Prevention of Reynolds-Averaging with Regard to Turbulent Force Densities

Reynolds-averaging of the Navier-Stokes equations is an approach to derive equations of motion for averaged quantities of the flow field. The treatment of averaged quantities in fluid dynamics is justified with the ratio of masses and eigentimes being generally large between a body subject to flow forces and the particles of the fluid itself. A given state of the flow-field exhibits an averaged effect on its surrounding. Contrary, the development of a turbulent flow-field itself is determined by the interaction of fluid elements of comparable masses and eigentimes. Therewith, the averaging of the equations of motion describing the evolution of the flow-field is not immediately reasoned for. While for linear processes the averaging of physical quantities does directly carry through to the averaging of the underlying equations of motion it is a topic of concern for non-linear processes. In view of that it appears meaningful to distinguish between the averaging of a state of quantities and the averaging of evolutionary equations