Quantifying irreversible transport and mixing of biogeochemical scalars in a stratified shear flow

Biogeochemical scalars, representing many different species of phytoplankton, zooplankton, nutrients, etc., play an important role in marine ecosystems. Here we examine a simplified two-species system of generic phytoplankton and nutrient scalars. We construct a model that governs the biological reaction (nutrient uptake, phytoplankton death/remineralization) and examine, via direct numerical simulation, how these two scalars interact when mixed by stratified shear instabilities (Kelvin-Helmholtz, Holmboe). Turbulent advective fluxes show large oscillations during the evolution of the shear instabilities, associated with reversible fluid motions. To isolate the irreversible turbulent scalar fluxes, we instead calculate diascalar fluxes, that is, diffusive fluxes across isoscalar surfaces. This concept has been previously used to quantify irreversible mixing of buoyancy in stratified mixing events; here, we extend this approach to also account for the effects of biogeochemical reactions. Our results show that this analysis proves useful for measuring the net effect of mixing, as well as for capturing the downward propagation of a phytoplankton front as it grows and consumes nutrients beneath the interface of our simulated domain.