2015/12/31 by Alexei A. Mailybaev · 2 citations
Physics and Astronomy · #physics.flu-dyn
paper · pdf · doi:10.1088/0951-7715/29/8/2238
published as Nonlinearity 29 (2016) 2238-2252
arxiv created 2016/06/28 · arxiv updated 2016/06/29
In this paper, we study the inviscid limit of the Sabra shell model of turbulence, which is considered as a particular case of a viscous conservation law in one space dimension with a nonlocal quadratic flux function. We present a theoretical argument (with a detailed numerical confirmation) showing that a classical deterministic solution before a finite-time blowup, t < tb, must be continued as a stochastic process after the blowup, t > tb, representing a unique physically relevant description in the inviscid limit. This theory is based on the dynamical system formulation written for the logarithmic time τ= log(t-tb), which features a stable traveling wave solution for the inviscid Burgers equation, but a stochastic traveling wave for the Sabra model. The latter describes a universal onset of stochasticity immediately after the blowup.