Representing anisotropy of twopoint secondorder turbulence velocity correlations using structure tensors
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2008Source
Physics of FluidsVolume
20Google Scholar check
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A locally homogeneous representation for the twopoint, secondorder turbulent velocity fluctuation Rij(x,r) = 〈u′i(x)u′i(x+r)〉 is formulated in terms of three linearly independent structure tensors [Kassinos et al., J. Fluid Mech. 428, 213 (2001)]: Reynolds stress Bij, dimensionality Dij, and stropholysis Q*ijk. These structure tensors are singlepoint moments of the derivatives of vector stream functions that contain information about the directional and componential anisotropies of the correlation. The representation is a sum of several rotationally invariant component tensors. Each component tensor scales like a power law in r, while its variation in r/r depends linearly on the structure tensors. Continuity and selfconsistency constraints reduce the number of degrees of freedom in the model to 17. A finite Re correction is introduced to the representation for separations of the order of Kolmogorov's length scale. To evaluate our representation, we construct a model correlation by fitting the representation to correlations calculated from direct numerical simulation (DNS) of homogeneous turbulence and channel flow. Comparison of the model correlation to the DNS data shows that the representation can capture the character of the anisotropy of twopoint secondorder velocity correlation tensors. © 2008 American Institute of Physics.
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