Toward analytic theory of the Rayleigh–Taylor instability: lessons from a toy model. (12th May 2017)

• Record Type: Journal Article
• Authors: Mailybaev, Alexei A
• Is Part Of: Nonlinearity. Volume 30:Number 6(2017:Jun.)
• Page Start: 2466
• Page End: 2484
• Publication Date: 2017-05-12
• Subjects: Rayleigh–Taylor instability -- turbulence -- spontaneous stochasticity -- chaos -- renormalization; 76F20 -- 76F35 -- 76F55; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aa6eb5
• Languages: English
• ISSNs: 0951-7715

Abstract

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.