An Application of Gradient Theory of Grade Two 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. The necessary boundary conditions for real (dissipative) boundaries are generated by using so-called porosity tensors. This theory is applied to a velocity profile of a turbulent COUETTE flow of water. On the basis of these experimental data the material and porosity coefficients are identified by numerical algorithms like evolution strategies.