Kolmogorov similarity scaling for one-particle Lagrangian statistics

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We use direct numerical simulation data up to a Taylor scale Reynolds number Rλ = 1000 to investigate Kolmogorov similarity scaling in the inertial sub-range for one-particle Lagrangian statistics. Although similarity scaling is not achieved at these Reynolds numbers for the Lagrangian velocity structure function, we show clearly that it is achieved for the Lagrangian acceleration frequency spectrum and the scaling range becomes wider with increasing Reynolds number. Stochastic and heuristic model calculations suggest that the difference in behavior observed for the structure function and spectrum is simply a consequence of different rates of convergence to scaling behavior with increasing Reynolds number. Our estimate C0 ≈ 6.9 ± 0.2 for the Lagrangian structure function constant is close to earlier estimates based on extrapolation of the peak value of the compensated structure function. The results presented here suggest prospects for studying Kolmogorov similarity for Lagrangian statistics using the latest innovations in simulation, and measurement techniques are more hopeful than previously suggested in the literature.