Tracer-based estimates of eddy-induced diffusivities

Abstract

This study provides estimates of the mean eddy-induced diffusivities of passive tracers in a threelayer, double-gyre quasigeostrophic (QG) simulation. A key aspect of this study is the use of a spatial filter to separate the flow and tracer fields into small-scale and large-scale components, and we compare results with those obtained using Reynolds temporal averaging. The eddy tracer flux is related to a rank-2 diffusivity tensor via the flux-gradient relation, which is solved for a pair of tracers with misaligned large-scale gradients. We concentrate on the symmetric part of the resulting diffusivity tensor which represents irreversible mixing processes. The eigenvalues of the symmetric tensor exhibit complicated behaviour, but a particularly dominant and robust feature is the positive/negative eigenvalue pairs, which physically represent filamentation of the tracer concentration. The large off-diagonal diffusivity tensor component is the primary contributor to the eigenvalue polarity, and since this is such a prevalent feature we argue that the (horizontal) eddy-induced diffusivity should always be treated as a full 2 × 2 tensor.Diffusivity magnitudes are largest in the upper layer and in the eastward jet region, where the eddying flow is strongest. After removing the rotational part of the eddy tracer flux, typical mean diffusivities (eigenvalues) in the upper-layer are on the order of 10 3 m 2 s −1 in the jet region and 10 2 m 2 s −1 elsewhere. We also confirm that the time-mean of the diffusivity calculated from instantaneous fluxes is not the same as the diffusivity associated with the time-mean fluxes.

Vertical Structure of Ocean Mesoscale Eddies with Implications for Parameterizations of Tracer Transport

“…Though the horizontal structure of K is not the focus of this investigation, we offer the following brief preliminary results for the case where the vertical structure is proportional to ϕ 1 . The eigenvalues of K appear to come in positive/negative pairs of approximately equal magnitude, as also observed recently for the Redi/diffusive part of the parameterization by Haigh et al (2020). It is not yet clear if the diffusive and anti‐diffusive directions are in any way related to the large‐scale flow, potential vorticity gradients, and so on.…”

Complexity of Mesoscale Eddy Diffusivity in the Ocean

“…The other serious complication is that F contains some large nondivergent (“rotational”) component (Haigh et al., 2020; Jayne & Marotzke, 2002; Marshall & Shutts, 1981) that does not affect tracer distribution, because only divergence of the eddy fluxes matters, but influences K in the flux‐gradient relation (Equation ). The rotational flux can be tracer‐dependent (Bachman et al., 2015) and can lead to negative diffusivities (Marshall & Shutts, 1981).…”

Complexity of Mesoscale Eddy Diffusivity in the Ocean

“…In realistic oceanic flows, all K-tensor elements are generally nonzero, distinct (i.e., the eddy-induced mixing is anisotropic) and vary in space and time (i.e., the mixing is inhomogeneous and nonstationary). Observation-and model-based estimates of the simplified eddy diffusivity exhibit strong dependence on depth, geographical location (Abernathey & Marshall, 2013;Cole et al, 2015;Canuto et al, 2019;Griesel et al, 2010;Groeskamp et al, 2020;Lumpkin et al, 2002;Marshall et al, 2006), and time (Busecke & Abernathey, 2019;Haigh et al, 2020). These estimates usually involve some spatio-temporal averaging and can be based on either drifter ("particle") trajectories or tracer distributions.…”

“…These estimates usually involve some spatio-temporal averaging and can be based on either drifter ("particle") trajectories or tracer distributions. Both particle-based statistics (Griesel et al, 2010;Kamenkovich et al, 2009Kamenkovich et al, , 2015McClean et al, 2002;O'Dwyer et al, 2000;Rypina et al, 2012;Sallee et al, 2008) and tracer-based estimates Bachman et al, 2017Bachman et al, , 2020Eden, 2007;Haigh et al, 2020) also exhibit significant anisotropy. This anisotropy is important in the typical oceanic case of strong eddies embedded in relatively weak large-scale circulation (Kamenkovich et al, 2015).…”

“…The diffusion approach (Equation 1) is built on an inherent assumption that the K-tensor is unique for any given turbulent flow. However, some model estimates report significant sensitivity of a simplified K-tensor to the tracer field Bachman et al, 2020Bachman et al, , 2015Eden & Greatbatch, 2009;Haigh et al, 2020). This sensitivity complicates interpretation of the K-tensor because even the exact solution of Equation 1 for one particular pair of tracers will lead to biases in F for another set.…”