Large-scale length that determines the mean rate of energy dissipation in turbulence

The mean rate of energy dissipation [ε] per unit mass of turbulence is often written in the form of [ε]=C(u)[u(2)](3/2)/L(u), where the root-mean-square velocity fluctuation [u(2)](1/2) and the velocity correlation length L(u) are parameters of the energy-containing large scales. However, the dimensionless coefficient C(u) is known to depend on the flow configuration that is to induce the turbulence. We define the correlation length L(u(2)) of the local energy u(2), study C(u(2))=[ε]L(u(2))/[u(2)](3/2) with experimental data of several flows, and find that C(u(2)) does not depend on the flow configuration. Not L(u) but L(u(2)) could serve universally as the typical size of the energy-containing eddies, so that [u(2)](3/2)/L(u(2)) is proportional to the rate at which the kinetic energy is removed from those eddies and is eventually dissipated into heat. The independence from the flow configuration is also found for the two-point correlations and so on when L(u(2)) is used to normalize the scale.