Mixing of tracers in stratified sheared flows

Understanding small-scale turbulent mixing in the ocean is fundamental for accurately modeling oceanic processes, predicting currents, and managing marine ecosystems. Global and regional ocean models rely on parameterizing turbulent mixing, yet this remains a significant source of uncertainty due to technical constraints and model-specific empirical assumptions. Furthermore, when coupled with biogeochemical models, a uniform mixing parameterization is typically applied to all tracers, overlooking the distinct properties of each. This study investigates the influence of turbulent mixing on macroscopic scales and examines the role of molecular diffusion coefficients, which are intrinsically the only irreversible processes affecting passive tracers. Using the CROCO model in a non-hydrostatic, compressible configuration, we conduct direct 3D numerical simulations of turbulence and mixing driven by Kelvin-Helmholtz instabilities. The analysis is based on tracking the properties of fluid particles in a tracer-density space and calculating an effective diffusion coefficient to quantify how fine-scale mixing impacts larger scales redistribution of tracer. The macroscopic scale is associated with the adiabatic rearrangement of the 3D density field into a stable 1D profile, following Lorenz rearrangement. The evolution of these 1D profiles, which only occurs during irreversible mixing, forms the basis for calculating the effective diffusion coefficient. Both theoretical considerations and numerical results in simplified configurations demonstrate that when the molecular diffusion coefficients for tracers and density are equal, the macroscopic effective diffusivity deduced from the density field can be applied to the passive tracer. To evaluate this principle of equality of macroscopic diffusivity, we conduct an experimental study of a gravity current in a large tank (3x0.15x0.2 meters) using a dual light attenuation technique to simultaneously observe the density and passive tracer fields. The same domain is simulated in the numerical model, enabling direct comparisons of mixing dynamics between experimental and numerical gravity currents. Results highlight the critical role of transverse instabilities in driving irreversible mixing. The latter locally modify mixing at macroscopic scale and possibly alter the equality principle.