Bridging between eddy-viscosity-type and second-order turbulence models through a two-scale turbulence theory

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Abstract
A gap between eddy-viscosity-type and second-order models is bridged using the results of a two-scale direct-interaction approximation developed for the study of turbulent shear flows. This work provides a method for incorporating the findings from models of eddy-viscosity-type into second-order models, and vice versa. Specifically, the effect of helicity controlling energy-cascade processes is incorporated into a second-order model. Then, a higher-order eddy-viscosity-type expression for the Reynolds stress is derived through the application of an iterative approximation to the second-order model. The latter result is tested in a turbulent rotating channel flow and its usefulness is confirmed. Effects of flow trajectory are also discussed in the context of the effect of an adverse pressure gradient on the isotropic eddy viscosity.