Abstract
The scaling behavior of the SO(3) irreducible amplitudes \(d_n^1 (r)\) 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.
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Grossmann, S., Lohse, D. & Reeh, A. Scaling of the Irreducible SO(3)-Invariants of Velocity Correlations in Turbulence. Journal of Statistical Physics 93, 715–724 (1998). https://doi.org/10.1023/B:JOSS.0000033250.57019.46
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DOI: https://doi.org/10.1023/B:JOSS.0000033250.57019.46