A Conditionally Cubic-Gaussian Stochastic Lagrangian Model for   Acceleration in Isotropic Turbulence
  The modelling of fluid particle accelerations in homogeneous, isotropic turbulence in terms of second-order stochastic models for the Lagrangian velocity is considered. The basis for the Reynolds model (A. M. Reynolds, \textit{Phys. Rev. Lett.} $\mathbf{91}(8)$, 084503 (2003)) is reviewed and examined by reference to DNS data. In particular, we show DNS data that support stochastic modelling of the logarithm of pseudo-dissipation as an Ornstein-Uhlenbeck process (Pope and Chen 1990) and reveal non-Gaussianity of the conditional acceleration PDF. The DNS data are used to construct a simple stochastic model that is exactly consistent with Gaussian velocity and conditionally cubic-Gaussian acceleration statistics. This model captures the effects of intermittency of dissipation on acceleration and the conditional dependence of acceleration on pseudo-dissipation (which differs from that predicted by the refined Kolmogorov (1962) hypotheses). Non-Gaussianity of the conditional acceleration PDF is accounted for in terms of model nonlinearity. The diffusion coefficient for the new model is chosen based on DNS data for conditional two-time velocity statistics. The resulting model predictions for conditional and unconditional velocity statistics and timescales are shown to be in good agreement with DNS data. 
A.G. Lamorgese, S.B. Pope, P.K. Yeung and B. L. Sawford