The present study aims to estimate effective diahaline turbulent salinity fluxes and diffusivities in numerical model simulations of estuarine scenarios. The underlying method is based on a quantification of salinity mixing per salinity class, which is shown to be twice the turbulent salinity transport across the respective isohaline. Using this relation, the recently derived universal law of estuarine mixing, predicting that average mixing per salinity class is twice the respective salinity times the river run-off, can be directly derived. The turbulent salinity transport is accurately decomposed into physical (due to the turbulence closure) and numerical (due to truncation errors of the salinity advection scheme) contributions. The effective diahaline diffusivity representative for a salinity class and an estuarine region results as the ratio of the diahaline turbulent salinity transport and the respective (negative) salinity gradient, both integrated over the isohaline area in that region and averaged over a specified period. With this approach, the physical (or numerical) diffusivities are calculated as half of the product of physical (or numerical) mixing and the isohaline volume, divided by the square of the isohaline area. The method for accurately calculating physical and numerical diahaline diffusivities is tested and demonstrated for a three-dimensional idealized exponential estuary. As a major product of this study, maps of the spatial distribution of the effective diahaline diffusivities are shown for the model estuary.

Plain Language Summary Eddy diffusivity determines how intensively concentrations in a fluid are spreading due to turbulent motion. Here, we analyze the diffusivity that spreads salt concentration (i.e., salinity) across a surface of constant salinity (the isohalines), also called effective diahaline diffusivity. A new method is presented that calculates effective diahaline diffusivities based on the specific volume between two specified isohalines, on the salinity mixing within this volume as well as on the surface area of the isohalines. We define mixing as the rate of destruction of salinity variance per unit volume due to turbulent mixing processes. The method applies to computer models of ocean dynamics on scales ranging from coastal to global. In such models, the mixing is determined by statistical mathematical equations of turbulent processes, which is the so-called physical mixing. In models, additional (numerical) mixing occurs due to numerical inaccuracies of algorithms that move around water masses passively with the currents, a process called advection. Using our method, the total effective diffusivity determined for each isohaline surface can be accurately separated into contributions from physical mixing and numerical mixing. We demonstrate the functioning of the new method for an idealized model simulation of an estuary.