Parameterizing eddy fluxes of reactive biogeochemical tracers

Motions at the mesoscale and below play a key role in setting the distribution of oceanic biogeochemical tracers. These motions are typically parameterized in global climate models using an eddy flux-gradient formulation, in which turbulent transport is represented in terms of large-scale gradients in the mean fields. However, this form of the eddy flux is not necessarily appropriate for reactive tracers, such as nutrients and phytoplankton. Using an idealized nutrient-phytoplankton system, we demonstrate that the eddy flux of an individual reactive tracer depends on the gradients of both tracers; including these "cross-fluxes" can significantly improve the representation of turbulent tracer transport in certain parameter regimes. We further show that the efficacy of the flux-gradient representation, even when appropriate for non-reacting tracers, requires separation between the flow and reaction timescales. This result has ramifications for the representation of tracer transport in reacting systems in general, and for ocean biogeochemistry in particular where the timescales of many biological processes are comparable to submesoscale motions.