On transport tensor of dynamically unresolved oceanic mesoscale eddies

Abstract

Parameterizing mesoscale eddies in ocean circulation models remains an open problem due to the ambiguity with separating the eddies from large-scale flow, so that their interplay is consistent with the resolving skill of the employed non-eddy-resolving model. One way to address the issue is by using recently formulated dynamically filtered eddies. These eddies are obtained as the field errors of fitting some given reference ocean circulation into the employed coarse-grid ocean model. The main strengths are (i) no explicit spatio-temporal filter is needed for separating the large-scale and eddy flow components, (ii) the eddies are dynamically translated into the error-correcting forcing that perfectly augments the coarse-grid model towards reproducing the reference circulation. We uncovered physical properties of the eddies by interpreting involved nonlinear eddy/large-scale interactions via the classical flux-gradient relation. We described the eddies in terms of their full, space–time dependent transport tensor, which was made unique by constraining it to be the same for the potential vorticity, momentum and buoyancy fluxes. Both diffusive and advective parts of the transport tensor were found to be significant. The diffusive tensor component is characterised by polar eigenvalues and is further decomposed into isotropic and filamentation components. The latter component completely dominates, therefore, it should be taken into account by eddy parameterizations, which is not yet the case. We also showed that spatial inhomogeneities of the transport tensor components are important. Comparing these properties with those obtained for more common, locally filtered eddies revealed that they are distinctly different.

Generative Data‐Driven Approaches for Stochastic Subgrid Parameterizations in an Idealized Ocean Model

“…The existing approaches may lead to numerical instabilities due to the presence of negative eddy viscosity or diffusivity. For example, the tracer diffusivity tensor produced by mesoscale eddies contains one negative eigenvalue (Bachman et al., 2020; Haigh & Berloff, 2021, 2022; Haigh et al., 2021; Kamenkovich et al., 2021; Lu et al., 2022; Ryzhov & Berloff, 2022). Parameterization of mesoscale momentum fluxes by the eddy viscosity operator is also challenging: the crucial physical process of kinetic energy backscatter can be captured only with negative eddy viscosity (Bachman, 2019; Jansen & Held, 2014; Jansen et al., 2019; Juricke et al., 2020).…”

The Importance of Being Asymmetric for Geophysical Vortices

“…Baroclinic vortices (also called eddies) with nearly vertical axes dominate in the kinetic energy of mesoscale variability, transporting masses of water in their cores for thousands of kilometers (Dong et al [9]). They often persist for many rotational periods, challenging parameterization schemes of mesoscale eddies in the global numerical models of climate variability (e.g., Thompson and Young [10], Gallet and Ferrari,[11], Ryzhov and Berloff, [12] and Sutyrin et al [13]).…”

Global coarse-grained mesoscale eddy statistics based on integrated kinetic energy and enstrophy correlations

“…Detailed comparisons show that all Eulerian methods have pros and cons, and none of them is superior to another (Souza et al, 2011;Escudier et al, 2016). Methods based on identifying Lagrangian coherent structures obey a much better mathematical foundation (Haller, 2015;Beron-Vera et al, 2018;Haller et al, 2018;El Aouni, 2021;Ryzhov and Berloff, 2022). However, they are computationally rather demanding and the (relatively low) spatial resolution of the input fields is a challenging aspect of them (Amores et al, 2018).…”