Flux flummoxed: a proposal for consistent usage.

I would like to bring to the attention of the hydrogeology community an ongoing inconsistency in the published literature concerning the use of the term flux. The definition of flux that is most pertinent to Ground Water readers comes from the field of transport phenomena, where the flux of some quantity (e.g., mass, energy, momentum, entropy) is defined as the flow rate of that quantity per unit area. For example, a mass flow rate, which has SI units of kg/s, when referenced to a unit area, results in mass flux having SI units of kg/(m2 s). Because this definition includes a direction (i.e., the surface normal of the unit area), flux is a vector. I would like to propose that the community agrees to consistently use this definition in technical presentations, published literature, and, most importantly, classrooms. To support this proposal, I first present details on the two primary definitions of flux currently used in physics, describe the fluxes most commonly found in hydrogeology, continue with a brief history of the usage of the term flux, and then give some examples of uses that are either incorrect or confusing.