Rayleigh-Taylor turbulence with singular nonuniform initial conditions

Abstract

We perform direct numerical simulations of three dimensional Rayleigh-Taylor turbulence with a nonuniform singular initial temperature background. In such conditions, the mixing layer evolves under the driving of a varying effective Atwood number; the long-time growth is still self-similar, but not anymore proportional to $t^2$ and depends on the singularity exponent $c$ of the initial profile $\Delta T\propto z^c$. We show that the universality is recovered when looking at the efficiency, defined as the ratio of the variation rates of the kinetic energy over the heat flux. A closure model is proposed that is able to reproduce analytically the time evolution of the mean temperature profiles, in excellent agreement with the numerical results. Finally, we reinterpret our findings in the light of spontaneous stochasticity where the growth of the mixing layer is mapped into the propagation of a wave of turbulent fluctuations on a rough background.

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Cited by in corpus (11)

• From the butterfly effect to intrinsic randomness: the spontaneous growth of singular shear flows
• A Renormalization Group Approach to Spontaneous Stochasticity
• Hidden spatiotemporal symmetries and intermittency in turbulence
• Experimental assessment of mixing layer scaling laws in Rayleigh-Taylor instability
• Spontaneous stochasticity and renormalization group in discrete multi-scale dynamics
• Statistical determinism in non-Lipschitz dynamical systems
• Immiscible Rayleigh-Taylor turbulence using mesoscopic lattice Boltzmann algorithms
• RG analysis of spontaneous stochasticity on a fractal lattice: stability and bifurcations
• Validation and application of the lattice Boltzmann algorithm for a turbulent immiscible Rayleigh-Taylor system
• RG approach to the inviscid limit for shell models of turbulence
• "Life after death" in ordinary differential equations with a non-Lipschitz singularity