Eulerian acceleration statistics as a discriminator between Lagrangian stochastic models in uniform shear flow

Direct numerical simulation (DNS) calculations of Eulerian acceleration sta tistics for homogeneous turbulence in uniform shear flow are used to test t he closures implied by two different Lagrangian stochastic models for turbu lent dispersion. These different models, due to Thomson [J. Fluid Mech. 180 , 529 (1987)] and Borgas [Preprints of the Eighth Symposium on Turbulence a nd Diffusion (American Meteorological Society, Boston, 1988), p. 96], are r epresentative of the range of a class of models which are quadratic in the velocity and are both consistent with the Eulerian velocity statistics whic h characterize the flow. This is the so-called nonuniqueness problem; Euler ian velocity statistics are not sufficient to uniquely define a Lagrangian stochastic model. We show here that these two models give different Euleria n acceleration statistics, which thus serve to discriminate between the mod els. The drift term in these stochastic models is related to the mean of th e acceleration conditioned on the velocity, enabling related joint statisti cs of the velocity and the acceleration, such as their covariance and their cross product, to be determined. The model closures represent these joint statistics in terms of the mean shear, the Reynolds stress tensor, and its rate of change. Differences between the two models show up in the direct co ntribution of the mean shear to off-diagonal components of the conditional mean acceleration and the acceleration-velocity covariance in the shear pla ne, and in the mean rate of rotation of the velocity vector in the shear pl ane. In particular, Thomson's model allocates the direct shear contribution to the correct component of the acceleration-velocity covariance in the sh ear plane, whereas Borgas's model does not. Other components are identical in the two models. Overall, Thomson's model represents the DNS results very well. However, the relatively small deviations from Thomson's model are re al and these are reflected in the fact that the mean rotation of the veloci ty vector has a nonzero contribution from terms that are not closed in term s of the mean flow, the Reynolds stress, and its rate of change. (C) 2000 A merican Institute of Physics. [S1070-6631(00)02007-9].