Scaling of the irreducible SO(3)-invariants of velocity correlations in turbulence

Abstract

The scaling behavior of the SO(3) irreducible amplitudes $d_n^l(r)$ of velocity structure tensors (see L'vov, Podivilov, and Procaccia, Phys. Rev. Lett. (1997)) is numerically examined for Navier-Stokes turbulence. Here, l characterizes the irreducible representation by the index of the corresponding Legendre polynomial, and n denotes the tensorial rank, i.e., the order of the moment. For moments of different order n but with the same representation index l extended self similarity (ESS) towards large scales is found. Intermittency seems to increase with l. We estimate that a crossover behavior between different inertial subrange scaling regimes in the longitudinal and transversal structure functions will hardly be detectable for achievable Reynolds numbers.