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

Abstract

Direct numerical simulation calculations of Lagrangian statistics for homogeneous 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 statistics. In particular one of the models imparts an excessively large mean rotation to the trajectories in the plane of the shear, while the other is nonrotational. We show that this rotation degrades the model’s prediction of Lagrangian statistics such as the velocity correlation function and the dispersion. Compared with the predictions of the nonrotational model, the excessive rotation reduces dispersion in the shear plane by up to a factor of 2 and introduces spurious oscillations into the velocity covariance. These differences are typical of those for shear flows at equilibrium, and may be even greater for flows not at equilibrium. The Eulerian differences thus also serve as a useful indication of the performance of these models in predicting Lagrangian statistics. We also show that for the present shear flow the behavior of the Lagrangian velocity structure function for time lags between the Kolmogorov and energy-containing time scales is consistent with corresponding analyses of forced isotropic turbulence. The present results are consistent with a revised value C0≈6 for the universal constant in the inertial subrange of the Lagrangian velocity structure function. This finding suggests that the artificial forcing of the isotropic turbulence simulations does not distort estimates of C0.