GRADIENT THEORY OF SECOND ORDER WITH APPLICATION TO TURBULENT FLOWS

A gradient theory of grade two based on an axiomatic conception of a no local continuum theory for materials of grade n is presented. The total stress tensor of rank two in the equation of linear momentum contains two higher stress tensors of rank two and three. In the case of isotropic materials both the tensor of rank two and three are tensor-valued functions of the second order strain rate tensor and its first gradient so that the equation of motion is of order four. This theory is applied to a velocity profile of a turbulent Couette flow of water.

کلیدواژه ها:

Turbulent flow ، Gradient theory ، Continuum mechanics