# zbMATH — the first resource for mathematics

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
Full Text: