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The mean rate of energy dissipation ⟨ε⟩ per unit mass of turbulence is often written in the form of ⟨ε⟩ = Cu⟨u2⟩3/2/Lu, where ⟨u2⟩1/2 is the root-mean-square fluctuation of the longitudinal velocity u and Lu is its correlation length. However, Cu is known to depend on the large-scale configuration of the flow. We define the correlation length Lu2 of the local energy u2 and find that Cu2 = ⟨ε⟩Lu2 /⟨u2 ⟩3/2 does not depend on the flow configuration. The independence from the flow configuration is also found for the two-point velocity correlation and so on when Lu2 is used to normalize the scale.
Author(s):
Hideaki Mouri
Meteorological Research Institute
Japan