Conditional and unconditional acceleration statistics in turbulence

In this paper we study acceleration statistics from laboratory measurements and direct numerical simulations in three-dimensional turbulence at Taylor-scale Reynolds numbers ranging from 38 to 1000. Using existing data, we show that at present it is not possible to infer the precise behavior of the unconditional acceleration variance in the large Reynolds number limit, since empirical functions satisfying both the Kolmogorov and refined Kolmogorov theories appear to fit the data equally well. We also present entirely new data for the acceleration covariance conditioned on the velocity, showing that these conditional statistics are strong functions of velocity, but that when scaled by the unconditional variance they are only weakly dependent on Reynolds number. For large values of the magnitude u of the conditioning velocity we speculate that the conditional covariance behaves like $u^6$ and show that this is qualitatively consistent with the stretched exponential tails of the unconditional acceleration probability density function (pdf). The conditional pdf is almost identical in shape to the unconditional pdf. From these conditional covariance data, we are able to calculate the conditional mean rate of change of the acceleration, and show that it is consistent with the drift term in second-order Lagrangian stochastic models of turbulent transport. We also calculate the correlation between the square of the acceleration and the square of the velocity, showing that it is small but not negligible.