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Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer. (English) Zbl 1181.76084
Summary: A nominally-zero-pressure-gradient incompressible boundary layer over a smooth flat plate was simulated for a continuous momentum thickness Reynolds number range of \(80 \leq Re_{\theta } \leq 940\). Transition which is completed at approximately \(Re_{\theta } = 750\) was triggered by intermittent localized disturbances arising from patches of isotropic turbulence introduced periodically from the free stream at \(Re_{\theta } = 80\). Streamwise pressure gradient is quantified with several measures and is demonstrated to be weak. Blasius boundary layer is maintained in the early transitional region of \(80 < Re_{\theta } < 180\) within which the maximum deviation of skin friction from the theoretical solution is less than 1%. Mean and second-order turbulence statistics are compared with classic experimental data, and they constitute a rare DNS dataset for the spatially developing zero-pressure-gradient turbulent flat-plate boundary layer. Our calculations indicate that in the present spatially developing low-Reynolds-number turbulent flat-plate boundary layer, total shear stress mildly overshoots the wall shear stress in the near-wall region of 2-20 wall units with vanishing normal gradient at the wall. Overshoots as high as 10% across a wider percentage of the boundary layer thickness exist in the late transitional region. The former is a residual effect of the latter. The instantaneous flow fields are vividly populated by hairpin vortices. This is the first time that direct evidence (in the form of a solution of the Navier-Stokes equations, obeying the statistical measurements, as opposed to synthetic superposition of the structures) shows such dominance of these structures. Hairpin packets arising from upstream fragmented \(\varLambda \) structures are found to be instrumental in the breakdown of the present boundary layer bypass transition.

MSC:
76F40 Turbulent boundary layers
76F65 Direct numerical and large eddy simulation of turbulence
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