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1. Wave-averaged balance: a simple example

   https://doi.org/10.1017/jfm.2020.1032  

   Kafiabad, Hossein A.; Vanneste, Jacques; Young, William R. (March 2021, Journal of Fluid Mechanics)

   null (Ed.)

   In the presence of inertia-gravity waves, the geostrophic and hydrostatic balance that characterises the slow dynamics of rapidly rotating, strongly stratified flows holds in a time-averaged sense and applies to the Lagrangian-mean velocity and buoyancy. We give an elementary derivation of this wave-averaged balance and illustrate its accuracy in numerical solutions of the three-dimensional Boussinesq equations, using a simple configuration in which vertically planar near-inertial waves interact with a barotropic anticylonic vortex. We further use the conservation of the wave-averaged potential vorticity to predict the change in the barotropic vortex induced by the waves. 

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2. Stirring of interior potential vorticity gradients as a formation mechanism for large subsurface-intensified eddies in the Beaufort Gyre

   https://doi.org/10.1175/JPO-D-21-0040.1  

   Manucharyan, Georgy E.; Stewart, Andrew L. (August 2022, Journal of Physical Oceanography)

   Abstract The Beaufort Gyre (BG) is hypothesized to be partially equilibrated by those mesoscale eddies that form via baroclinic instabilities of its currents. However, our understanding of the eddy field’s dependence on the mean BG currents and the role of sea ice remains incomplete. This theoretical study explores the scales and vertical structures of eddies forming specifically due to baroclinic instabilities of interior BG flows. An idealized quasi-geostrophic model is used to show that flows driven only by the Ekman pumping contain no interior potential vorticity (PV) gradients and generate weak and large eddies, ℴ(200km) in size, with predominantly barotropic and first baroclinic mode energy. However, flows containing realistic interior PV gradients in the Pacific halocline layer generate significantly smaller eddies of about 50 km in size, with a distinct second baroclinic mode structure and a subsurface kinetic energy maximum. The dramatic change in eddy characteristics is shown to be caused by the stirring of interior PV gradients by large-scale barotropic eddies. The sea ice-ocean drag is identified as the dominant eddy dissipation mechanism, leading to realistic sub-surface maxima of eddy kinetic energy for drag coefficients higher than about 2×10 −3 . A scaling law is developed for the eddy potential enstrophy, demonstrating that it is directly proportional to the interior PV gradient and the square root of the barotropic eddy kinetic energy. This study proposes a possible formation mechanism of large BG eddies and points to the importance of accurate representation of the interior PV gradients and eddy dissipation by ice-ocean drag in BG simulations and theory. 

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3. Eddy–Internal Wave Interactions and Their Contribution to Cross-Scale Energy Fluxes: A Case Study in the California Current

   https://doi.org/10.1175/JPO-D-23-0181.1  

   Delpech, Audrey; Barkan, Roy; Srinivasan, Kaushik; McWilliams, James_C; Arbic, Brian_K; Siyanbola, Oladeji_Q; Buijsman, Maarten_C (March 2024, Journal of Physical Oceanography)

   Abstract Oceanic mixing, mostly driven by the breaking of internal waves at small scales in the ocean interior, is of major importance for ocean circulation and the ocean response to future climate scenarios. Understanding how internal waves transfer their energy to smaller scales from their generation to their dissipation is therefore an important step for improving the representation of ocean mixing in climate models. In this study, the processes leading to cross-scale energy fluxes in the internal wave field are quantified using an original decomposition approach in a realistic numerical simulation of the California Current. We quantify the relative contribution of eddy–internal wave interactions and wave–wave interactions to these fluxes and show that eddy–internal wave interactions are more efficient than wave–wave interactions in the formation of the internal wave continuum spectrum. Carrying out twin numerical simulations, where we successively activate or deactivate one of the main internal wave forcing, we also show that eddy–near-inertial internal wave interactions are more efficient in the cross-scale energy transfer than eddy–tidal internal wave interactions. This results in the dissipation being dominated by the near-inertial internal waves over tidal internal waves. A companion study focuses on the role of stimulated cascade on the energy and enstrophy fluxes. 

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4. A generalized wave-vortex decomposition for rotating Boussinesq flows with arbitrary stratification

   https://doi.org/10.1017/jfm.2020.995  

   Early, Jeffrey J.; Lelong, M.P.; Sundermeyer, M.A. (April 2021, Journal of Fluid Mechanics)

   null (Ed.)

   The energetically independent linear wave and geostrophic (vortex) solutions are shown to be a complete basis for velocity and density variables $$(u,v,w,\rho )$$ in a rotating non-hydrostatic Boussinesq fluid with arbitrary stratification and non-periodic vertical boundaries. This work extends the familiar wave-vortex decomposition for triply periodic domains with constant stratification. As a consequence of the decomposition, the fluid can be unambiguously separated into decoupled linear wave and geostrophic components at each instant in time, without the need for temporal filtering. The fluid can then be diagnosed for temporal changes in wave and geostrophic coefficients at each unique wavenumber and mode, including those that inevitably occur due to nonlinear interactions. We demonstrate that this methodology can be used to determine which physical interactions cause the transfer of energy between modes by projecting the nonlinear equations of motion onto the wave-vortex basis. In the particular example given, we show that an eddy in geostrophic balance superimposed with inertial oscillations at the surface transfers energy from the inertial oscillations to internal gravity wave modes. This approach can be applied more generally to determine which mechanisms are involved in energy transfers between wave and vortices, including their respective scales. Finally, we show that the nonlinear equations of motion expressed in a wave-vortex basis are computationally efficient for certain problems. In cases where stratification profiles vary strongly with depth, this approach may be an attractive alternative to traditional spectral models for rotating Boussinesq flow. 

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5. Coastally Generated Near-Inertial Waves

   https://doi.org/10.1175/JPO-D-18-0148.1  

   Kelly, Samuel M. (November 2019, Journal of Physical Oceanography)

   Wind directly forces inertial oscillations in the mixed layer. Where these currents hit the coast, the no-normal-flow boundary condition leads to vertical velocities that pump both the base of the mixed layer and the free surface, producing offshore-propagating near-inertial internal and surface waves, respectively. The internal waves directly transport wind work downward into the ocean’s stratified interior, where it may provide mechanical mixing. The surface waves propagate offshore where they can scatter over rough topography in a process analogous to internal-tide generation. Here, we estimate mixed layer currents from observed winds using a damped slab model. Then, we estimate the pressure, velocity, and energy flux associated with coastally generated near-inertial waves at a vertical coastline. These results are extended to coasts with arbitrary across-shore topography and examined using numerical simulations. At the New Jersey shelfbreak, comparisons between the slab model, numerical simulations, and moored observations are ambiguous. Extrapolation of the theoretical results suggests that [Formula: see text](10%) of global wind work (i.e., 0.03 of 0.31 TW) is transferred to coastally generated barotropic near-inertial waves. 

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