Direct numerical simulation of a non-equilibrium three-dimensional turbulent boundary layer over a flat plate

Direct numerical simulations (DNS) are used to examine a spatially developing non-equilibrium three-dimensional turbulent boundary layer (3DTBL) over a flat plate. The present flow is a 'shear-driven' 3DTBL owing to a sudden imposition of a surface spanwise velocity W-S. Particular attention is given to the effects of cross-flow and Reynolds number. In the DNS, three values of the inlet momentum thickness Reynolds number, Re-theta 0 = 300, 600 and 900, are used with several values of W-S. The present largest W-S is twice the free-stream velocity U-0, comparable to the maximum value of the spinning cylinder experiment by Lohmann (Trans. ASME I: J. Fluids Engng, vol. 98, 1976, pp. 354-363). After imposing W-S, the mean streamwise vorticity (Omega) over bar (x) increasingly propagates away from the wall where there is close relationship between a deficit of mean streamwise velocity and inviscid skewing (i.e. three-dimensionality). At a downstream station of a 3DTBL, near-plateaus appear in the skin friction coefficients where the magnitudes depend intrinsically on W-S. The approach to the collateral state is, however, slow for mean streamwise velocity (U) over bar where the Reynolds shear stress uv extracts energy from the mean flow inefficiently. As the Reynolds number increases, the mean velocity magnitude Q(r) tends to show the log law but with a larger von Karman constant than in a two-dimensional turbulent boundary layer. Instantaneously, toppling u structures dominate owing to cross-flow and become more prominent with increasing Re. Statistically, the latter spanwise length scale increases linearly with respect to y below y/delta(99) = 0.2, which indicates that cross-flow yields a self-similar behaviour.