ISSN:
1089-7666
Source:
AIP Digital Archive
Topics:
Physics
Notes:
Direct numerical simulation (DNS) calculations of Eulerian acceleration statistics for homogeneous turbulence in uniform shear flow are used to test the closures implied by two different Lagrangian stochastic models for turbulent dispersion. These different models, due to Thomson [J. Fluid Mech. 180, 529 (1987)] and Borgas [Preprints of the Eighth Symposium on Turbulence and Diffusion (American Meteorological Society, Boston, 1988), p. 96], are representative of the range of a class of models which are quadratic in the velocity and are both consistent with the Eulerian velocity statistics which characterize the flow. This is the so-called nonuniqueness problem; Eulerian velocity statistics are not sufficient to uniquely define a Lagrangian stochastic model. We show here that these two models give different Eulerian acceleration statistics, which thus serve to discriminate between the models. The drift term in these stochastic models is related to the mean of the acceleration conditioned on the velocity, enabling related joint statistics 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 contribution of the mean shear to off-diagonal components of the conditional mean acceleration and the acceleration–velocity covariance in the shear plane, and in the mean rate of rotation of the velocity vector in the shear plane. In particular, Thomson's model allocates the direct shear contribution to the correct component of the acceleration–velocity covariance in the shear 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 real and these are reflected in the fact that the mean rotation of the velocity vector has a nonzero contribution from terms that are not closed in terms of the mean flow, the Reynolds stress, and its rate of change. © 2000 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.870449
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