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

摘要

Experimental data on the Reynolds number dependence of the area-averaged turbulent kinetic energy K and dissipation rate 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/U~2∝ K/(u*~2Re_D~θ) = const (θ≈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≈ 10~5.