Secondary flows in a plane channel: their relationship and comparison with turbulent flows

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Abstract
Two- and three-dimensional non-stationary viscous-fluid flows in a plane channel are considered. By means of efficient computational algorithms for direct integration of the incompressible Navier-Stokes equations the evolution of these flows over large time intervals is simulated. Classes of two- and three-dimensional non-stationary flows with stationary integral characteristics (the flow rate, mean pressure gradient, total energy of pulsations etc.) were found. Such flows are called secondary flows. Two-dimensional secondary flows have only qualitative similarity to turbulent flows observed in experiments. Three-dimensional secondary flows agree very well, even quantitatively, with turbulent flows. The principal characteristics of turbulent flows such as drag coefficient, mean-velocity profile, the distributions of the pulsation velocity components and some others are reproduced in three-dimensional secondary flows with good accuracy.