Application of minimal energy dissipation principle to turbulence modeling

A new model of turbulence is proposed to solve Reynolds equations for fully-developed flow in a wall-bounded straight channel. We show that Reynolds number can be defined as a ratio of flow kinetic energy to the work of friction/dissipation forces. Then, we introduce a turbulent Reynolds number that represent a balance between energy loses due to the momentum exchange by turbulent vortices travelling from low to high velocity areas and wall friction. The main idea of Multi-Scale Viscosity (MSV) model that is expressed in the following phenomenological rule: A local deformation of the axial velocity profile can and should generate the turbulence with such intensity that keeps the local turbulent Reynolds number below the critical value. Thus, in MSV, the only empirical parameter is the critical Reynolds number. MSV has been applied to the several basic channel flows such as a circular tube, an infinitive plane channel and an annulus. The MSV model can be considered as an integral-equation algebraic model of turbulence. (author)