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

The scaling behavior of the SO(3) irreducible amplitudes [..] of velocity structure tensors 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.