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  • 1
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    A Geometric Interpretation of Eddy Reynolds Stresses in Barotropic Ocean Jets (2016)
    American Meteorological Society
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    Publication Date: 2016-07-19
    Description: Barotropic eddy fluxes are analyzed through a geometric decomposition of the eddy stress tensor. Specifically, the geometry of the eddy variance ellipse, a two-dimensional visualization of the stress tensor describing the mean eddy shape and tilt, is used to elucidate eddy propagation and eddy feedback on the mean flow. Linear shear and jet profiles are analyzed and theoretical results are compared against fully nonlinear simulations. For flows with zero planetary vorticity gradient, analytic solutions for the eddy ellipse tilt and anisotropy are obtained that provide a direct relationship between the eddy tilt and the phase difference of a normal-mode solution. This allows a straightforward interpretation of the eddy–mean flow interaction in terms of classical stability theory: the initially unstable jet gives rise to eddies that are tilted “against the shear” and extract energy from the mean flow; once the jet stabilizes, eddies become tilted “with the shear” and return their energy to the mean flow. For a nonzero planetary vorticity gradient, ray-tracing theory is used to predict ellipse geometry and its impact on eddy propagation within a jet. An analytic solution for the eddy tilt is found for a Rossby wave on a constant background shear. The ray-tracing results broadly agree with the eddy tilt diagnosed from a fully nonlinear simulation.
    Print ISSN: 0022-3670
    Electronic ISSN: 1520-0485
    Topics: Geosciences , Physics
    Published by American Meteorological Society
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  • 2
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    A Framework for Parameterizing Eddy Potential Vorticity Fluxes (2012)
    American Meteorological Society
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    Publication Date: 2012-04-01
    Description: A framework for parameterizing eddy potential vorticity fluxes is developed that is consistent with conservation of energy and momentum while retaining the symmetries of the original eddy flux. The framework involves rewriting the residual-mean eddy force, or equivalently the eddy potential vorticity flux, as the divergence of an eddy stress tensor. A norm of this tensor is bounded by the eddy energy, allowing the components of the stress tensor to be rewritten in terms of the eddy energy and nondimensional parameters describing the mean shape and orientation of the eddies. If a prognostic equation is solved for the eddy energy, the remaining unknowns are nondimensional and bounded in magnitude by unity. Moreover, these nondimensional geometric parameters have strong connections with classical stability theory. When applied to the Eady problem, it is shown that the new framework preserves the functional form of the Eady growth rate for linear instability. Moreover, in the limit in which Reynolds stresses are neglected, the framework reduces to a Gent and McWilliams type of eddy closure where the eddy diffusivity can be interpreted as the form proposed by Visbeck et al. Simulations of three-layer wind-driven gyres are used to diagnose the eddy shape and orientations in fully developed geostrophic turbulence. These fields are found to have large-scale structure that appears related to the structure of the mean flow. The eddy energy sets the magnitude of the eddy stress tensor and hence the eddy potential vorticity fluxes. Possible extensions of the framework to ensure potential vorticity is mixed on average are discussed.
    Print ISSN: 0022-3670
    Electronic ISSN: 1520-0485
    Topics: Geosciences , Physics
    Published by American Meteorological Society
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  • 3
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    Eddy saturation and frictional control of the Antarctic Circumpolar Current (2017)
    American Geophysical Union
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    Publication Date: 2017-01-09
    Description: The Antarctic Circumpolar Current is the strongest current in the ocean and has a pivotal impact on ocean stratification, heat content, and carbon content. The circumpolar volume transport is relatively insensitive to surface wind forcing in models that resolve turbulent ocean eddies, a process termed “eddy saturation.” Here a simple model is presented that explains the physics of eddy saturation with three ingredients: a momentum budget, a relation between the eddy form stress and eddy energy, and an eddy energy budget. The model explains both the insensitivity of circumpolar volume transport to surface wind stress and the increase of eddy energy with wind stress. The model further predicts that circumpolar transport increases with increased bottom friction, a counterintuitive result that is confirmed in eddy-permitting calculations. These results suggest an unexpected and important impact of eddy energy dissipation, through bottom drag or lee wave generation, on ocean stratification, ocean heat content, and potentially atmospheric CO2. ©2016. The Authors.
    Print ISSN: 0094-8276
    Electronic ISSN: 1944-8007
    Topics: Geosciences , Physics
    Published by American Geophysical Union
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  • 4
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    Adapting and optimising Fluidity for high-fidelity coastal modelling (2018)
    Elsevier
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    Publication Date: 2018-05-01
    Print ISSN: 0045-7930
    Electronic ISSN: 1879-0747
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Published by Elsevier
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  • 5
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    fenics_ice 1.0: a framework for quantifying initialization uncertainty for time-dependent ice sheet models (2021)
    Copernicus
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    Publication Date: 2021-09-24
    Description: Mass loss due to dynamic changes in ice sheets is a significant contributor to sea level rise, and this contribution is expected to increase in the future. Numerical codes simulating the evolution of ice sheets can potentially quantify this future contribution. However, the uncertainty inherent in these models propagates into projections of sea level rise is and hence crucial to understand. Key variables of ice sheet models, such as basal drag or ice stiffness, are typically initialized using inversion methodologies to ensure that models match present observations. Such inversions often involve tens or hundreds of thousands of parameters, with unknown uncertainties and dependencies. The computationally intensive nature of inversions along with their high number of parameters mean traditional methods such as Monte Carlo are expensive for uncertainty quantification. Here we develop a framework to estimate the posterior uncertainty of inversions and project them onto sea level change projections over the decadal timescale. The framework treats parametric uncertainty as multivariate Gaussian and exploits the equivalence between the Hessian of the model and the inverse covariance of the parameter set. The former is computed efficiently via algorithmic differentiation, and the posterior covariance is propagated in time using a time-dependent model adjoint to produce projection error bars. This work represents an important step in quantifying the internal uncertainty of projections of ice sheet models.
    Print ISSN: 1991-959X
    Electronic ISSN: 1991-9603
    Topics: Geosciences
    Published by Copernicus on behalf of European Geosciences Union.
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  • 6
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    A Geometric Interpretation of Southern Ocean Eddy Form Stress (2019)
    American Meteorological Society
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    Publication Date: 2019-10-01
    Description: An interpretation of eddy form stress via the geometry described by the Eliassen–Palm flux tensor is explored. Complimentary to previous works on eddy Reynolds stress geometry, this study shows that eddy form stress is fully described by a vertical ellipse, whose size, shape, and orientation with respect to the mean flow shear determine the strength and direction of vertical momentum transfers. Following a recent proposal, this geometric framework is here used to form a Gent–McWilliams eddy transfer coefficient that depends on eddy energy and a nondimensional geometric parameter α, bounded in magnitude by unity. The parameter α expresses the efficiency by which eddies exchange energy with baroclinic mean flow via along-gradient eddy buoyancy flux—a flux equivalent to eddy form stress along mean buoyancy contours. An eddy-resolving ocean general circulation model is used to estimate the spatial structure of α in the Southern Ocean and assess its potential to form a basis for parameterization. The eddy efficiency α averages to a low but positive value of 0.043 within the Antarctic Circumpolar Current, consistent with an inefficient eddy field extracting energy from the mean flow. It is found that the low eddy efficiency is mainly the result of that eddy buoyancy fluxes are weakly anisotropic on average. The eddy efficiency is subject to pronounced vertical structure and is maximum at ~3-km depth, where eddy buoyancy fluxes tend to be directed most downgradient. Since α partly sets the eddy form stress in the Southern Ocean, a parameterization for α must reproduce its vertical structure to provide a faithful representation of vertical stress divergence and eddy forcing.
    Print ISSN: 0022-3670
    Electronic ISSN: 1520-0485
    Topics: Geosciences , Physics
    Published by American Meteorological Society
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