Retarding viscous Rayleigh-Taylor mixing by an optimized additional mode

The Rayleigh-Taylor (RT) mixing induced by random interface disturbances between two incompressible viscous fluids is simulated numerically. The ensemble averaged spike velocity is found to be remarkably retarded when the random interface disturbances are superimposed with an optimized additional mode. The mode's wavenumber is selected to be large enough to avoid enhancing the dominance of long-wavelength modes, but not so large that its saturated spike and bubble velocities are too small to stimulate a growing effective density-gradient layer suppressing the long-wavelength modes. Such an optimized suppressing mode is expected to be found in the RT mixing including other diffusion processes, e.g., concentration diffusion and thermal diffusion.

Figure 1

Temporal evolutions of the fluid interfaces disturbed initially by random perturbations with (blue) and without (red) a superimposed additional mode of wavenumber $n_a$.

Figure 2

Temporal evolutions of the ensemble-averaged values of the spike penetration $h_s$ (a) and the spike velocity (b) with and without the superposed additional modes. (c) The velocity suppression factor $\sigma$ as a function of the additional wavenumber $n_a$ at different times. The dashed vertical line in (c) represents the wavenumber of the most unstable linear viscous mode. (d) Temporal evolution of $h_s$ and $h_b$ for $n_a=35$ at different initial amplitude $a/L=0.01,0.02,0.04$, respectively.

Figure 3

Wavenumber dependence of the interface evolution for a single viscous RT mode. The bubble velocity and the spike velocity multiplied with $\sqrt{n}$ are compared with their inviscid saturated values $v_b\sqrt{n}=\sqrt{\frac{AL}{3\pi (1+A)}}=2.576$ and $v_s\sqrt{n}=\sqrt{\frac{AL}{3\pi (1-A)}}=5.593$ [27] shown by the dashed lines in (a) and (b), respectively. The temporal evolution of a viscous mode interface with a large wavenumber $n=60$ is shown in (f)–(h), and the results for the low-wavenumber mode with $n=5$ are shown in (c)–(e) as references.

Figure 4

The ensemble-averaged density spectra calculated at the midplane (the original interface) and different times for cases with (black) and without (red) the additional mode.