomogeneity are observed due to the atomic fluctuation. Detailed processes of the shock propagation and interface deformation for the single-mode interface impacted by a converging shock are clearly captured. Different from the macroscopic-scale situation, the intense molecular thermal motions in the present microscale flow introduce massive small wavelength perturbations at the single-mode interface, which later significantly impede the formation of the roll-up structure. Influences of the initial conditions including the initial amplitude, wave number and density ratio on the instability growth are carefully analyzed. It is found that the late-stage instability development for interfaces with a large perturbation does not depend on its initial amplitude any more. Surprisingly, as the wave number increases from 8 to 12, the growth rate after the reshock drops gradually. The distinct behaviors induced by the amplitude and wave number increments indicate that the present microscopic RM instability cannot be simply characterized by the amplitude over wavelength ratio ($\eta$). The pressure history at the convergence center shows that the first pressure peak caused by the shock focusing is insensitive to $\eta$, while the second one depends heavily on it.
This work was supported by the China Postdoctoral Science Foundation (Grant No. 2016M602026), the National Natural Science Foundation of China (Grant Nos. 11625211, and 11621202), the Science Challenge Project (Grant No. TZ2016001) and the Fundamental Research Funds for the Central Universities.
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Figure 1
(Color online) Configuration of a cylindrical shock interacting with a sinusoidal Cu-He interface.
Figure 2
Temporal variation of the shock position for numerical and theoretical results.
Figure 3
(Color online) Representative atom distribution snapshots of the unperturbed Cu-He interface subjected to a cylindrical shock. ICS: incident cylindrical shock interface; IS: initial interface; RW: rarefaction wave; TS: transmitted shock; SI: shocked interface; RTS: reflected transmitted shock; STS, secondary transmitted shock.
Figure 4
(Color online) The $r$-$t$ diagram showing the cylindrical shock interaction with an unperturbed Cu-He interface. The symbols are the same as those in
Figure 5
(Color online) Atom distribution snapshots showing the single-mode Cu-He interface impacted by a cylindrical shock. The symbols are the same as those in
Figure 6
(Color online) The displacements of bubble and spike tips for the single-mode interface superposed with the unperturbed interface locus.
Figure 7
(Color online) The whole amplitude history (a) as well as the bubble and the spike developments (b) for different initial amplitude interfaces.
Figure 8
(Color online) The whole amplitude history (a) as well as the bubble and the spike developments (b) for different wave number interfaces.
Figure 9
(Color online) The whole amplitude history (a) as well as the bubble and the spike developments (b) for various He density cases.
Figure 10
(Color online) The pressure history at the geometry center for different initial amplitude interfaces.
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