On non-uniqueness of the mesoscale eddy diffusivity

Sun, Luolin; Haigh, Michael; Shevchenko, Igor; Berloff, Pavel; Kamenkovich, Igor

doi:10.1017/jfm.2021.472

Cited by 14 publications

(32 citation statements)

References 47 publications

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“…The last analyses are separate comparisons of the reference transport tensor properties with those obtained for the full eddy fluxes and locally filtered eddies. In the past, analysis of transport tensors for passive tracers showed that they are significantly different between reduced and full eddy fluxes (Sun et al 2021). Whether this is true for the dynamical tracers considered here remains to be checked.…”

Section: Transport Tensor Analysismentioning

confidence: 82%

“…This is because different models with different resolutions normally miss different eddy effects and, thus, no universal parameterization can be effectively employed to augment them. Third, in order to define the unique (recognising its non-uniqueness and dealing with it is also an option Sun et al 2021) transport tensor, we assumed that it is the same for the relative-vorticity (i.e. momentum) and isopycnal-thickness (i.e.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…Although, this approach is legitimate, it results in different K for different tracer pairs. This fundamental non-uniqueness problem is thoroughly discussed in Sun et al (2021), but its implications…”

Section: Transport Tensor Analysismentioning

confidence: 99%

“…This fundamental non-uniqueness problem is thoroughly discussed in Sun et al. (2021), but its implications are not yet properly understood. Here, we avoid using extra tracer and overcome the problem by considering the following additional constraint.…”

Section: Transport Tensor Analysismentioning

confidence: 99%

“…This raises an important question on whether K is unique, given that it can be estimated from an ensemble of many different tracer concentration pairs. The answer is negative (Kamenkovich et al 2021;Sun et al 2021), and how to interpret this uncovered non-uniqueness remains an open problem. In this paper we will address and get around it, in the context of dynamically active tracers constrained by the potential vorticity (PV) conservation law.…”

Section: Introductionmentioning

confidence: 99%

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On transport tensor of dynamically unresolved oceanic mesoscale eddies

Ryzhov

Berloff

2022

J. Fluid Mech.

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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.

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Section: Transport Tensor Analysismentioning

confidence: 82%

Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Transport Tensor Analysismentioning

confidence: 99%

Section: Transport Tensor Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On transport tensor of dynamically unresolved oceanic mesoscale eddies

Ryzhov

Berloff

2022

J. Fluid Mech.

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A multifaceted isoneutral eddy transport diagnostic framework and its application in the Southern Ocean

Xie

Liu

Lin

2022

Preprint

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We propose a multifaceted isoneutral eddy transport diagnostic framework that combines the stationary-transient and Leonard's decomposition in large eddy simulation (LES). We diagnose the subfilter flux, the isotropic transport coefficient, and the anisotropic transport tensor or eigenvalues in the Southern Ocean (SO). The anisotropic tensor greatly reduces the reconstruction error of the subfilter flux because of its ability to distinguish the directionality of dynamic information, especially the topographic effect. A thorough analysis of the anisotropic tensor or transport eigenvalues reveals that the sign combination of the transport eigenvalues of the symmetric tensor links to the evolution of domainintegral large-scale PV enstrophy and the combination of different signs is most often, meaning the dominance of filamentation process in the SO. In the region with intense anisotropy, the dominant eigenvector tends to be perpendicular to the large-scale PV gradient, indicating an important role of the PV barrier mechanism in the SO transport process. The two distinct decompositions leveraged in our framework generate intriguing and profound results. Under the stationary-transient decomposition, we find a significant stationary contribution and the duality of the topographic effect which can not only anchors stationary structures but also organizes transient motions. Leonard's decomposition, allows us to investigate the collective effects of the standing wave train, cross-scale interaction, and subfilter eddy-eddy interaction on the filtered space-time scale. We emphasize the complete subgrid flux, not the mere Reynolds term, and the LES framework needs to be considered in the subgrid parameterization of the coarse resolution ocean model.

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