A tracer-based inversion method for diagnosing eddy-induced diffusivity and advection

Bachman, Scott; Fox‐Kemper, Baylor; Bryan, Frank O.

doi:10.1016/j.ocemod.2014.11.006

Cited by 52 publications

(110 citation statements)

References 47 publications

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“…This flux‐gradient relationship can include both an advective (antisymmetric) part and a diffusive (symmetric) part [ Griffies , ], which allows for the standard mesoscale eddy tracer transport schemes [ Gent and McWilliams , ; Redi , ] along with other similar closures [e.g., Fox‐Kemper et al ., ]. It will be assumed that all tracers are approximated to use the same coefficient tensor R jk [ Bachman and Fox‐Kemper , ; Bachman et al ., ].

\frac{D ω_{i}}{D t} = \partial_{j} true[ω_{j} u_{i} + ϵ_{i j z} b + ϵ_{i ℓ k} \partial_{ℓ} ν_{j k m n} (\partial_{m} u_{n} + \partial_{n} u_{m}) true],

\frac{D q_{e}}{D t} = \partial_{i} true[ω_{i} \partial_{j} true(α_{θ} R_{j k} \partial_{k} θ - β_{S} R_{j k} \partial_{k} S true) + ϵ_{i j ℓ} true(\partial_{k} ν_{j k m n} (\partial_{m} u_{n} + \partial_{n} u_{m}) true) \partial_{ℓ} B true],

= \partial_{i} true[ω_{i} \partial_{j} true(R_{j k} \partial_{k} B true) + ϵ_{i j ℓ} true(\partial_{k} ν_{j k m}

…”

Section: Background and Theorymentioning

confidence: 74%

“…The first term in square brackets in (45) is the effect of eddy diffusion (symmetric part of R jk , or

S_{j k} = (R_{j k} + R_{k j}) / 2

) and eddy advection (antisymmetric part of R jk , or

A_{j k} = (R_{j k} - R_{k j}) / 2

) on Ertel PV [ Griffies , ; Bachman et al ., ]. If, as argued by Redi [] and many others, eddy‐induced diffusion is oriented along isopycnals, then

S_{j k} \nabla_{k} B = 0

, and there is no eddy diffusion of buoyancy [see also Dukowicz and Smith , ; Smith and Marshall , ; Abernathey et al ., ] and thus no dissipation of Ertel PV by eddy diffusion in (45).…”

Section: Background and Theorymentioning

confidence: 99%

“…Idealized simulations with a potential enstrophy cascade of varying depth (similar to Bachman and Fox‐Kemper [] and Bachman et al . []) are used to test the new methods versus extant MOLES subgrid models (section 3). Implications of the new method are discussed in section 4.…”

Section: Introductionmentioning

confidence: 99%

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A scale-aware subgrid model for quasi-geostrophic turbulence

Bachman

Fox‐Kemper

Pearson

2017

J. Geophys. Res. Oceans

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This paper introduces two methods for dynamically prescribing eddy‐induced diffusivity, advection, and viscosity appropriate for primitive equation models with resolutions permitting the forward potential enstrophy cascade of quasi‐geostrophic dynamics, such as operational ocean models and high‐resolution climate models with O(25) km horizontal resolution and finer. Where quasi‐geostrophic dynamics fail (e.g., the equator, boundary layers, and deep convection), the method reverts to scalings based on a matched two‐dimensional enstrophy cascade. A principle advantage is that these subgrid models are scale‐aware, meaning that the model is suitable over a range of grid resolutions: from mesoscale grids that just permit baroclinic instabilities to grids below the submesoscale where ageostrophic effects dominate. Two approaches are presented here using Large Eddy Simulation (LES) techniques adapted for three‐dimensional rotating, stratified turbulence. The simpler approach has one nondimensional parameter, Λ, which has an optimal value near 1. The second approach dynamically optimizes Λ during simulation using a test filter. The new methods are tested in an idealized scenario by varying the grid resolution, and their use improves the spectra of potential enstrophy and energy in comparison to extant schemes. The new methods keep the gridscale Reynolds and Péclet numbers near 1 throughout the domain, which confers robust numerical stability and minimal spurious diapycnal mixing. Although there are no explicit parameters in the dynamic approach, there is strong sensitivity to the choice of test filter. Designing test filters for heterogeneous ocean turbulence adds cost and uncertainty, and we find the dynamic method does not noticeably improve over setting Λ = 1.

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\frac{D ω_{i}}{D t} = \partial_{j} true[ω_{j} u_{i} + ϵ_{i j z} b + ϵ_{i ℓ k} \partial_{ℓ} ν_{j k m n} (\partial_{m} u_{n} + \partial_{n} u_{m}) true],

\frac{D q_{e}}{D t} = \partial_{i} true[ω_{i} \partial_{j} true(α_{θ} R_{j k} \partial_{k} θ - β_{S} R_{j k} \partial_{k} S true) + ϵ_{i j ℓ} true(\partial_{k} ν_{j k m n} (\partial_{m} u_{n} + \partial_{n} u_{m}) true) \partial_{ℓ} B true],

= \partial_{i} true[ω_{i} \partial_{j} true(R_{j k} \partial_{k} B true) + ϵ_{i j ℓ} true(\partial_{k} ν_{j k m}

…”

Section: Background and Theorymentioning

confidence: 74%

“…The first term in square brackets in (45) is the effect of eddy diffusion (symmetric part of R jk , or

S_{j k} = (R_{j k} + R_{k j}) / 2

) and eddy advection (antisymmetric part of R jk , or

A_{j k} = (R_{j k} - R_{k j}) / 2

) on Ertel PV [ Griffies , ; Bachman et al ., ]. If, as argued by Redi [] and many others, eddy‐induced diffusion is oriented along isopycnals, then

S_{j k} \nabla_{k} B = 0

, and there is no eddy diffusion of buoyancy [see also Dukowicz and Smith , ; Smith and Marshall , ; Abernathey et al ., ] and thus no dissipation of Ertel PV by eddy diffusion in (45).…”

Section: Background and Theorymentioning

confidence: 99%

See 1 more Smart Citation

A scale-aware subgrid model for quasi-geostrophic turbulence

Bachman

Fox‐Kemper

Pearson

2017

J. Geophys. Res. Oceans

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show abstract

“…Diagnosing a single, scalar transport coefficient is thus no longer sufficient to inform the eddy transport operator in this approach; rather, each element of

boldK

must be diagnosed and further tensor algebra must be used to untangle the directionality and magnitude of the transport—in the horizontal as well as the vertical. Both Eulerian (e.g., Bachman & Fox‐Kemper, ; Bachman et al, ) and Lagrangian (e.g., Wolfram et al, ) diagnostic techniques have been developed that are well suited to this task. A key advantage of this extension to anisotropy is that eddy fluxes need not be aligned with the tracer gradients—indeed that is the exception, even though the diffusive and advective character of the eddy transport is preserved.…”

Section: Introductionmentioning

confidence: 99%

“…Fox‐Kemper et al () discussed many implications of anisotropic eddy transport and presented an earlier version of this diagnosis in comparison to a similar analysis using surface drifters but without the present focus on the horizontal symmetric tensor. This work aims to present an updated version of their analysis, except with a proper tensor decomposition and using improved diagnostic techniques that better account for the consequences of dissipation of tracer anomalies in the analysis (Bachman et al, ). Though the horizontal symmetric tensor is explicitly not part of the GM transport, the GM transport is mathematically related (Smith & Gent, ).…”

Section: Introductionmentioning

confidence: 99%

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

Bachman

Fox‐Kemper

Bryan

2020

J Adv Model Earth Syst

100

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Oceanic mesoscale eddies are known to diffuse and stir tracers, and the development of skillful eddy closures is aided considerably by the accurate diagnosis of these processes from eddy‐resolving model statistics. In this work a multiple‐tracers inversion method is applied to a global mesoscale eddy‐resolving simulation, with the intent to solve for the eddy transport tensor that describes the eddy diffusion (symmetric part) and stirring (antisymmetric part). Special emphasis is placed on diagnosing the anisotropy of the horizontal transport, which is described by the eigenvalues and eigenvectors of the 2×2 horizontal symmetric subtensor. Global diagnoses of these quantities, along with an examination of their vertical structures, are used to recommend an algorithm for extending the Gent and McWilliams and Redi parameterizations to include anisotropic effects.

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Effects of submesoscale turbulence on ocean tracers

2016

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Ocean tracers such as carbon dioxide, nutrients, plankton, and oil advect, diffuse, and react primarily in the oceanic mixed layer where air‐sea gas exchange occurs and light is plentiful for photosynthesis. There can be substantial heterogeneity in the spatial distributions of these tracers due to turbulent stirring, particularly in the submesoscale range where partly geostrophic fronts and eddies and small‐scale three‐dimensional turbulence are simultaneously active. In this study, a large eddy simulation spanning horizontal scales from 20 km down to 5 m is used to examine the effects of multiscale turbulent mixing on nonreactive passive ocean tracers from interior and sea‐surface sources. The simulation includes the effects of both wave‐driven Langmuir turbulence and submesoscale eddies, and tracers with different initial and boundary conditions are examined in order to understand the respective impacts of small‐scale and submesoscale motions on tracer transport. Tracer properties are characterized using spatial fields and statistics, multiscale fluxes, and spectra, and the results detail how tracer mixing depends on air‐sea tracer flux rate, tracer release depth, and flow regime. Although vertical fluxes of buoyancy by submesoscale eddies compete with mixing by Langmuir turbulence, vertical fluxes of tracers are often dominated by Langmuir turbulence, particularly for tracers that are released near the mixed‐layer base or that dissolve rapidly through the surface, even in regions with pronounced submesoscale activity. Early in the evolution of some tracers, negative eddy diffusivities occur co‐located with regions of negative potential vorticity, suggesting that symmetric instabilities or other submesoscale phenomenon may act to oppose turbulent mixing.

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A tracer-based inversion method for diagnosing eddy-induced diffusivity and advection

Cited by 52 publications

References 47 publications

A scale-aware subgrid model for quasi-geostrophic turbulence

A scale-aware subgrid model for quasi-geostrophic turbulence

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

Effects of submesoscale turbulence on ocean tracers

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