The Rough Ocean

• Hajduk, Hennes (2025). Improvements of algebraic flux-correction schemes based on Bernstein finite elements. Journal of Numerical Mathematics. ISSN 1570-2820. 33(4), p. 375–402. doi: 10.1515/jnma-2024-0098. Full text in Research Archive Show summary

  In Galerkin finite element schemes, the discrete first derivative operator for each spatial dimension is a square matrix that is skew-symmetric under restrictive assumptions for certain types of discretizations and boundary conditions. In most settings, however, this desirable property is violated, often only for a few pairs of nodes. These exceptions can invalidate certain design principles based on the skew-symmetry assumption made for these operators. This paper demonstrates that algebraic manipulations can be performed to make the discrete gradient operators of Bernstein polynomial-based finite element methods skew symmetric. Interest in such discretizations has recently been increasing because they represent natural extensions of second-order algebraic flux correction schemes to higher-order spaces. We employ the new operators in the context of such property-preserving methods, mostly based on discontinuous Galerkin discretizations of arbitrary order. Additional theoretical results for the schemes under investigation are derived, including local and global entropy inequalities, among others. Moreover, a discussion on the optimality of CFL-like time step restrictions arising in explicit Runge–Kutta methods shows that our new approach is superior to earlier representatives of operators employed in similar contexts. These techniques use the monolithic convex limiting paradigm and are applied to the compressible Euler equations.

• Sjur, Anna Lina Petruseviciute; Isachsen, Pål Erik; Johan, Nilsson; Lacasce, Joseph Henry & Ryseth, Magnus Dyrmose (2025). The Wind-Driven Time-Variable Circulation in the Arctic Mediterranean. Journal of Geophysical Research (JGR): Oceans. ISSN 2169-9275. 130(4), p. 1–20. doi: 10.1029/2024JC021713. Full text in Research Archive Show summary

  The Arctic Ocean is a key component of Earth's climate system, and an understanding of ocean dynamics in this region is central for predicting how the Arctic is responding to a changing climate. In this study, we examine the ocean circulation in a high-resolution numerical model of the Arctic Ocean and Nordic Seas. Based on what is observed in this simulation, we reexamine an existing idealized linear model estimating the time-variable large-scale circulation in ocean basins, and test it against the highly nonlinear numerical model. The idealized model is an integral relation derived from the linear momentum equations and assumes that the circulation around a closed depth contour is driven by surface stresses and regulated by bottom friction. We show that the idealized model estimates agree very well with the numerical simulations. This indicates that much of the variability of the large-scale circulation can be explained by linear processes. In particular, a correct description of the net surface stress over partially ice-covered areas improves the correlation between linear model and numerical simulations significantly in the Arctic Ocean compared to a previous study. However, undetected in that previous study, we now find that the linear model might be lacking a cyclonic tendency.

• Sterl, Miriam F.; Palóczy, André; Groeskamp, Sjoerd; Baatsen, Michiel; Lacasce, Joseph Henry & Isachsen, Pål Erik (2025). The joint effects of planetary β, topography and friction on baroclinic instability in a two-layer QG model. Journal of Fluid Mechanics. ISSN 0022-1120. 1012. doi: 10.1017/jfm.2025.10172. Full text in Research Archive Show summary

  The quasi-geostrophic two-layer model is a widely used tool to study baroclinic instability in the ocean. One instability criterion for the inviscid two-layer model is that the potential vorticity (PV) gradient must change sign between the layers. This has a well-known implication if the model includes a linear bottom slope: for sufficiently steep retrograde slopes, instability is suppressed for a flow parallel to the isobaths. This changes in the presence of bottom friction as well as when the PV gradients in the layers are not aligned. We derive the generalised instability condition for the two-layer model with non-zero friction and arbitrary mean flow orientation. This condition involves neither the friction coefficient nor the bottom slope; even infinitesimally weak bottom friction destabilises the system regardless of the bottom slope. We then examine the instability characteristics as a function of varying slope orientation and magnitude. The system is stable across all wavenumbers only if friction is absent and if the planetary, topographic and stretching PV gradients are aligned. Strong bottom friction decreases the growth rates but also alters the dependence on bottom slope. In conclusion, the often mentioned stabilisation by steep bottom slopes in the two-layer model holds only in very specific circumstances, thus probably plays only a limited role in the ocean.

• Johnston, Shaun; Sjur, Anna Lina Petruseviciute; Isachsen, Pål Erik & Lacasce, Joseph Henry (2025). Eddy- and wind-driven circulation in the enclosed basins of the Norwegian Sea evaluated using a model and absolute geostrophic flow from Argo. Journal of Geophysical Research (JGR): Oceans. ISSN 2169-9275. 130(7). doi: 10.1029/2024JC021990. Full text in Research Archive Show summary

  Cyclonic flow in enclosed basins arises from cyclonic vorticity input from either winds or eddies. Previous observations show winds account for about half of the circulation (integral of parallel velocity around a closed isobath) in the Lofoten Basin of the Norwegian Sea, implying a comparable contribution from eddies. In contrast, in the Norwegian Basin, winds explain much of the circulation. We use Argo data from 2012 to 2022, a linear wind-forced and bottom friction-regulated model, and a primitive equation model to investigate how winds and eddies drive the circulation. While Argo cannot resolve individual eddies, it does resolve mesoscale spatial variability. Absolute geostrophic velocities to 2,000 m are calculated by referencing geostrophic shear from objective maps of the profile data to the trajectories at 1,000 m. The time-mean shear is anticyclonic. However, the flow is mostly cyclonic, bottom-intensified, and isobath following. The linear model explains less than half of the observed circulation, suggesting a contribution from an unobserved eddy flux. This interpretation is supported by a numerical model with 800-m horizontal resolution, which resolves the 10–15-km deformation radius. In this model, the difference between the full and linear response comes from an eddy-driven vorticity flux, which produces a largely cyclonic circulation. This result is consistent with the observed global prevalence of positive topostrophy (anticyclonic flow around elevations and cyclonic flow around basins). The observations also show a seasonal shift in the eddy flux, which maybe related to a decadal-scale fresh inflow that alters the density gradient and influences eddy production.

• Sterl, Miriam F.; Lacasce, Joseph Henry; Groeskamp, Sjoerd; Nummelin, Aleksi Henrynpoika; Isachsen, Pål Erik & Baatsen, Michiel L. J. (2024). Suppression of Mesoscale Eddy Mixing by Topographic PV Gradients. Journal of Physical Oceanography. ISSN 0022-3670. 54(5), p. 1089–1103. doi: 10.1175/JPO-D-23-0142.1. Full text in Research Archive Show summary

  Oceanic mesoscale eddy mixing plays a crucial role in Earth’s climate system by redistributing heat, salt, and carbon. For many ocean and climate models, mesoscale eddies still need to be parameterized. This is often done via an eddy diffusivity K , which sets the strength of turbulent downgradient tracer fluxes. A well-known effect is the modulation of K in the presence of background potential vorticity (PV) gradients, which suppresses mixing in the direction of the PV gradients. Topographic slopes can induce such suppression through topographic PV gradients. However, this effect has received little attention, and topographic effects are often not included in parameterizations for K . In this study, we show that it is possible to describe the effect of topography on K analytically in a barotropic framework, using a simple stochastic representation of eddy–eddy interactions. We obtain an analytical expression for the depth-averaged K as a function of the bottom slope, which we validate against diagnos

• Madan, Gaurav; Gjermundsen, Ada; Iversen, Silje Christine & Lacasce, Joseph Henry (2023). The weakening AMOC under extreme climate change. Climate Dynamics. ISSN 0930-7575. 62, p. 1291–1309. doi: 10.1007/s00382-023-06957-7. Full text in Research Archive Show summary

  Changes in the Atlantic Meridional Overturning Circulation (AMOC) in the quadrupled CO₂ experiments conducted under the sixth Coupled Model Intercomparison Project (CMIP6) are examined. Increased CO₂ triggers extensive Arctic warming, causing widespread melting of sea ice. The resulting freshwater spreads southward, frst from the Labrador Sea and then the Nordic Seas, and proceeds along the eastern coast of North America. The freshwater enters the subpolar gyre north of the separated Gulf Stream, the North Atlantic Current. This decreases the density gradient across the current and the current weakens in response, reducing the infow to the deepwater production regions. The AMOC cell weakens in tandem, frst near the North Atlantic Current and then spreading to higher and lower latitudes. This contrasts with the common perception that freshwater caps the convection regions, stifing deepwater production; rather, it is the infow to the subpolar gyre that is suppressed. Changes in surface temperature have a much weaker effect, and there are no consistent changes in local or remote wind forcing among the models. Thus an increase in freshwater discharge, primarily from the Labrador Sea, is the precursor to AMOC weakening in these simulations.

• Brown, Nicola; Mauritzen, Cecilie; Li, Camille; Madonna, Erica; Isachsen, Pål Erik & Lacasce, Joseph Henry (2023). Rapid Response of the Norwegian Atlantic Slope Current to Wind Forcing. Journal of Physical Oceanography. ISSN 0022-3670. 53(2), p. 389–408. doi: 10.1175/JPO-D-22-0014.1. Full text in Research Archive Show summary

  We explore drivers of variability in the Norwegian Atlantic Slope Current, which carries relatively warm Atlantic Water toward the Barents Sea and Arctic Ocean, using Copernicus Marine Environment Monitoring Service (CMEMS) satellite altimetry data and TOPAZ4 ocean reanalysis data. Previous studies have pointed to a variety of causes, on a variety of time scales. We use data with daily resolution to investigate day-to-day changes in ocean transport across three sections crossing the shelf-slope of Norway (Svinøy, Gimsøy, and the Barents Sea Opening). The highest (lowest) extremes in transport at all sections develop over two days as a cyclonic (anticyclonic) atmospheric pressure system approaches from the southwest, piling up (extracting) water at the coast of Norway. The actual peak is reached when the pressure system passes the site of measurement, and the transport then relaxes for the next two days as the system continues northward along the coast. Other sources of short-term variability, such as propagating continental shelf waves and baroclinic instability, are unlikely to yield covariability over large separations. Monthly variability in the current can also be explained by passing weather systems since their numbers and intensity vary greatly from month to month. Many studies of longer-term variability, especially in the Barents Sea Opening, have pointed to the North Atlantic Oscillation (NAO) as the main cause of variability. Our results show that passing weather systems offer a better explanation of month-to-month variability.

• Klocker, Andreas; Munday, David; Gayen, Bishakhdatta; Roquet, Fabien & Lacasce, Joseph Henry (2023). Deep-Reaching Global Ocean Overturning Circulation Generated by Surface Buoyancy Forcing. Tellus A: Dynamic Meteorology and Oceanography. ISSN 0280-6495. 75(1), p. 392–409. doi: 10.16993/tellusa.3231. Full text in Research Archive Show summary

  In contrast with the atmosphere, which is heated from below by solar radiation, the ocean is both heated and cooled from above. To drive a deep-reaching overturning circulation in this context, it is generally assumed that either intense interior mixing by winds and internal tides, or wind-driven upwelling is required; in their absence, the circulation is thought to collapse to a shallow surface cell. We demonstrate, using a primitive equation model with an idealized domain and no wind forcing, that the surface temperature forcing can in fact drive an interhemispheric overturning provided that there is an open channel unblocked in the zonal direction, such as in the Southern Ocean. With this geometry, rotating horizontal convection, in combination with asymmetric surface cooling between the north and south, drives a deep-reaching two-cell overturning circulation. The resulting vertical mid-depth stratification closely resembles that of the real ocean, suggesting that wind-driven pumping is not necessary to produce a deep-reaching overturning circulation, and that buoyancy forcing plays a more important role than is usually assumed.

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