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The log behaviour of the Reynolds shear stress in accelerating turbulent boundary layers. (English) Zbl 1403.76025
Summary: Direct numerical simulation of highly accelerated turbulent boundary layers (TBLs) reveals that the Reynolds shear stress, \(\overline{u'v'}\,^{+}\), monotonically decreases downstream and exhibits a logarithmic behaviour (e.g. \(-\overline{u'v'}\,^{+}=-(1/A_{uv})\ln y^{+}+B_{uv}\)) in the mesolayer region (e.g. \(50\leq y^{+}\leq 170\)). The thickness of the log layer of \(\overline{u'v'}\,^{+}\) increases with the streamwise distance and with the pressure gradient strength, extending over a large portion of the TBL thickness (up to 55 %). Simulations reveal that \(V^{+},\partial U^{+}/\partial y^{+}\sim 1/y^{+}\sim \partial \overline{u'v'}\,^{+}/\partial y^{+}\), resulting in a logarithmic \(\overline{u'v'}\,^{+}\) profile. Also, \(V^{+}\sim -y^{+}\) is no longer negligible as in zero-pressure-gradient (ZPG) flows. Other experimental/numerical data at similar favourable-pressure-gradient (FPG) strengths also show the presence of a log region in \(\overline{u'v'}^{+}\). This log region in \(\overline{u'v'}\,^{+}\) is larger in sink flows than in other spatially developing FPG flows. The latter flows exhibit the presence of a small power-law region in \(\overline{u'v'}\,^{+}\), which is non-existent in sink flows.

MSC:
76F40 Turbulent boundary layers
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