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Length scale to determine the 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⟩ = 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