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1. On Baroclinic Instability over Continental Shelves: Testing the Utility of Eady-Type Models

   https://doi.org/10.1175/JPO-D-19-0175.1  

   Chen, Shih-Nan; Chen, Chiou-Jiu; Lerczak, James A. (January 2020, Journal of Physical Oceanography)

   null (Ed.)

   Abstract This study examines the utility of Eady-type theories as applied to understanding baroclinic instability in coastal flows where depth variations and bottom drag are important. The focus is on the effects of nongeostrophy, boundary dissipation, and bottom slope. The approach compares theoretically derived instability properties against numerical model calculations, for experiments designed to isolate the individual effects and justified to have Eady-like basic states. For the nongeostrophic effect, the theory of Stone (1966) is shown to give reasonable predictions for the most unstable growth rate and wavelength. It is also shown that the growing instability in a fully nonlinear model can be interpreted as boundary-trapped Rossby wave interactions—that is, wave phase locking and westward phase tilt allow waves to be mutually amplified. The analyses demonstrate that both the boundary dissipative and bottom slope effects can be represented by vertical velocities at the lower boundary of the unstable interior, via inducing Ekman pumping and slope-parallel flow, respectively, as proposed by the theories of Williams and Robinson (1974; referred to as the Eady–Ekman problem) and Blumsack and Gierasch (1972). The vertical velocities, characterized by a friction parameter and a slope ratio, modify the bottom wave and thus the scale selection. However, the theories have inherent quantitative limitations. Eady–Ekman neglects boundary layer responses that limit the increase of bottom stress, thereby overestimating the Ekman pumping and growth rate reduction at large drag. Blumsack and Gierasch’s (1972) model ignores slope-induced horizontal shear in the mean flow that tilts the eddies to favor converting energy back to the mean, thus having limited utility over steep slopes. 

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2. Energetics and mixing in buoyancy-driven near-bottom stratified flow

   https://doi.org/10.1017/jfm.2019.184  

   Puthan, Pranav; Jalali, Masoud; Chalamalla, Vamsi K.; Sarkar, Sutanu (June 2019, Journal of Fluid Mechanics)

   Turbulence and mixing in a near-bottom convectively driven flow are examined by numerical simulations of a model problem: a statically unstable disturbance at a slope with inclination $$\unicode[STIX]{x1D6FD}$$ in a stable background with buoyancy frequency $$N$$ . The influence of slope angle and initial disturbance amplitude are quantified in a parametric study. The flow evolution involves energy exchange between four energy reservoirs, namely the mean and turbulent components of kinetic energy (KE) and available potential energy (APE). In contrast to the zero-slope case where the mean flow is negligible, the presence of a slope leads to a current that oscillates with $$\unicode[STIX]{x1D714}=N\sin \unicode[STIX]{x1D6FD}$$ and qualitatively changes the subsequent evolution of the initial density disturbance. The frequency, $$N\sin \unicode[STIX]{x1D6FD}$$ , and the initial speed of the current are predicted using linear theory. The energy transfer in the sloping cases is dominated by an oscillatory exchange between mean APE and mean KE with a transfer to turbulence at specific phases. In all simulated cases, the positive buoyancy flux during episodes of convective instability at the zero-velocity phase is the dominant contributor to turbulent kinetic energy (TKE) although the shear production becomes increasingly important with increasing  $$\unicode[STIX]{x1D6FD}$$ . Energy that initially resides wholly in mean available potential energy is lost through conversion to turbulence and the subsequent dissipation of TKE and turbulent available potential energy. A key result is that, in contrast to the explosive loss of energy during the initial convective instability in the non-sloping case, the sloping cases exhibit a more gradual energy loss that is sustained over a long time interval. The slope-parallel oscillation introduces a new flow time scale $$T=2\unicode[STIX]{x03C0}/(N\sin \unicode[STIX]{x1D6FD})$$ and, consequently, the fraction of initial APE that is converted to turbulence during convective instability progressively decreases with increasing $$\unicode[STIX]{x1D6FD}$$ . For moderate slopes with $$\unicode[STIX]{x1D6FD}<10^{\circ }$$ , most of the net energy loss takes place during an initial, short ( $$Nt\approx 20$$ ) interval with periodic convective overturns. For steeper slopes, most of the energy loss takes place during a later, long ( $Nt>100$ ) interval when both shear and convective instability occur, and the energy loss rate is approximately constant. The mixing efficiency during the initial period dominated by convectively driven turbulence is found to be substantially higher (exceeds 0.5) than the widely used value of 0.2. The mixing efficiency at long time in the present problem of a convective overturn at a boundary varies between 0.24 and 0.3. 

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3. 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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4. A Stable Implementation of a Data‐Driven Scale‐Aware Mesoscale Parameterization

   https://doi.org/10.1029/2023MS004104  

   Perezhogin, Pavel; Zhang, Cheng; Adcroft, Alistair; Fernandez‐Granda, Carlos; Zanna, Laure (October 2024, Journal of Advances in Modeling Earth Systems)

   Ocean mesoscale eddies are often poorly represented in climate models, and therefore, their effects on the large scale circulation must be parameterized. Traditional parameterizations, which represent the bulk effect of the unresolved eddies, can be improved with new subgrid models learned directly from data. Zanna and Bolton (ZB20) applied an equation‐discovery algorithm to reveal an interpretable expression parameterizing the subgrid momentum fluxes by mesoscale eddies through the components of the velocity‐gradient tensor. In this work, we implement the ZB20 parameterization into the primitive‐equation GFDL MOM6 ocean model and test it in two idealized configurations with significantly different dynamical regimes and topography. The original parameterization was found to generate excessive numerical noise near the grid scale. We propose two filtering approaches to avoid the numerical issues and additionally enhance the strength of large‐scale energy backscatter. The filtered ZB20 parameterizations led to improved climatological mean state and energy distributions, compared to the current state‐of‐the‐art energy backscatter parameterizations. The filtered ZB20 parameterizations are scale‐aware and, consequently, can be used with a single value of the non‐dimensional scaling coefficient for a range of resolutions. The successful application of the filtered ZB20 parameterizations to parameterize mesoscale eddies in two idealized configurations offers a promising opportunity to reduce long‐standing biases in global ocean simulations in future studies. 

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5. Investigation of oscillations in katabatic Prandtl slope flows

   https://doi.org/10.1002/qj.4405  

   Henao‐Garcia, Sebastian; Xiao, Cheng‐Nian; Senocak, Inanc (January 2023, Quarterly Journal of the Royal Meteorological Society)

   Abstract Dynamically unstable katabatic Prandtl slope flows are studied via numerical simulations and spectral analysis. Results confirm the presence of aperiodic temporal and spatial oscillations in the flow fields due to the emergence and propagation of flow instabilities. Dampeden masseoscillations are observed to dominate the initial oscillatory stage of laminar katabatic slope flows. Stationary longitudinal rolls, which are dominant at shallow slopes, are observed to meander with increasing stratification perturbation parameter and the average distance between the rolls exhibits a strong dependence on slope inclination for slope angles less than . At much steeper slopes, traveling slope waves emerge and they are transported at the mean jet velocity. Both types of instability rolls coexist for certain combinations of dimensionless parameters, forming intricate structures that break into smaller eddies as the flow becomes more dynamically unstable. In the dynamically unstable nonturbulent regime,en masseoscillations are insignificant, but their normalised frequency can be used to discern the type of flow instability. 

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