Angular momentum conservation law and Navier-Stokes theory

Abstract

A Navier-Stokes fluid is defined to be an isotropic, non-micromorph material for which a linear relation between the viscous pressure tensor and the stretching holds in every theoretical flow situation. However, as to the dynamical representation of this fluid's state quantities, the conservation law of angular momentum is generally ignored. The paper deals with the impact of this principle on the mathematical structure of the ordinary Navier-Stokes equation of motion. It is known that the physics of fluids is strongly influenced by the form of the dissipation law which is assumed to be valid. Obviously, most of the real flow patterns cannot be described adequately by this fluid model unless the well-known paradoxes of the equation's solutions are accepted in practice. This is especially true for incompressible flows. Thus, severe consequences for the vorticity equation are inevitable; particularly, the theory of turbulent flows is strongly affected. Hence, engineering work is considerably influenced. Why these fundamental conclusions are widely disregarded in research and education is discussed. The inadequate behavior is mainly caused by the traditional viewpoint of classical mechanics which is founded on incomplete conservation laws. A realistic flow field description, however, may be established by means of non-equilibrium concepts for the stress rate quantities. A respective new theory of thermofluid dynamics is briefly summarized. It allows the elimination of some serious inconsistencies which are inherent in the present state of the Navier-Stokes theory.