Two-dimensional and three-dimensional secondary flows in a plane channel, and their relationship and comparison with turbulent flows

An effort is made to find a class of unsteady flows with steady-state integral characteristics in the case of constant external conditions, the investigation being conducted only on the basis of the Navier-Stokes equations for a viscous incompressible fluid without the aid of additional assumptions. These so-called secondary flows are examined for the case of a plane channel on the basis of the numerical integration of the Navier-Stokes equations using effective sufficiently precise algorithms. A class of two- and three-dimensional secondary flows is obtained whose quantitative and qualitative characteristics resemble those for turbulent flows as measured in physical experiments. An important finding is the good agreement between values of drag coefficient and mean velocity profile measured in turbulent flows and corresponding values for three-dimensional secondary flows.