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1. Diffusive Staircases in Shear: Dynamics and Heat Transport

   https://doi.org/10.1175/JPO-D-20-0193.1  

   Brown, Justin M.; Radko, Timour (March 2021, Journal of Physical Oceanography)

   null (Ed.)

   Abstract Arctic staircases mediate the heat transport from the warm water of Atlantic origin to the cooler waters of the Arctic mixed layer. For this reason, staircases have received much due attention from the community, and their heat transport has been well characterized for systems in the absence of external forcing. However, the ocean is a dynamic environment with large-scale currents and internal waves being omnipresent, even in regions shielded by sea-ice. Thus, we have attempted to address the effects of background shear on fully developed staircases using numerical simulations. The code, which is pseudo-spectral, evolves the governing equations for a Boussinesq fluid with temperature and salinity in a shearing coordinate system. We find that—– unlike many other double-diffusive systems—the sheared staircase requires three-dimensional simulations to properly capture the dynamics. Our simulations predict shear patterns that are consistent with observations and show that staircases in the presence of external shear should be expected to transport heat and salt at least twice as efficiently as in the corresponding non-sheared systems. These findings may lead to critical improvements in the representation of micro-scale mixing in global climate models. 

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2. Staircase patterns in Hirzebruch surfaces

   https://doi.org/10.4171/cmh/571  

   Magill, Nicki; McDuff, Dusa; Weiler, Morgan (July 2024, Commentarii Mathematici Helvetici)

   The ellipsoidal capacity function of a symplectic four manifoldXmeasures how much the form onXmust be dilated in order for it to admit an embedded ellipsoid of eccentricityz. In most cases there are just finitely many obstructions to such an embedding besides the volume. If there are infinitely many obstructions,Xis said to have a staircase. This paper gives an almost complete description of the staircases in the ellipsoidal capacity functions of the family of symplectic Hirzebruch surfacesH_{b}formed by blowing up the projective plane with weightb. We describe an interweaving, recursively defined, family of obstructions to symplectic embeddings of ellipsoids that show there is an open dense set of shape parametersbthat are blocked, i.e. have no staircase, and an uncountable number of other values ofbthat do admit staircases. The remainingb-values form a countable sequence of special rational numbers that are closely related to the symmetries discussed in Magill–McDuff (arXiv:2106.09143). We show that none of them admit ascending staircases. Conjecturally, none admit descending staircases. Finally, we show that, as long asbis not one of these special rational values, any staircase inH_{b}has irrational accumulation point. A crucial ingredient of our proofs is the new, more indirect approach to using almost toric fibrations in the analysis of staircases by Magill (arXiv:2204.12460). In particular, the structure of the relevant mutations of the set of almost toric fibrations onH_{b}is echoed in the structure of the set of blockedb-intervals. 

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3. An overview of Beaufort Sea eddies, internal waves, and spice from several recent field efforts and implications for acoustic propagation

   https://doi.org/doi.org/10.1121/1.5067423  

   Colosi, John (October 2018, The Journal of the Acoustical Society of America)

   Several recent field efforts have revealed surprisingly complex and dynamic thermohaline structure in the upper ocean of the Beaufort Sea. Solitary and compact eddies with strong temperature contrasts and currents have been observed in multiple locations and are associated with vigorous mixing, staircase structure and intrusive feature formation. While many of the eddies are primarily found in the upper 300-m of the water column, rare deep eddies with cores near 500 to 1000-m depth have also been observed. Internal waves are generally weak with energies an order of magnitude less than mid-latitude values and they show marked dominance by near inertial waves, intermittency, spatial inhomogeneity, and deviations from the Garrett-Munk model. Strong intrusive structure, termed spice, is observed in the upper 150-m of the water column and is associated with the mixed layer and eddy activity. Acoustic implications of the associated sound speed structure will be discussed. 

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4. Initiation of diffusive layering by time-dependent shear

   https://doi.org/10.1017/jfm.2018.790  

   Brown, Justin M.; Radko, Timour (January 2019, Journal of Fluid Mechanics)

   null (Ed.)

   The Arctic halocline is generally stable to the development of double-diffusive and dynamic instabilities – the two major sources of small-scale mixing in the mid-latitude oceans. Despite this, observations show the abundance of double-diffusive staircases in the Arctic Ocean, which suggests the presence of some destabilizing process facilitating the transition from smooth-gradient to layered stratification. Recent studies have shown that an instability can develop in such circumstances if weak static shear is present even when the flow is dynamically and diffusively stable. However, the impact of oscillating shear, associated with the presence of internal gravity waves, has not yet been addressed for the diffusive case. Through two-dimensional simulations of diffusive convection, we have investigated the impact of the magnitude and frequency of externally forced oscillatory shear on the thermohaline-shear instability. Simulations with stochastic shear – characterized by a continuous spectrum of frequencies from inertial to buoyancy – indicate that thermohaline layering does occur due to the presence of destabilizing modes (oscillations of near the buoyancy frequency). These simulations show that such layers appear as well-defined steps in the temperature and salinity profiles. Thus, the thermohaline-shear instability is a plausible mechanism for staircase formation in the Arctic and merits substantial future study. 

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5. 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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