Integral formula for determination of the reynolds stress in canonical flow geometries

We present a theoretical framework for solving for the Reynolds stress in turbulent flows, based on fundamental physics of turbulence transport. Results thus far indicate that the good agreement between the current theoretical results with experimental and DNS (direct numerical simulation) data is not a fortuitous coincidence, and in the least the current approach is the best hypothesis available in canonical flow geometries. The theory leads to simple and correct expressions for the Reynolds stress in various flow geometries, in terms of the root variables, such as the mean velocity, velocity gradient, turbulence kinetic energy and a viscous term. The applications for this theory are construction of effective turbulence models based on correct physics, and potentially augmenting or replacing turbulence models in simple flows. However, as the method is thus far proven only for relatively simple flow geometries, and implications and nuances for full, three-dimensional flows need to be further examined.