A generalized Langevin model for turbulent flows

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Abstract
A Langevin model appropriate to constant property turbulent flows is developed from the general equation for the fluid particle velocity increment proposed by Pope in an earlier paper [Phys. Fluids 26, 404 (1983)]. This model can be viewed as an analogy between the turbulent velocity of a fluid particle and the velocity of a particle undergoing Brownian motion. It is consistent with Kolmogorov’s inertial range scaling, satisfies realizability, and is consistent with second-order closure models. The objective of the present work is to determine the form of a second-order tensor appearing in the general model equation as a function of local mean quantities. While the model is not restricted to homogeneous turbulence, the second-order tensor is evaluated by considering the evolution of the Reynolds stresses in homogeneous flows. A functional form for the tensor is chosen that is linear in the normalized anisotropy tensor and in the mean velocity gradients. The resulting coefficients are evaluated by matching the modeled Reynolds stress evolution to experimental data in homogeneous flows. Constraints are applied to ensure consistency with rapid distortion theory and to satisfy a consistency condition in the limit of two-dimensional turbulence. A set of coefficients is presented for which the model yields good agreement with available data in homogeneous flows.