Persistent Small Scale Anisotropy in Homogeneous Shear Flows

The turbulent velocity fluctuations in a homogeneous shear flow (mean velocity →U0ex0ex=0ex0exSy^x) are studied numerically, in the range of Reynolds number 2600≤Re≤11300. The skewness of the z component of vorticity is independent of the Reynolds number in this range, suggesting that some small scale anisotropy remains at very high Reynolds numbers. This anisotropy is not seen in the two-point correlation functions. An analogy is drawn with earlier results on turbulent mixing of a passive scalar with a mean gradient. The relevance of this work for turbulent boundary layers is discussed.