Suppression of Rayleigh-Taylor turbulence by time-periodic acceleration

The dynamics of Rayleigh-Taylor turbulence convection in the presence of an alternating, time-periodic acceleration is studied by means of extensive direct numerical simulations of the Boussinesq equations. Within this framework, we discover a mechanism of relaminarization of turbulence: the alternating acceleration, which initially produces a growing turbulent mixing layer, at longer times suppresses turbulent fluctuation and drives the system toward an asymptotic stationary configuration. Dimensional arguments and linear stability theory are used to predict the width of the mixing layer in the asymptotic state as a function of the period of the acceleration.

Figure 1

Vertical sections of size $L_x\times L_z$ of the temperature field (yellow hot, blue cold) for Rayleigh-Taylor turbulence in periodic acceleration of period $T=3\tau$ at times $t=1.5T$ (left), $t=4T$ (center), and $t=10T$ (right). Simulation at resolution $M=512$.

Figure 2

rms of the vertical velocity component in the mixing layer, made dimensionless with $U=A{g}_0\tau$, as a function of dimensionless time for the case of period $T=\tau$. Inset: the same quantity for the case of period $T=3\tau$ with gray (white) regions representing the unstable (stable) phase. Simulations with $M=512$.

Figure 3

(a) Evolution of the width of the mixing layer for four simulations at resolution $M=512$ starting from the same set of initial conditions with different periods of the acceleration: $T=\infty$ (black dot-dashed line), $T=2\tau$ (red dotted line), $T=3\tau$ (blue dashed line), and $T=4\tau$ (green continuous line). The dot-dot-dashed light blue line represents the case $T=3\tau$ for resolution $M=256$ with larger viscosity. (b) The same data plotted by rescaling time with the period $T$ and space with $A{g}_0{T}^2$, with ensemble rms (shadow area).

Figure 4

(a) Mean temperature profile $\langle \theta \rangle$ for the simulation with period $T=3\tau$ at times $t=1.5T$ (red continuous line), $t=3T$ (blue dashed line), $t=6T$ (green dotted line), $t=8T$ (magenta dot-dashed line), and $t=10T$ (black full line). (b) Temperature standard deviation $\sigma$ for the simulation with period $T=3\tau$ at times $t=6T$ (green dotted line), $t=8T$ (magenta dot-dashed line), and $t=10T$ (black full line). Simulations with $M=512$.

Figure 5

Time evolution of the Nusselt number for the case $T=2\tau$. Inset: time evolution of the correlation $C(w,\theta )=\langle w\theta \rangle /\left(w_{\text{rms}}{\theta }_{\text{rms}}\right)$. Simulations with $M=512$.