Studies of the relation between the shear parameter S^* and the Reynoldsnumber Re are presented for a nearly homogeneous and statistically stationaryturbulent shear flow. The parametric investigations are in line with ageneralized perspective on the return to local isotropy in shear flows that wasoutlined recently [Schumacher, Sreenivasan and Yeung, Phys. Fluids, vol.15, 84(2003)]. Therefore, two parameters, the constant shear rate S and the level ofinitial turbulent fluctuations as prescribed by an energy injection rateepsilon_{in}, are varied systematically. The investigations suggest that theshear parameter levels off for larger Reynolds numbers which is supported bydimensional arguments. It is found that the skewness of the transversederivative shows a different decay behavior with respect to Reynolds numberwhen the sequence of simulation runs follows different pathways across thetwo-parameter plane. The study can shed new light on different interpretationsof the decay of odd order moments in high-Reynolds number experiments.
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