A Statistical Investigation of Transport Equation for Energy Dissipation in Shear Turbulence

The transport equation for energy dissipation rate in turbulent shear flows is examined by the use of a statistical theory, which is founded on the Direct-Interaction formalism as well as on the separation between the space and time scales of the mean and fluctuating fields. Various quantities appearing in the equation are expressed in terms of the turbulent energy and the energy dissipation rate as well as the mean velocity. On this basis, discussion is made on a model equation for energy dissipation rate which is frequently used in the turbulence closure models. As a result it is suggested that the usual model equation is not always justifiable from the standpoint of a statistical shear-turbulence theory.