A new Reynolds stress constitutive formula is constructed using the first-order statistics of turbulent fluctuations instead of the mean strain rate. It includes zero empirical coefficients. The formula is validated with the direct numerical simulation (DNS) data of turbulent channel flow at Reτ=180. The Reynolds stresses given by the proposed formula agree very well with the DNS results. The good agreement persists even after the multi-angle rotation of the coordinate system, indicating the rotation in-variance of the formula. The autocorrelation of the fluctuating velocity rather than the mean strain rate is close to the essence of the Reynolds stress.
Jinglei XU;Zhengguang TU;Ning HU
. Rotation invariant constitutive relation for Reynolds stress structure parameter[J]. Applied Mathematics and Mechanics, 2015
, 36(4)
: 517
-522
.
DOI: 10.1007/s10483-015-1927-9
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