Convolutions on the sphere: commutation with differential operators

Aluie, Hussein

doi:10.1007/s13137-019-0123-9

Cited by 26 publications

(73 citation statements)

References 84 publications

(161 reference statements)

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“…The coarse-graining approach, described in Materials and Methods and in (26,27), allows us to identify the energy deposited by wind stress, , into any band of oceanic scales by a simple spatial filtering of the governing dynamics and deriving the corresponding kinetic energy budget. It is then straightforward to show that the "eddy power" (EP) input by wind is…”

Section: Resultsmentioning

confidence: 99%

Scale of oceanic eddy killing by wind from global satellite observations

et al. 2021

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Wind is the primary driver of the oceanic general circulation, yet the length scales at which this energy transfer occurs are unknown. Using satellite data and a recent method to disentangle multiscale processes, we find that wind deposits kinetic energy into the geostrophic ocean flow only at scales larger than 260 km, on a global average. We show that wind removes energy from scales smaller than 260 km at an average rate of −50 GW, a process known as eddy killing. To our knowledge, this is the first objective determination of the global eddy killing scale. We find that eddy killing is taking place at almost all times but with seasonal variability, peaking in winter, and it removes a substantial fraction (up to 90%) of the wind power input in western boundary currents. This process, often overlooked in analyses and models, is a major dissipation pathway for mesoscales, the ocean’s most energetic scales.

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Section: Resultsmentioning

confidence: 99%

Scale of oceanic eddy killing by wind from global satellite observations

et al. 2021

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“…(B1)] is a reasonable choice. Future research could compare the fluxes with those computed by a convolution on a sphere (Aluie 2019).…”

Section: Conclusion and Discussionmentioning

confidence: 99%

The Submesoscale Kinetic Energy Cascade: Mesoscale Absorption of Submesoscale Mixed Layer Eddies and Frontal Downscale Fluxes

Schubert

Gula

Greatbatch

et al. 2020

Journal of Physical Oceanography

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Mesoscale eddies can be strengthened by the absorption of submesoscale eddies resulting from mixed-layer baroclinic instabilities. This is shown for mesoscale eddies in the Agulhas Current system by investigating the kinetic energy cascade with a spectral and a coarse-graining approach in two model simulations of the Agulhas region. One simulation resolves mixed-layer baroclinic instabilities and one does not. When mixed-layer baroclinic instabilities are included, the largest submesoscale near-surface fluxes occur in winter-time in regions of strong mesoscale activity for upscale as well as downscale directions. The forward cascade at the smallest resolved scales occurs mainly in frontogenetic regions in the upper 30 m of the water column. In the Agulhas ring path, the forward cascade changes to an inverse cascade at a typical scale of mixed-layer eddies (15 km). At the same scale, the largest sources of the upscale flux occur. After the winter, the maximum of the upscale flux shifts to larger scales. Depending on the region, the kinetic energy reaches the mesoscales in spring or early summer aligned with the maximum of mesoscale kinetic energy. This indicates the importance of submesoscale flows for the mesoscale seasonal cycle. A case study shows that the underlying process is the mesoscale absorption of mixed-layer eddies. When mixed-layer baroclinic instabilities are not included in the simulation, the open-ocean upscale cascade in the Agulhas ring path is almost absent. This contributes to a 20 %-reduction of surface kinetic energy at mesoscales larger than 100 km when submesoscale dynamics are not resolved by the model.

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“…On this tangent plane, the distance is defined with respect to latitude θ and longitude φ as

R_{E} {((), {false(θ - θ^{'} false)}^{2} + \frac{{false(φ - φ^{'} false)}^{2}}{\cos^{2} false(θ false)})}^{1 false/ 2},

where R E is the radius of the Earth. This spatial filter does not commute with derivatives and is not appropriate for analyzing energy budgets; more sophisticated methods are required for such applications (Aluie, 2019). The GM parameterization is primarily used in ocean models that do not resolve mesoscale eddies, so it is appropriate to choose a filter width that ensures that mesoscales are smaller than the filter scale.…”

Section: Data and Diagnostic Methodsmentioning

confidence: 99%

Vertical Structure of Ocean Mesoscale Eddies with Implications for Parameterizations of Tracer Transport

Stanley

Bachman

Grooms

2020

J Adv Model Earth Syst

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The Gent-McWilliams parameterization is commonly used in global ocean models to model the advective component of tracer transport effected by unresolved mesoscale eddies. The vertical structure of the transfer coefficient in this parameterization is studied using data from a 0.1 • resolution global ocean-ice simulation. The vertical structure is found to be well approximated by a baroclinic mode structure with no flow at the bottom, though horizontal anisotropy is crucial for obtaining a good fit. This vertical structure is motivated by reference to the vertical structure of mesoscale eddy velocity and density anomalies, which are also diagnosed from the data. Plain Language Summary Ocean mesoscale eddies transport tracers like heat, salt, and dissolved carbon dioxide, inter alia. In numerical models where these eddies are not resolved, their effects need to be parameterized. This research addresses the vertical structure of a widely used parameterization, and connects the results to vertical structure of the eddies themselves. In this combined parameterization there is one J that applies for every tracer (Bachman et al., 2015). The symmetric part of the 3 × 3 matrix J corresponds to diffusion (or anti-diffusion, depending on the sign of the

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Convolutions on the sphere: commutation with differential operators

Cited by 26 publications

References 84 publications

Scale of oceanic eddy killing by wind from global satellite observations

Scale of oceanic eddy killing by wind from global satellite observations

The Submesoscale Kinetic Energy Cascade: Mesoscale Absorption of Submesoscale Mixed Layer Eddies and Frontal Downscale Fluxes

Vertical Structure of Ocean Mesoscale Eddies with Implications for Parameterizations of Tracer Transport

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