The mechanism of zero mean absolute vorticity state in rotating channel flow

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, reproduce well 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 means that a nonzero absolute vorticity creates a difference between the normal stresses, leading to a large shear stress in a rapidly rotating system. Since the actual value of the shear stress does not increase with the rotation rate, the absolute vorticity needs to be very small. To confirm the memory effect of the nonlinear term, anisotropic and temporally nonlocal effects of the mean velocity on the Reynolds stress are evaluated using Green's function for the velocity fluctuation. (c) 2006 American Institute of Physics.