Scaling of global properties of turbulence and skin friction in pipe and channel flows

Experimental data on the Reynolds number dependence of the area-averaged turbulent kinetic energy K and dissipation rate ℰ are presented. It is shown that while in the interval ReD > 105 the total kinetic energy scales with friction velocity (K/u*2 = const), a new scaling law K/〈U〉2 ∝ K/(u*2ReDθ) = const (θ ≈ 1/4) has been discovered in the interval ReD < 105. 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 ReD ≈ 105.