# zbMATH — the first resource for mathematics

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 $$Re_D \approx 10^5$$.

##### MSC:
 76-05 Experimental work for problems pertaining to fluid mechanics 76F10 Shear flows and turbulence
Full Text:
##### References:
 [1] DOI: 10.1016/j.physd.2006.01.012 · Zbl 1331.76058 [2] DOI: 10.1017/S0022112098002419 · Zbl 0941.76510 [3] DOI: 10.1088/1367-2630/9/4/089 [4] DOI: 10.1209/0295-5075/80/54001 [5] DOI: 10.1017/S0022112009007721 · Zbl 1183.76025 [6] Schlichting, Boundary-Layer Theory (1968) [7] DOI: 10.1017/S0022112009994071 · Zbl 1189.76028 [8] DOI: 10.1098/rsta.2006.1948 · Zbl 1152.76412 [9] DOI: 10.1063/1.2162185 [10] DOI: 10.1017/S0022112004008985 · Zbl 1060.76508 [11] DOI: 10.1103/PhysRevLett.92.144502 [12] DOI: 10.1103/PhysRevLett.96.044502 [13] DOI: 10.1017/S0022112087000892 · Zbl 0616.76071 [14] Frisch, Turbulence: The Legacy of A. N. Kolmogorov (1995) · Zbl 0832.76001 [15] DOI: 10.1017/S0022112095001984 [16] DOI: 10.1103/PhysRevLett.103.014502 [17] DOI: 10.1017/S0022112006004526 · Zbl 1178.76058 [18] DOI: 10.1017/S0022112008002085 · Zbl 1145.76393
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.