Reynolds number effects on the single-mode Richtmyer-Meshkov instability

The Reynolds number effects on the nonlinear growth rates of the Richtmyer-Meshkov instability are investigated using two-dimensional numerical simulations. A decrease in Reynolds number gives an increased time to reach nonlinear saturation, with Reynolds number effects only significant in the range $\text{Re}<256$. Within this range there is a sharp change in instability properties. The bubble and spike amplitudes move towards equal size at lower Reynolds numbers and the bubble velocities decay faster than predicted by Sohn's model [S.-I. Sohn, Phys. Rev. E 80, 055302 (2009)]. Predicted amplitudes show reasonable agreement with the existing theory of Carles and Popinet [P. Carles and S. Popinet, Phys. Fluids Lett. 13, 1833 (2001); Eur. J. Mech. B 21, 511 (2002)] and Mikaelian [K. O. Mikaelian, Phys. Rev. E 47, 375 (1993); K. O. Mikaelian, Phys. Rev. E 87, 031003 (2013)], with the former being the closest match to the current computations.

Figure 1

Grid convergence of layer width $x_{\mathrm{bubble}}-x_{\mathrm{spike}}$ for $\text{Re}=20$.

Figure 2

Visualization volume fraction for the single-mode case for a range of Reynolds numbers.

Figure 3

Amplitude (left) and velocity (right) for $\text{Re}=128$ and various initial amplitudes.

Figure 4

Bubble and spike amplitudes for various Reynolds number cases: (a) $\text{Re}=8$, (b) $\text{Re}=16$, (c) $\text{Re}=32$, and (d) $\text{Re}=128$.

Figure 5

Spike-to-bubble ratio for ${\eta }_0=0.1\pi$ (left) and ${\eta }_0=0.01\pi$ (right).

Figure 6

Layer center and extremes of the layer for $\text{Re}=8$, where the upper extreme is on the spike side and the lower extreme is on the bubble side.

Figure 7

Bubble velocity comparison with the theoretical model of Sohn.

Figure 8

Comparison of layer amplitude (black) and bubble (gray) amplitude against the theoretical models of Mikaelian [18] and Carles and Popinet [19].

Figure 9

Saturation time as a function of Reynolds number