We 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 limit but for 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 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 and neglects terms of order Preliminary analysis of this set of equations indicates a K41 normal scaling at with a birth of anomalous exponents at larger values of ε, in agreement with the numerical simulations.
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April 2000
Research Article|
April 01 2000
Anomalous scaling from controlled closure in a shell model of turbulence
Victor S. L’vov;
Victor S. L’vov
Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
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Daniela Pierotti;
Daniela Pierotti
Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
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Anna Pomyalov;
Anna Pomyalov
Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
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Itamar Procaccia
Itamar Procaccia
Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
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Physics of Fluids 12, 803–821 (2000)
Article history
Received:
October 15 1998
Accepted:
December 09 1999
Citation
Victor S. L’vov, Daniela Pierotti, Anna Pomyalov, Itamar Procaccia; Anomalous scaling from controlled closure in a shell model of turbulence. Physics of Fluids 1 April 2000; 12 (4): 803–821. https://doi.org/10.1063/1.870337
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