The second approximation of Navier–Stokes equations

Equations of motion of a viscous Newtonian fluid are derived, which, in addition to the terms of the Navier–Stokes equations, contain additional terms taking into account the relaxation effect of vorticity on the rate of strain. An independent experimental method for measuring a new parameter involved in the equations is described. As an application of the Navier–Stokes equations in the second approximation, Stokes’ hypothesis is rigorously substantiated. New similarity criteria for incompressible viscous flows are presented. The Poynting effect for viscous incompressible Newtonian fluids is theoretically explained.