Diagnosing diapycnal dispersion from tracer evolution and distribution

Turbulence measurements over the last twenty years have shown that mixing becomes more vigorous toward the ocean bottom and inspired several recent theoretical and modeling studies exploring the diabatic pathways of the abyssal ocean. Deep mixing is inferred either with tracer release experiments or with turbulent probes, and tracer release-based estimates have been found to consistently exceed microstructure-based estimates. Here we revisit the assumptions behind estimates of deep ocean mixing from the spreading of tracers. First, we show that both the turbulent fluxes and the turbulent diffusivity can be inferred directly from the tracer distribution in density space without any approximation. The new formulas are particularly useful when dealing with tracer releases close to ocean topography where mixing rates change rapidly with depth. Second, we apply the formulas to infer mixing in numerical simulations of the deep ocean, where we release numerical tracers both above and close to the ocean seafloor. This provides a test for the approach, as turbulent fluxes and diffusivities can be computed directly from the model output.