Vorticity transport in modeling three-dimensional unsteady shear flows

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Abstract
This Letter examines how intrinsic three-dimensionality influences the flow structure of unsteady shear flows, and models its effects by considering spanwise averages of vorticity fluctuations. In particular, uniform flow past a half-cylinder is considered: the two-dimensional wake is very different from its three-dimensional counterpart and the evolution equation for the spanwise spatially averaged vorticity is analyzed. It is shown that the vector flux which transports spanwise vorticity due to spatial vorticity fluctuations is of considerable magnitude (large in comparison with molecular diffusion) and is far from co-linear with the gradient of the spanwise averaged vorticity. Modeling this flux using classical eddy viscosity ideas would therefore seem inappropriate.