Dispersion and turbulence: A close relationship unveiled by means of state function

This article reviews the physical conditions that natural, turbulent flows meet to be considered in “Dynamic Equilibrium”, a condition that greatly facilitates the analysis of flows, thanks to the concept of “equiprobability”, in such a way that the tracer dyes can give an essential information of the dynamics of the current. A general State Function is proposed for this dynamic, which allows to study Advection and Dispersion for virtually all types of river beds, achieving a series of compact and precise relationships, both in hydraulics and thermodynamics. This approach allows us to obviate the limiting use of non-linear differential equations, as "mandatory" characterization of fluid dynamics. With this new method, a practical case from the technical literature is analyzed, and it is solved in detail, comparing it with the classic method of Statistical Moments. Conclusions on results, and recommendations are made.