title: 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" l). For different values of l, the second-order correlation function is characterized by different scaling exponents zeta(2)(l). In this paper, we compute these scaling exponents in a closure approximation. By linearizing the closure 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 l 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)(l) form a strictly increasing spectrum at least until l=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.
authors.affiliation: Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel.
authors.forename: Victor S
authors.initials: VS
authors.lastname: L'vov
authors.forename: Itamar
authors.initials: I
authors.lastname: Procaccia
authors.forename: Vasil
authors.initials: V
authors.lastname: Tiberkevich