Lagrangian statistics in uniform shear flow: Direct numerical simulation and Lagrangian stochastic models

Direct numerical simulation calculations of Lagrangian statistics for homog eneous turbulence in uniform shear flow are used to test the performance of two different Lagrangian stochastic models of turbulent dispersion. These two models differ in their representation of Eulerian acceleration statisti cs. In particular one of the models imparts an excessively large mean rotat ion to the trajectories in the plane of the shear, while the other is nonro tational. We show that this rotation degrades the model's prediction of Lag rangian statistics such as the velocity correlation function and the disper sion. Compared with the predictions of the nonrotational model, the excessi ve rotation reduces dispersion in the shear plane by up to a factor of 2 an d introduces spurious oscillations into the velocity covariance. These diff erences are typical of those for shear flows at equilibrium, and may be eve n greater for flows not at equilibrium. The Eulerian differences thus also serve as a useful indication of the performance of these models in predicti ng Lagrangian statistics. We also show that for the present shear flow the behavior of the Lagrangian velocity structure function for time lags betwee n the Kolmogorov and energy-containing time scales is consistent with corre sponding analyses of forced isotropic turbulence. The present results are c onsistent with a revised value C(0)approximate to6 for the universal consta nt in the inertial subrange of the Lagrangian velocity structure function. This finding suggests that the artificial forcing of the isotropic turbulen ce simulations does not distort estimates of C-0. (C) 2001 American Institu te of Physics.