On a generalized nonlinear K-ε model and the use of extended thermodynamics in turbulence

A resent extension of the nonlinear K-epsilon model is critically discussed from a basic theoretical standpoint. While it was said in the paper that this model was formulated to incorporate relaxation effects, it will be shown that the model is incapable of describing one of the most basic such turbulent flows as is obvious but is described for clarity. It will be shown in detail that this generalized nonlinear K-epsilon model yields erroneous results for the Reynolds stress tensor when the mean strains are set to zero in a turbulent flow - the return-to-isotropy problem which is one of the most elementary relaxational turbulent flows. It is clear that K-epsilon type models cannot describe relaxation effects. While their general formalism can describe relaxation effects, the nonlinear K-epsilon model - which the paper is centered on - cannot. The deviatoric part of the Reynolds stress tensor is predicted to be zero when it actually only gradually relaxes to zero. Since this model was formulated by using the extended thermodynamics, it too will be critically assessed. It will be argued that there is an unsubstantial physical basis for the use of extended thermodynamics in turbulence. The role of Material Frame-Indifference and the implications for future research in turbulence modeling are also discussed.