Numerical study of initial perturbation effects on Richtmyer-Meshkov instability in nonuniform flows

The effects of an initial perturbation on Richtmyer-Meshkov instability are numerically studied by simulating the process of incident shock ($\mathrm{Ma}=1.27$) impacting different groups of initial multimode cosine interfaces formed by different amplitudes in initially nonuniform flows whose density is a Gaussian function. The numerical results indicate that the evolution of the interface with a large initial amplitude in a low-density nonuniform area grows fastest, while that with a small initial amplitude in a high-density nonuniform area grows slowly. Further analysis of vorticity and circulation illustrates these phenomena. The interface with a large initial amplitude in a low-density zone possesses a larger density gradient, which results in a larger amount of vorticity and circulation, leading to the fast-changing evolution of the interface. Distinctive evolution mechanisms of Richtmyer-Meshkov instability between the nonuniform flows and the uniform flows are analyzed in detail.

Figure 1

Initial structure diagram.

Figure 2

Density profiles of nonuniform flows with a Gaussian function and uniform flows in the vertical direction.

Figure 3

Density contour images of the numerical simulation result in a nonuniform Gaussian function flow without initial perturbation on the interface.

Figure 4

Density contour images of the numerical simulation result at $t=1\mathrm{ms}$ under different groups of initial amplitudes: (a) ($A_{01}=2.5\mathrm{mm}\text{−}{A}_{02}=7.5\mathrm{mm}$), (b) ($A_{01}=5.0\mathrm{mm}\text{−}{A}_{02}=7.5\mathrm{mm}$), (c) ($A_{01}=7.5\mathrm{mm}\text{−}{A}_{02}=7.5\mathrm{mm}$), and (d) ($A_{01}=7.5\mathrm{mm}\text{−}{A}_{02}=10.0\mathrm{mm}$). The left column shows low-density uniform flows; the middle column, high-density uniform flows; and the right column, nonuniform Gaussian function flows.

Figure 5

Density contour images of the numerical simulation result at $t=1.8\mathrm{ms}$ under different groups of initial amplitudes: (a) ($A_{01}=2.5\mathrm{mm}\text{−}{A}_{02}=7.5\mathrm{mm}$), (b) ($A_{01}=5.0\mathrm{mm}\text{−}{A}_{02}=7.5\mathrm{mm}$), (c) ($A_{01}=7.5\mathrm{mm}\text{−}{A}_{02}=7.5\mathrm{mm}$), (d) ($A_{01}=7.5\mathrm{mm}\text{−}{A}_{02}=10.0\mathrm{mm}$). The left column shows the low-density uniform flows; the middle column, high-density uniform flows; and the right column, nonuniform Gaussian function flows.

Figure 6

Perturbation amplitude of $A_0=7.5\mathrm{mm}$ initial amplitude with four other initial amplitudes: $A_0=2.5$ (solid line), 5.0 (dashed line), 7.5 (dash-dotted line), and 10.0 (dotted line) mm under four different flows: (a) low-density (black lines) zone and high-density [red (light gray) lines] zone in nonuniform flow and (b) low-density (black lines) zone and high-density [red (light gray) lines] zone in uniform flow.

Figure 7

Perturbation amplitudes of four different initial amplitudes: 2.5 (circles), 5 (triangles), 7.5 (squares), and 10 (diamonds) mm in (a) low- [red (light gray) lines] and high- (black lines) density zones of nonuniform flows and (b) low- [red (light gray) lines] and high- (black lines) density zones in uniform flows.

Figure 8

Average vorticity of S3 (spike trough) in the low-density zone of nonuniform flows with four different initial amplitudes: 2.5 (dashed line), 5 (dotted line), 7.5 (dash-dotted line), and 10 (solid line) mm at $t=1\mathrm{ms}$.

Figure 9

Average vorticity of four conditions: the spike trough in low-density zone of nonuniform flows S3 (dash line), the spike trough in high-density zone of nonuniform flows S1 (solid line), and the spike trough in low-density uniform flows (dash-dotted line) and high-density uniform flows (dotted line) with four initial amplitudes (a) 2.5, (b) 5, (c) 7.5, and (d) 10 mm at $t=1\mathrm{ms}$.

Figure 10

Total circulation over time with four different initial amplitudes: 0.0 [red (light gray) dash–double-dotted line], 2.5 (dashed line), 5 (dotted line), 7.5 (dash-dotted line), and 10 (solid line) mm in (a) the low-density zone and (b) the high-density zone of nonuniform flows.

Figure 11

Circulation over time in four conditions: the low-density zone of nonuniform flows (dashed line), the high-density zone of nonuniform flows (solid line), low-density uniform flows (dash-dotted line), and high-density uniform flows (dotted line) under four initial amplitudes: (a) 7.5 mm, (b) 2.5 mm (black lines) and 0.0 mm [red (light gray) lines], (c) 5 mm (black lines) and 0.0 mm [red (light gray) lines], (d) 7.5 mm (black lines) and 0.0 mm [red (light gray) lines], and (e) 10 mm (black lines) and 0.0 mm [red (light gray) lines].