In the core region of spanwise rotating channel flows, the mean velocity profile is approximately linear with a slope of twice the system rotation rate. The mechanism of this zero mean absolute vorticity state is investigated from the turbulence modeling point of view. The mean velocity profile is calculated using three simple nonlinear eddy-viscosity models. It is shown that two models, the curvature corrected type of explicit algebraic Reynolds stress model and the model with the corotational derivative of the second-order nonlinear term, well reproduce the zero mean absolute vorticity profile. Both models are derived by taking into account the effect of the advection of the Reynolds stress in the rotating frame. In particular, the latter model reflects the memory effect of the second-order nonlinear term. This effect is confirmed by an analysis using the Green's function for the velocity fluctuation.
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