Possibility of determining secondary flows from the Reynolds equations

An analysis of various ways of generalizing the Bussinesq hypothesis for closing the Reynolds equations is presented. On introducing the turbulent viscosity in the form of a scalar function, the secondary flows are identically equal to zero. On expressing the turbulent viscosity in the form of a tensor of the second or fourth rank, the secondary flows are no longer equal to zero. It was concluded that the intensity of these flows depends on the degree of nonuniformity in the distribution of the main-flow velocity over the cross section of the channel.