A new gauge-invariant method for diagnosing eddy diffusivities

Abstract

Coarse resolution numerical ocean models must typically include a parameterisation for mesoscale turbulence. A common recipe for such parameterisations is to invoke down-gradient mixing, or diffusion, of some tracer quantity, such as potential vorticity or buoyancy. However, it is well known that eddy fluxes include large rotational components which necessarily do not lead to any mixing; eddy diffusivities diagnosed from unfiltered fluxes are thus contaminated by the presence of these rotational components. Here a new methodology is applied whereby eddy diffusivities are diagnosed directly from the eddy force function. The eddy force function depends only upon flux divergences, is independent of any rotational flux components, and is inherently non-local and smooth. A one-shot inversion procedure is applied, minimising the mis-match between parameterised force functions and force functions derived from eddy resolving calculations. This enables diffusivities associated with the eddy potential vorticity and buoyancy fluxes to be diagnosed. The methodology is applied to multi-layer quasi-geostrophic ocean gyre simulations. It is found that: (i) a strictly down-gradient mixing scheme has limited success in reducing the mis-match compared to one with no sign constraint on the diffusivity; (ii) negative signals of diffusivities are prevalent around the time-mean jet; (iii) there is some indication that the magnitude of the diffusivity correlates well the eddy energy. Implications for parameterisation are discussed in light of these diagnostic results.Comment: 22 pages, 14 figures, Elsevier template, submitted to Ocean Modelling; comments welcom

Data‐Driven Equation Discovery of Ocean Mesoscale Closures

“…To further improve the energetics of the model, an additional prognostic equation for the eddy energy can be solved to account for all sources and sinks of energy within the system. However, the prognostic eddy energy equation is unknown and must therefore be constructed (Cessi, 2008; Eden & Greatbatch, 2008; Jansen et al., 2015; Mak et al., 2016; Marshall & Adcroft, 2010). For both the barotropic and baroclinic models, the RVM algorithm constructs a prognostic equation which is the advection of eddy kinetic energy (EKE) and captures 50–60% of the variance in the validation data (Supporting Information S7).…”

A Diagnosis of Anisotropic Eddy Diffusion From a High‐Resolution Global Ocean Model

“…The properties of tracer transport by these eddies have been of longstanding interest to the oceanographic community, where the transport is generally conceived as a combination of irreversible mixing, or diffusion, and reversible stirring, or advection. Mesoscale eddies themselves do not mix tracers (Bryan & Bachman, ); rather, stirring occurs as the eddies strain and fold the tracer isolines, and only after analyzing the bulk characteristics of the Lagrangian decorrelation of the tracer is the transport usefully approximated as eddy “diffusion.” The conception of eddy transport as a diffusive process has been used to describe the broad behavior of eddies over a wide variety of flow regimes (Kraichnan, ) and has spurred the development of techniques and observational tools to quantify the efficiency of the eddy transport (i.e., the “eddy diffusivity”; Abernathey et al, ; Davis, ; Mak et al, ; Nakamura, ; Wolfram et al, ).…”

On non-uniqueness of the mesoscale eddy diffusivity

“…2015; Mak et al. 2016), i.e. The decomposition is not, however, unique in a bounded or singly periodic domain owing to a dependence on boundary conditions (Fox-Kemper, Ferrari & Pedlosky 2003; Maddison et al.…”

“…However, more recent results from Haigh et al. (2020) and Mak, Maddison & Marshall (2016) using active and passive tracers showed that the negative diffusivities persist after removing the rotational flux. In contrast, Bachman et al.…”