title: Scalar dissipation rates in non-conservative transport systems.
abstract: This work considers how the inferred mixing state of diffusive and advective-diffusive systems will vary over time when the solute masses are not constant over time. We develop a number of tools that allow the scalar dissipation rate to be used as a mixing measure in these systems without calculating local concentration gradients. The behavior of dissipation rates is investigated for single and multi-component kinetic reactions and a commonly studied equilibrium reaction. The scalar dissipation rate of a tracer experiencing first-order decay can be determined exactly from the decay constant and the dissipation rate of a passive tracer, and the mixing rate of a conservative component is not the superposition of the solute specific mixing rates. We then show how the behavior of the scalar dissipation rate can be determined from a limited subset of an infinite domain. Corrections are derived for constant and time dependent limits of integration the latter is used to approximate dissipation rates in advective-diffusive systems. Several of the corrections exhibit similarities to the previous work on mixing, including non-Fickian mixing. This illustrates the importance of accounting for the effects that reaction systems or limited monitoring areas may have on the inferred mixing state.
authors.affiliation: Department of Land, Air and Water Resources, University of California, Davis, USA. nbengdahl@ucdavis.edu
authors.forename: Nicholas B
authors.initials: NB
authors.lastname: Engdahl
authors.forename: Timothy R
authors.initials: TR
authors.lastname: Ginn
authors.forename: Graham E
authors.initials: GE
authors.lastname: Fogg
mesh_terms: D004784:Environmental Monitoring / Q000379:methods; D060587:Groundwater / Q000032:analysis*; D007700:Kinetics