Turbulent mixing of a passive scalar in the ocean mixed layer

Abstract

We study the 2D turbulent mixing of a passive scalar in the ocean mixed layer.As an example, we examine a steady-state convective mixed layer in which the boundary conditions are chosen so that the system reaches a dynamical equilibrium. In this idealized case, we parameterize the horizontally and temporally averaged fluxes as a functional of the horizontally and temporally averaged property gradients. Here, w c = − dz K(z|z )∂ c /∂z , where K(z|z ) is the eddy diffusivity kernel which describes the vertical transport by eddies at any vertical location z. The full kernel K(z|z ) is computed by adding passive scalars to a buoyancy-driven flow field in a 2D DNS of the ocean surface layer. This functional form of the eddy diffusivity highlights both local and non-local effects of the mixing of a passive scalar, and is based on an unapproximated representation of the idealized physics. This type of formulation can be further extended to other problems in turbulence concerning the mixing of a passive scalar to determine a parameterization based on an accurate representation of ocean physics.

Parameterizing Eddy Transport of Biogeochemical Tracers

“…As was shown in Manucharyan et al (2017), the large-scale eddy field has a finite memory of past ocean states. Recent efforts have also incorporated nonlocal effects into eddy parameterizations using an effective diffusivity kernel that depends on the statistics of the field (Bhamidipati et al, 2020). Extending these frameworks to reactive tracers is worth investigation given the key role of phytoplankton in marine ecosystems and the global carbon cycle.…”

Statistical non-locality of dynamically coherent structures

“…An insight from (2.36) is the dependence of turbulent fluxes at location as a weighted sum of gradients of the mean variable at locations . The operator is linear and amenable to computation, even in turbulent flows (Bhamidipati, Souza & Flierl 2020).…”

Ineffective diffusivity

“…However, a proposed closure can now be couched as an approximation to , and having access to an exact expression should greatly help with validation. In an earlier recent paper, some of the same authors used this formalism to numerically compute the exact kernel for a passive scalar in the ocean mixed layer (Bhamidipati, Souza & Flierl 2020).…”