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  • 1
    Online Resource
    Online Resource
    Cambridge University Press (CUP) ; 2020
    In:  Journal of Fluid Mechanics Vol. 885 ( 2020-02-25)
    In: Journal of Fluid Mechanics, Cambridge University Press (CUP), Vol. 885 ( 2020-02-25)
    Abstract: We study the term in the eddy energy budget of continuously stratified quasigeostrophic turbulence that is responsible for energy extraction by eddies from the background mean flow. This term is a quadratic form, and we derive Euler–Lagrange equations describing its eigenfunctions and eigenvalues, the former being orthogonal in the energy inner product and the latter being real. The eigenvalues correspond to the instantaneous energy growth rate of the associated eigenfunction. We find analytical solutions in the Eady problem. We formulate a spectral method for computing eigenfunctions and eigenvalues, and compute solutions in Phillips-type and Charney-type problems. In all problems, instantaneous growth is possible at all horizontal scales in both inviscid problems and in problems with linear Ekman friction. We conjecture that transient growth at small scales is matched by linear transfer to decaying modes with the same horizontal structure, and we provide simulations supporting the plausibility of this hypothesis. In Charney-type problems, where the linear problem has exponentially growing modes at small scales, we expect net energy extraction from the mean flow to be unavoidable, with an associated nonlinear transfer of energy to dissipation.
    Type of Medium: Online Resource
    ISSN: 0022-1120 , 1469-7645
    Language: English
    Publisher: Cambridge University Press (CUP)
    Publication Date: 2020
    detail.hit.zdb_id: 1472346-3
    detail.hit.zdb_id: 218334-1
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  • 2
    Online Resource
    Online Resource
    Cambridge University Press (CUP) ; 2015
    In:  Journal of Fluid Mechanics Vol. 762 ( 2015-01-10), p. 256-272
    In: Journal of Fluid Mechanics, Cambridge University Press (CUP), Vol. 762 ( 2015-01-10), p. 256-272
    Abstract: Ocean submesoscale baroclinic instability is studied in the framework of the balance equations. These equations are an intermediate model that includes balanced ageostrophic effects with higher accuracy than the quasigeostrophic approximation, but rules out unbalanced wave motions. As such, the balance equations are particularly suited to the study of baroclinic instability in submesoscale ocean dynamics. The linear baroclinic instability problem is developed in generality and then specialized to the case of constant vertical shear. It is found that non-quasigeostrophic effects appear only for perturbations with cross-front variation, and that perturbation energy can be generated through both baroclinic production and shear production. The Eady problem is solved analytically in the balance equation framework. Ageostrophic effects are shown to increase the range of unstable modes and the growth rate of the instability for perturbations with cross-front variation. The increased level of instability is attributed to both ageostrophic baroclinic production and shear production of perturbation energy; these results are verified in the primitive equations. Finally, submesoscale baroclinic instability is examined in a case where the buoyancy frequency increases rapidly near the bottom boundary, mimicking the increase of stratification at the base of the oceanic mixed layer. The qualitative results of the Eady problem are repeated in this case, with increased growth rates attributed to the production of perturbation energy by the ageostrophic velocity. The results show that submesoscale baroclinic instability acts to reduce lateral buoyancy gradients and their associated geostrophic shear simultaneously through lateral buoyancy fluxes and vertical momentum fluxes.
    Type of Medium: Online Resource
    ISSN: 0022-1120 , 1469-7645
    Language: English
    Publisher: Cambridge University Press (CUP)
    Publication Date: 2015
    detail.hit.zdb_id: 1472346-3
    detail.hit.zdb_id: 218334-1
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  • 3
    Online Resource
    Online Resource
    Wiley ; 2023
    In:  Quarterly Journal of the Royal Meteorological Society Vol. 149, No. 752 ( 2023-04), p. 1018-1037
    In: Quarterly Journal of the Royal Meteorological Society, Wiley, Vol. 149, No. 752 ( 2023-04), p. 1018-1037
    Abstract: The ensemble forecast dominates the computational cost of many data assimilation methods, especially for high‐resolution and coupled models. In situations where the cost is prohibitive, one can either use a lower‐cost model or a lower‐cost data assimilation method, or both. Ensemble optimal interpolation (EnOI) is a classical example of a lower‐cost ensemble data assimilation method that replaces the ensemble forecast with a single forecast and then constructs an ensemble about this single forecast by adding perturbations drawn from climatology. This research develops lower‐cost ensemble data assimilation methods that add perturbations to a single forecast, where the perturbations are obtained from analogs of the single model forecast. These analogs can either be found from a catalog of model states, constructed using linear combinations of model states from a catalog, or constructed using generative machine‐learning methods. Four analog ensemble data assimilation methods, including two new ones, are compared with EnOI in the context of a coupled model of intermediate complexity: Q‐GCM. Depending on the method and on the physical variable, analog methods can be up to 40% more accurate than EnOI.
    Type of Medium: Online Resource
    ISSN: 0035-9009 , 1477-870X
    URL: Issue
    RVK:
    RVK:
    Language: English
    Publisher: Wiley
    Publication Date: 2023
    detail.hit.zdb_id: 3142-2
    detail.hit.zdb_id: 2089168-4
    SSG: 14
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  • 4
    Online Resource
    Online Resource
    American Meteorological Society ; 2013
    In:  Journal of Physical Oceanography Vol. 43, No. 9 ( 2013-09-01), p. 1911-1923
    In: Journal of Physical Oceanography, American Meteorological Society, Vol. 43, No. 9 ( 2013-09-01), p. 1911-1923
    Abstract: This paper investigates the energy budget of mesoscale eddies in wind-driven two-layer quasigeostrophic simulations. Intuitively, eddy energy can be generated, dissipated, and fluxed from place to place; regions where the budget balances generation and dissipation are “local” and regions that export or import large amounts of eddy energy are “nonlocal.” Many mesoscale parameterizations assume that statistics of the unresolved eddies behave as local functions of the resolved large scales, and studies that relate doubly periodic simulations to ocean patches must assume that the ocean patches have local energetics. This study derives and diagnoses the eddy energy budget in simulations of wind-driven gyres. To more closely approximate the ideas of subgrid-scale parameterization, the authors define the mean and eddies using a spatial filter rather than the more common time average. The eddy energy budget is strongly nonlocal over nearly half the domain in the simulations. In particular, in the intergyre region the eddies lose energy through interactions with the mean, and this energy loss can only be compensated by nonlocal flux of energy from elsewhere in the domain. This study also runs doubly periodic simulations corresponding to ocean patches from basin simulations. The eddy energy level of ocean patches in the basin simulations matches the level in the periodic simulations only in regions with local eddy energy budgets.
    Type of Medium: Online Resource
    ISSN: 0022-3670 , 1520-0485
    Language: English
    Publisher: American Meteorological Society
    Publication Date: 2013
    detail.hit.zdb_id: 2042184-9
    detail.hit.zdb_id: 184162-2
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  • 5
    Online Resource
    Online Resource
    AIP Publishing ; 2015
    In:  Physics of Fluids Vol. 27, No. 10 ( 2015-10-01)
    In: Physics of Fluids, AIP Publishing, Vol. 27, No. 10 ( 2015-10-01)
    Abstract: Energy transport by eddies is diagnosed from a series of simulations of stochastically forced, inhomogeneous two-dimensional turbulence—barotropic dynamics on the f-plane. The divergence of the energy flux is compared to diffusive models, both fractional and harmonic, and the inferred diffusivity κ is compared to a mixing-length model κ ∝ Vℓ where V and ℓ are eddy velocity and length scales, respectively. The flux-divergence is found to be well approximated by Laplacian diffusion with a mixing-length approximation. This study provides some support for diffusive modeling of mesoscale eddy energy transport in ocean model parameterizations.
    Type of Medium: Online Resource
    ISSN: 1070-6631 , 1089-7666
    Language: English
    Publisher: AIP Publishing
    Publication Date: 2015
    detail.hit.zdb_id: 1472743-2
    detail.hit.zdb_id: 241528-8
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  • 6
    Online Resource
    Online Resource
    Stockholm University Press ; 2023
    In:  Tellus A: Dynamic Meteorology and Oceanography Vol. 75, No. 1 ( 2023-02-27), p. 145-158
    In: Tellus A: Dynamic Meteorology and Oceanography, Stockholm University Press, Vol. 75, No. 1 ( 2023-02-27), p. 145-158
    Type of Medium: Online Resource
    ISSN: 1600-0870
    Language: English
    Publisher: Stockholm University Press
    Publication Date: 2023
    detail.hit.zdb_id: 2026987-0
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  • 7
    Online Resource
    Online Resource
    American Meteorological Society ; 2018
    In:  Monthly Weather Review Vol. 146, No. 8 ( 2018-08-01), p. 2433-2446
    In: Monthly Weather Review, American Meteorological Society, Vol. 146, No. 8 ( 2018-08-01), p. 2433-2446
    Abstract: This article shows that increasing the observation variance at small scales can reduce the ensemble size required to avoid collapse in particle filtering of spatially extended dynamics and improve the resulting uncertainty quantification at large scales. Particle filter weights depend on how well ensemble members agree with observations, and collapse occurs when a few ensemble members receive most of the weight. Collapse causes catastrophic variance underestimation. Increasing small-scale variance in the observation error model reduces the incidence of collapse by de-emphasizing small-scale differences between the ensemble members and the observations. Doing so smooths the posterior mean, though it does not smooth the individual ensemble members. Two options for implementing the proposed observation error model are described. Taking a discretized elliptic differential operator as an observation error covariance matrix provides the desired property of a spectrum that grows in the approach to small scales. This choice also introduces structure exploitable by scalable computation techniques, including multigrid solvers and multiresolution approximations to the corresponding integral operator. Alternatively the observations can be smoothed and then assimilated under the assumption of independent errors, which is equivalent to assuming large errors at small scales. The method is demonstrated on a linear stochastic partial differential equation, where it significantly reduces the occurrence of particle filter collapse while maintaining accuracy. It also improves continuous ranked probability scores by as much as 25%, indicating that the weighted ensemble more accurately represents the true distribution. The method is compatible with other techniques for improving the performance of particle filters.
    Type of Medium: Online Resource
    ISSN: 0027-0644 , 1520-0493
    RVK:
    Language: English
    Publisher: American Meteorological Society
    Publication Date: 2018
    detail.hit.zdb_id: 2033056-X
    detail.hit.zdb_id: 202616-8
    SSG: 14
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  • 8
    Online Resource
    Online Resource
    American Physical Society (APS) ; 2010
    In:  Physical Review Letters Vol. 104, No. 22 ( 2010-6-1)
    In: Physical Review Letters, American Physical Society (APS), Vol. 104, No. 22 ( 2010-6-1)
    Type of Medium: Online Resource
    ISSN: 0031-9007 , 1079-7114
    RVK:
    RVK:
    Language: English
    Publisher: American Physical Society (APS)
    Publication Date: 2010
    detail.hit.zdb_id: 1472655-5
    detail.hit.zdb_id: 208853-8
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  • 9
    Online Resource
    Online Resource
    American Meteorological Society ; 2016
    In:  Journal of Physical Oceanography Vol. 46, No. 1 ( 2016-01), p. 125-139
    In: Journal of Physical Oceanography, American Meteorological Society, Vol. 46, No. 1 ( 2016-01), p. 125-139
    Abstract: This study investigates the representation of solutions of the three-dimensional quasigeostrophic (QG) equations using Galerkin series with standard vertical modes, with particular attention to the incorporation of active surface buoyancy dynamics. This study extends two existing Galerkin approaches ( A and B ) and develops a new Galerkin approximation ( C ). Approximation A , due to Flierl, represents the streamfunction as a truncated Galerkin series and defines the potential vorticity (PV) that satisfies the inversion problem exactly. Approximation B , due to Tulloch and Smith, represents the PV as a truncated Galerkin series and calculates the streamfunction that satisfies the inversion problem exactly. Approximation C , the true Galerkin approximation for the QG equations, represents both streamfunction and PV as truncated Galerkin series but does not satisfy the inversion equation exactly. The three approximations are fundamentally different unless the boundaries are isopycnal surfaces. The authors discuss the advantages and limitations of approximations A , B , and C in terms of mathematical rigor and conservation laws and illustrate their relative efficiency by solving linear stability problems with nonzero surface buoyancy. With moderate number of modes, B and C have superior accuracy than A at high wavenumbers. Because B lacks the conservation of energy, this study recommends approximation C for constructing solutions to the surface active QG equations using the Galerkin series with standard vertical modes.
    Type of Medium: Online Resource
    ISSN: 0022-3670 , 1520-0485
    Language: Unknown
    Publisher: American Meteorological Society
    Publication Date: 2016
    detail.hit.zdb_id: 2042184-9
    detail.hit.zdb_id: 184162-2
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  • 10
    Online Resource
    Online Resource
    American Meteorological Society ; 2023
    In:  Journal of Physical Oceanography Vol. 53, No. 1 ( 2023-01), p. 157-176
    In: Journal of Physical Oceanography, American Meteorological Society, Vol. 53, No. 1 ( 2023-01), p. 157-176
    Abstract: Energy exchanges between large-scale ocean currents and mesoscale eddies play an important role in setting the large-scale ocean circulation but are not fully captured in models. To better understand and quantify the ocean energy cycle, we apply along-isopycnal spatial filtering to output from an isopycnal 1/32° primitive equation model with idealized Atlantic and Southern Ocean geometry and topography. We diagnose the energy cycle in two frameworks: 1) a non-thickness-weighted framework, resulting in a Lorenz-like energy cycle, and 2) a thickness-weighted framework, resulting in the Bleck energy cycle. This paper shows that framework 2 is more useful for studying energy pathways when an isopycnal average is used. Next, we investigate the Bleck cycle as a function of filter scale. Baroclinic conversion generates mesoscale eddy kinetic energy over a wide range of scales and peaks near the deformation scale at high latitudes but below the deformation scale at low latitudes. Away from topography, an inverse cascade transfers kinetic energy from the mesoscales to larger scales. The upscale energy transfer peaks near the energy-containing scale at high latitudes but below the deformation scale at low latitudes. Regions downstream of topography are characterized by a downscale kinetic energy transfer, in which mesoscale eddies are generated through barotropic instability. The scale- and flow-dependent energy pathways diagnosed in this paper provide a basis for evaluating and developing scale- and flow-aware mesoscale eddy parameterizations. Significance Statement Blowing winds provide a major energy source for the large-scale ocean circulation. A substantial fraction of this energy is converted to smaller-scale eddies, which swirl through the ocean as sea cyclones. Ocean turbulence causes these eddies to transfer part of their energy back to the large-scale ocean currents. This ocean energy cycle is not fully simulated in numerical models, but it plays an important role in transporting heat, carbon, and nutrients throughout the world’s oceans. The purpose of this study is to quantify the ocean energy cycle by using fine-scale idealized numerical simulations of the Atlantic and Southern Oceans. Our results provide a basis for how to include unrepresented energy exchanges in coarse global climate models.
    Type of Medium: Online Resource
    ISSN: 0022-3670 , 1520-0485
    Language: Unknown
    Publisher: American Meteorological Society
    Publication Date: 2023
    detail.hit.zdb_id: 2042184-9
    detail.hit.zdb_id: 184162-2
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