A stochastic Lagrangian model for acceleration in turbulent flows

A stochastic model is developed for the acceleration of a fluid particle in anisotropic and inhomogeneous turbulent flows. The model consists of an ordinary differential equation for velocity (which contains directly the acceleration due to the mean and rapid pressure gradients), and a stochastic model for the remainder of the acceleration, which is due to the slow pressure gradient and to viscosity. In addition to a rapid-pressure model, the stochastic model involves three tensor coefficients, For isotropic turbulence, the model reverts to that previously proposed by Sawford. At high Reynolds number the model is consistent with local isotropy and the Kolmogorov hypotheses, and tends to the generalized Langevin model for fluid-particle velocity. In this case two of the tensor coefficients are known in terms of the Kolmogorov constant C-o, while the third is related to the coefficient in the generalized Langevin model. A complete analysis of the model is performed for homogeneous turbulent shear flow, for which there are Lagrangian data from direct numerical simulations. The main result is to establish the one-to-one correspondence between the model coefficients and the primary statistics, namely. the velocity and acceleration covariances and the tensor of velocity integral time scales. The autocovariances of velocity and acceleration obtained from the model are in excellent agreement with the direct numerical simulation (DNS) data. Future DNS studies of homogeneous turbulence can be used to investigate the dependence of the model coefficients on Reynolds number and on the imposed mean velocity gradients. The acceleration model can be used to generate a range of turbulence models which. in a natural way, incorporate Reynolds-number effects. (C) 2002 American Institute of Physics.