Analysis and modeling of hybrid turbulence equation based on temporal filtering

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Analysis of the velocity equation in turbulent channel flow was made using spatial filtering. It was shown that the extra term due to the non-commutivity plays an important role in the stress fluctuation and the turbulent energy budget near the interface between the RANS and LES regions. A new length scale was introduced using the time integral to derive theoretically the transport equations for the eddy diffusivity and the eddy viscosity. The Reynolds stress, the eddy viscosity, and the new length scale were shown to be closely related to each other via the production term of each transport equation.