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Scaling Exponents in Anisotropic Hydrodynamic Turbulence

Victor S. L'vov·Itamar Procaccia·Vasil Tiberkevich
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Abstract

In anisotropic turbulence the correlation functions are decomposed in the irreducible representations of the SO(3) symmetry group (with different "angular momenta" $\ell$). For different values of $\ell$ the second order correlation function is characterized by different scaling exponents $ζ_2(\ell)$. In this paper we compute these scaling exponents in a Direct Interaction Approximation (DIA). By linearizing the DIA equations in small anisotropy we set up a linear operator and find its zero-modes in the inertial interval of scales. Thus the scaling exponents in each $\ell$-sector follow from solvability condition, and are not determined by dimensional analysis. The main result of our calculation is that the scaling exponents $ζ_2(\ell)$ form a strictly increasing spectrum at least until $\ell=6$, guaranteeing that the effects of anisotropy decay as power laws when the scale of observation diminishes. The results of our calculations are compared to available experiments and simulations.

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Victor S. L'vov, Itamar Procaccia, Vasil Tiberkevich. 2002-07-08. Scaling Exponents in Anisotropic Hydrodynamic Turbulence. https://doi.org/10.1103/physreve.67.026312

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