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A Conditionally Cubic-Gaussian Stochastic Lagrangian Model for Acceleration in Isotropic Turbulence

A. G. Lamorgese·S. B. Pope·P. K. Yeung·B. L. Sawford
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Abstract

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.

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A. G. Lamorgese, S. B. Pope, P. K. Yeung, B. L. Sawford. 2005-12-09. A Conditionally Cubic-Gaussian Stochastic Lagrangian Model for Acceleration in Isotropic Turbulence. https://arxiv.org/abs/cond-mat/0512212

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