Toward analytic theory of the Rayleigh-Taylor instability: lessons from a toy model

Abstract

In this work we suggest that a turbulent phase of the Rayleigh-Taylor instability can be explained as a universal stochastic wave traveling with constant speed in a properly renormalized system. This wave, originating from ordinary deterministic chaos in a renormalized time, has two constant limiting states at both sides. These states are related to the initial discontinuity at large scales and to stationary turbulence at small scales. The theoretical analysis is confirmed with extensive numerical simulations made for a new shell model, which features basic properties of the phenomenological theory for the Rayleigh-Taylor instability.

22 pages

References in corpus (5)

• Spontaneously stochastic solutions in one-dimensional inviscid systems
• Spontaneous stochasticity of velocity in turbulence models
• Continuous representation for shell models of turbulence
• Bifurcations of blowup in inviscid shell models of convective turbulence
• Gibbsian Hypothesis in Turbulence

Cited by in corpus (8)

• From the butterfly effect to intrinsic randomness: the spontaneous growth of singular shear flows
• Rayleigh-Taylor turbulence with singular nonuniform initial conditions
• A Renormalization Group Approach to Spontaneous Stochasticity
• Spontaneous stochasticity and renormalization group in discrete multi-scale dynamics
• Statistical determinism in non-Lipschitz dynamical systems
• RG analysis of spontaneous stochasticity on a fractal lattice: stability and bifurcations
• RG approach to the inviscid limit for shell models of turbulence
• "Life after death" in ordinary differential equations with a non-Lipschitz singularity