A generalized newtonian rheological model for laminar and turbulent flows

For the description of laminar and turbulent flows of incompressible liquids, a non-linear law of viscous friction is suggested which is the generalized Newtonian rheological model containing the apparent viscosity of specific form. An approach is suggested which allows to establish the apparent viscosity of incompressible liquid by using the experimental data on the flow of the liquid in circular pipes. By using this approach, the analytical approximation of the apparent viscosity of water is constructed. By using this approximation, the numerical simulations were made of the flow in a circular pipe, of the two-dimensional flow in the boundary layer near a plane plate, and of damping of a plane vortex having a sharp boundary. From these simulations, it was found that the suggested law of viscous friction allows to describe one- and two-dimensional fields of the averaged velocity of a fluid for laminar, transitional, and turbulent flows. In particular, the qualitative form of the suggested law explains the process of damping of strong long-lived atmospheric vortices.