Anomalous Scaling from Controlled Closure in a Shell Model of Turbulence

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dc.creatorL'vov, Victor S.
dc.creatorPierotti, Daniela
dc.creatorPomyalov, Anna
dc.creatorProcaccia, Itamar
dc.date1998-10-15
dc.date.accessioned2026-07-25T13:54:05Z
dc.descriptionWe present a model of hydrodynamic turbulence for which the program of computing the scaling exponents from first principles can be developed in a controlled fashion. The model consists of $N$ suitably coupled copies of the "Sabra" shell model of turbulence. The couplings are chosen to include two components: random and deterministic, with a relative importance that is characterized by a parameter called $ε$. It is demonstrated, using numerical simulations of up to 25 copies and 28 shells that in the $N\to \infty$ limit but for $0<ε\le 1$ this model exhibits correlation functions whose scaling exponents are anomalous. The theoretical calculation of the scaling exponents follows verbatim the closure procedure suggested recently for the Navier-Stokes problem, with the additional advantage that in the $N\to \infty$ limit the parameter $ε$ can be used to regularize the closure procedure. The main result of this paper is a finite and closed set of scale-invariant equations for the 2nd and 3rd order statistical objects of the theory. This set of equations takes into account terms up to order $ε^4$ and neglects terms of order $ε^6$. Preliminary analysis of this set of equations indicates a K41 normal scaling at $ε= 0 $, with a birth of anomalous exponents at larger values of $ε$, in agreement with the numerical simulations.
dc.descriptionPhys. Fluids, special issue in the honour of R.H. Kraichnan, submitted, REVTex, 22 pages, 15 eps figures
dc.identifierhttps://arxiv.org/abs/chao-dyn/9810021
dc.identifierhttp://arxiv.org/abs/chao-dyn/9810021
dc.identifier.urihttps://dspace.dare.co.zw/handle/123456789/21327
dc.subjectChaotic Dynamics
dc.titleAnomalous Scaling from Controlled Closure in a Shell Model of Turbulence
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