Scaling Exponents in Anisotropic Hydrodynamic Turbulence

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 ${\zeta }_2(\ell )$. 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 ${\zeta }_2(\ell )$ 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.

10 pages, 4 figures, PRE submitted. Fixed problems with figures

References in corpus (1)

• Anisotropic Homogeneous Turbulence: hierarchy and intermittency of scaling exponents in the anisotropic sectors

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