Evolution of the tracer in natural flows described by the state function ф(U, E, t): Analysis of the associated functions and their application to case studies

Abstract

The tracers as a method of measuring and characterizing the evolution of natural flows, in addition to providing information on the dynamics (advection) and dispersion as "local" phenomena themselves, can give additional, dense information on the global conditions (far from the point of measurement) under the thermodynamic connection that is established between all the points of the system, when there is a steady-state in the channel. As has been widely studied since the second half of the last century, this condition of dynamic equilibrium (steady-state) in natural flows, for phenomena that do not present pronounced irreversibility (linear region of irreversible thermodynamics), implies a series of remarkable features that simplify the interpretation of the complex phenomena of turbulent currents, and thus of the superimposed dispersive processes. Within this approach, a state function, Φ(U, E, t), dependent on the mean flow velocity, the longitudinal dispersion coefficient, and time, is defined that describes the evolution of the tracer cloud, such that in its approximate quality of thermodynamic potential, it allows one to discover and pinpoint certain particularities of the phenomenon. In this paper, the characteristics and practical applications of these principles are explored. It also includes a heuristic analysis of the so-called direct functions rq(F) and inverse rq(F)-, auxiliary to the state function F(U,E, t), which are used for the interpretation of the centroid time, as well as the longitudinal and transverse diffusion-dispersion coefficients employing these functions were applied experimentally in the old stream of the city of Bogotá, “La Vieja”, presenting good agreement with the theoretical references. This topic is intended to provide a theoretical and practical tool to fully understand these processes, which are of great interest for the modeling and control of water pollution.