Complexity of Mesoscale Eddy Diffusivity in the Ocean

Kamenkovich, Igor; Berloff, Pavel; Haigh, Michael; Sun, Luolin; Lu, Yueyang

doi:10.1029/2020gl091719

Cited by 22 publications

(35 citation statements)

References 58 publications

(94 reference statements)

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“…Using a quasigeostrophic model, Haigh et al (2021a) defined eddies and large scales using a spatial filter and found that the diffusion axis has complicated spatial and temporal dependence, but that it tends to align with the large-scale flow, agreeing with earlier studies. Another key finding was that the eigenvalues of the diffusion tensor S are arranged in opposite-signed pairs, as was also found with comprehensive GCMs (Stanley, Bachman & Grooms 2020;Kamenkovich et al 2021). Haigh et al (2020) confirmed that opposite-signed eigenvalues were a robust feature for a selection of spatial filter sizes and for eddy fluxes in a Reynolds eddy decomposition.…”

Section: Introductionsupporting

confidence: 70%

“…A diffusion tensor can be employed to account for the anisotropy, while simplified diagonal tensors can only have directions of preferential eddy diffusion aligned with the model grid and scalar diffusivities cannot account for anisotropy at all. Recent studies (Haigh et al 2020(Haigh et al , 2021aStanley et al 2020;Kamenkovich et al 2021) have diagnosed the diffusion tensor in both idealised models and realistic GCMs and found it to be characterised by opposite-signed eigenvalues. These diagnoses of opposite-signed eigenvalues suggest that the anisotropy is more pronounced than previously thought.…”

Section: Discussionmentioning

confidence: 99%

“…Haigh et al (2020) demonstrated that opposite-signed eigenvalues are a robust feature of S as they are obtained for a range of spatial filter sizes as well as for eddies defined as the deviation from the time mean. Other studies (Stanley et al 2020;Kamenkovich et al 2021) have shown that opposite-signed eigenvalues are also a prevalent feature of the diffusion tensor for passive tracer transport in GCM simulations. Although we are motivated by these past oceanographic studies, the results of this study are applicable to any fluid system which features diffusive processes, in particular those with any anti-diffusive or filamentation effects.…”

Section: The Parameterised Tracer Equation and The Diffusion Tensormentioning

confidence: 94%

See 2 more Smart Citations

On the stability of tracer simulations with opposite-signed diffusivities

Haigh

Berloff

2022

J. Fluid Mech.

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Many recent studies have diagnosed opposite-signed diffusion eigenvalues to be a prevalent feature of the transfer tensor for diffusive tracer transport by oceanic mesoscale eddies. This diagnosed tensor, which we refer to as the diffusion tensor, therefore accounts for tracer filamentation effects. The preferential orientation of this filamentation is quantified by the principal axis of the diffusion tensor, namely the diffusion axis. Parameterisations of eddy diffusion commonly invoke a diffusion tensor, typically one with non-negative eigenvalues to avoid numerical issues. Motivated by the need to parameterise tracer filamentation, in this study we examine diffusion of a Gaussian tracer patch with imposed opposite-signed diffusion eigenvalues, and in particular we focus on the time scale for the onset of instability. For a fixed diffusion axis, numerical instability is an inevitable consequence of persistent up-gradient fluxes associated with the negative eigenvalue. For typical oceanic scales and diffusion magnitudes, this time scale is of the order of $100$ days, but is shorter for larger negative eigenvalues or for finer grid resolutions. We show that imposing a time-dependent diffusion axis can lead to simulations with no onset of instability after 100 000 days of tracer evolution. Although motivated by oceanographic fluid dynamics, our results have much broader applications since diffusive processes are present in a wide range of fluid flows.

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Section: Introductionsupporting

confidence: 70%

Section: Discussionmentioning

confidence: 99%

Section: The Parameterised Tracer Equation and The Diffusion Tensormentioning

confidence: 94%

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On the stability of tracer simulations with opposite-signed diffusivities

Haigh

Berloff

2022

J. Fluid Mech.

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“…where μ j are the corresponding eigenvalues of L. Therefore, what the authors of [92] have proposed can be though as an index related to the solution of the backward diffusion equation, i.e., negative time, or as a diffusion equation with negative diffusivity D < 0 [65]. There are physical situations in which such negative diffusivity appears [48,140,173,225,226]. For instance, in the simultaneous diffusion of boron and point defect in silicon, the diffusivities of interstitial could be negative [225].…”

Section: Laplacian Estrada Index and Backward Diffusionmentioning

confidence: 99%

The many facets of the Estrada indices of graphs and networks

Estrada

2021

SeMA

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The Estrada index of a graph/network is defined as the trace of the adjacency matrix exponential. It has been extended to other graph-theoretic matrices, such as the Laplacian, distance, Seidel adjacency, Harary, etc. Here, we describe many of these extensions, including new ones, such as Gaussian, Mittag–Leffler and Onsager ones. More importantly, we contextualize all of these indices in physico-mathematical frameworks which allow their interpretations and facilitate their extensions and further studies. We also describe several of the bounds and estimations of these indices reported in the literature and analyze many of them computationally for small graphs as well as large complex networks. This article is intended to formalize many of the Estrada indices proposed and studied in the mathematical literature serving as a guide for their further studies.

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“…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%

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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Complexity of Mesoscale Eddy Diffusivity in the Ocean

Cited by 22 publications

References 58 publications

On the stability of tracer simulations with opposite-signed diffusivities

On the stability of tracer simulations with opposite-signed diffusivities

The many facets of the Estrada indices of graphs and networks

On transport tensor of dynamically unresolved oceanic mesoscale eddies

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