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Scaling of global properties of turbulence and skin friction in pipe and channel flows. (English) Zbl 1193.76015
Summary: Experimental data on the Reynolds number dependence of the area-averaged turbulent kinetic energy \(K\) and dissipation rate \(\mathcal E\) are presented. It is shown that while in the interval \(Re_D > 10^5\) the total kinetic energy scales with friction velocity \((K/u_*^2 =\) const), a new scaling law \(K/ \langle U \rangle^2 \propto K/(u_*^2 Re_D^{\theta}) =\) const \((\theta \approx 1/4)\) has been discovered in the interval \(Re_D < 10^5\). It is argued that this transition is responsible for the well-known change in the scaling behaviour of the friction factor observed in pipe and channels flows at \(Re_D \approx 10^5\).

76-05 Experimental work for problems pertaining to fluid mechanics
76F10 Shear flows and turbulence
Full Text: DOI
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