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Zonostrophic instability leads to the spontaneous emergence of zonal jets on a β plane from a jetless basic-state flow that is damped by bottom drag and driven by a random body force. Decomposing the barotropic vorticity equation into the zonal mean and eddy equations, and neglecting the eddy–eddy interactions, defines the quasilinear (QL) system. Numerical solution of the QL system shows zonal jets with length scales comparable to jets obtained by solving the nonlinear (NL) system. Starting with the QL system, one can construct a deterministic equation for the evolution of the two-point single-time correlation function of the vorticity, from which one can obtain the Reynolds stress that drives the zonal mean flow. This deterministic system has an exact nonlinear solution, which is an isotropic and homogenous eddy field with no jets. The authors characterize the linear stability of this jetless solution by calculating the critical stability curve in the parameter space and successfully comparing this analytic result with numerical solutions of the QL system. But the critical drag required for the onset of NL zonostrophic instability is sometimes a factor of 6 smaller than that for QL zonostrophic instability. Near the critical stability curve, the jet scale predicted by linear stability theory agrees with that obtained via QL numerics. But on reducing the drag, the emerging QL jets agree with the linear stability prediction at only short times. Subsequently jets merge with their neighbors until the flow matures into a state with jets that are significantly broader than the linear prediction but have spacing similar to NL jets.

We show that the submesoscale inverse cascade almost entirely drives the mesoscale kinetic energy (KE) seasonal cycle in the interior subtropical gyre. Using a coarse‐graining framework to diagnose cross‐scale energy fluxes (Πh${{\\Pi }}_{h}$ ), we show the forward cascade remains confined to <20 km within the mixed layer, peaking January–March. The inverse cascade exhibits a dramatic upscale shift: its peak scale expands from ∼30 km in January to ∼200 km by June while penetrating vertically below the mixed layer by March. The observed cascade timescale (∼180 days) far exceeds predictions from classical turbulence theory (∼40 days), revealing fundamental departures from idealized quasi‐geostrophic dynamics. This horizontal and vertical expansion establishes the pathway whereby submesoscale eddies energize mesoscale motions. Lead‐lag analysis reveals potential energy conversion precedes frontogenesis by 7–21 days, submesoscale eddies by 9–23 days, and peak Πh${{\\Pi }}_{h}$by 20–90 days, which in turn leads large‐scale KE by 30–70 days.

An idealized framework of steady barotropic flow past an isolated seamount in a background of constant stratification (with frequency N ) and rotation (with Coriolis parameter f ) is used to examine the formation, separation, instability of the turbulent bottom boundary layers (BBLs), and ultimately, the genesis of submesoscale coherent vortices (SCVs) in the ocean interior. The BBLs generate vertical vorticity ζ and potential vorticity q on slopes; the flow separates and spawns shear layers; barotropic and centrifugal shear instabilities form submesoscale vortical filaments and induce a high rate of local energy dissipation; the filaments organize into vortices that then horizontally merge and vertically align to form SCVs. These SCVs have O (1) Rossby numbers ( ) and horizontal and vertical scales that are much larger than those of the separated shear layers and associated vortical filaments. Although the upstream flow is barotropic, downstream baroclinicity manifests in the wake, depending on the value of the nondimensional height , which is the ratio of the seamount height to that of the Taylor height , where L is the seamount half-width. When , SCVs span the vertical extent of the seamount itself. However, for , there is greater range of variation in the sizes of the SCVs in the wake, reflecting the wake baroclinicity caused by the topographic interaction. The aspect ratio of the wake SCVs has the scaling , instead of the quasigeostrophic scaling .

We parameterize sub‐grid scale (SGS) fluxes in sinusoidally forced two‐dimensional turbulence on the β‐plane at high Reynolds numbers (Re ∼25,000) using simple 2‐layer convolutional neural networks (CNN) having only O(1000) parameters, two orders of magnitude smaller than recent studies employing deeper CNNs with 8–10 layers; we obtain stable, accurate, and long‐term online or a posteriori solutions at 16× downscaling factors. Our methodology significantly improves training efficiency and speed of online large eddy simulations runs, while offering insights into the physics of closure in such turbulent flows. Our approach benefits from extensive hyperparameter searching in learning rate and weight decay coefficient space, as well as the use of cyclical learning rate annealing, which leads to more robust and accurate online solutions compared to fixed learning rates. Our CNNs use either the coarse velocity or the vorticity and strain fields as inputs, and output the two components of the deviatoric stress tensor, Sd. We minimize a loss between the SGS vorticity flux divergence (computed from the high‐resolution solver) and that obtained from the CNN‐modeled Sd, without requiring energy or enstrophy preserving constraints. The success of shallow CNNs in accurately parameterizing this class of turbulent flows implies that the SGS stresses have a weak non‐local dependence on coarse fields; it also aligns with our physical conception that small‐scales are locally controlled by larger scales such as vortices and their strained filaments. Furthermore, 2‐layer CNN‐parameterizations are more likely to be interpretable. Plain Language Summary In this study, we demonstrate that simple, shallow neural networks can be used to effectively model complex turbulent flows in the atmosphere and oceans. By using these simpler NNs, we can improve the efficiency of our simulations and better understand the underlying physics of turbulent flows. We also explore different training techniques to make these models more accurate and robust. Our findings suggest that the stress in these turbulent flows has only a weak spatial dependence on larger‐scale features, which has important implications for our understanding of how turbulence behaves. Overall, our work can help improve climate and weather models by providing a more efficient and interpretable way to simulate turbulence. Key Points Shallow convolutional neural networks (CNNs) accurately parameterize high Reynolds number forced2D turbulence, with efficient training and high online large eddy simulations accuracy Extensive hyperparameter searching and cyclical learning rates yield robust and accurate online solutions for CNN‐based turbulence models The success of shallow CNNs implies nearly‐local dependence of SGS stresses providing insights into turbulent flow interactions

The distribution and strength of submesoscale (SM) surface layer fronts and filaments generated through mixed layer baroclinic energy conversion and submesoscale coherent vortices (SCVs) generated by topographic drag are analyzed in numerical simulations of the near-surface southwestern Pacific, north of 16°S. In the Coral Sea a strong seasonal cycle in the surface heat flux leads to a winter SM “soup” consisting of baroclinic mixed layer eddies (MLEs), fronts, and filaments similar to those seen in other regions farther away from the equator. However, a strong wind stress seasonal cycle, largely in sync with the surface heat flux cycle, is also a source of SM processes. SM restratification fluxes show distinctive signatures corresponding to both surface cooling and wind stress. The winter peak in SM activity in the Coral Sea is not in phase with the summer dominance of the mesoscale eddy kinetic energy in the region, implying that local surface layer forcing effects are more important for SM generation than the nonlocal eddy deformation field. In the topographically complex Solomon and Bismarck Seas, a combination of equatorial proximity and boundary drag generates SCVs with large-vorticity Rossby numbers (Ro ~ 10). River outflows in the Bismarck and Solomon Seas make a contribution to SM generation, although they are considerably weaker than the topographic effects. Mean to eddy kinetic energy conversions implicate barotropic instability in SM topographic wakes, with the strongest values seen north of the Vitiaz Strait along the coast of Papua New Guinea.

The upwelling of warm Circumpolar Deep Water is a key process in the global climate system, transporting heat, nutrients, and carbon poleward towards Antarctic ice shelves. Here we use physical and chemical seawater properties from repeat ship-based observations to classify Southern Ocean water masses and show changes in warm water abundance south of the Antarctic Circumpolar Current over the past two decades. We then train a random forest model ensemble to extend this classification to a monthly gridded Argo climatology beginning in 2004, enabling further decomposition of the spatial and temporal variability of the signal. Both analyses reveal an increase in upper-2000 m warm water thickness near the continent, consistent with a circumpolar-mean poleward redistribution of the upper Circumpolar Deep Water core of 1.26km yr −1 (95% CI: 0.53–1.98). Together, these shifts suggest enhanced heat flux towards the Antarctic shelf, with implications for basal ice shelf melting and sea-level rise. Circumpolar Deep Water is increasing in thickness towards Antarctica in the upper 2000 m of the Southern Ocean, according to analyses of ship-based observations combined with machine learning modelling applied to Argo float data.

Genetic regulation of gene expression, revealed by expression quantitative trait loci (eQTLs), exhibits complex patterns of tissue-specific effects. Characterization of these patterns may allow us to better understand mechanisms of gene regulation and disease etiology. We develop a constrained matrix factorization model, sn-spMF, to learn patterns of tissue-sharing and apply it to 49 human tissues from the Genotype-Tissue Expression (GTEx) project. The learned factors reflect tissues with known biological similarity and identify transcription factors that may mediate tissue-specific effects. sn-spMF, available at https://github.com/heyuan7676/ts_eQTLs , can be applied to learn biologically interpretable patterns of eQTL tissue-specificity and generate testable mechanistic hypotheses.

Oceanic internal waves are a major driver for turbulent mixing in the ocean, which controls the global overturning circulation and the oceanic heat and carbon transport. Internal waves are observed to have a continuous energy distribution across all wave frequencies and scales, commonly known as the internal wave continuum, despite being forced at near-inertial and tidal frequencies at large scales. This internal wave continuum is widely thought to be developed primarily through wave-wave interactions. Here we show, using realistic numerical simulations in the subpolar North Atlantic, that oceanic eddies rapidly distribute large-scale wind-forced near-inertial wave energy across spatio-temporal scales, thereby forming an internal wave continuum within three weeks. As a result, wave energy dissipation patterns are controlled by eddies and are substantially enhanced below the mixed layer. The efficiency of this process potentially explains why a phase lag between high-frequency and near-inertial wave energy was observed in eddy-poor regions but not in eddy-rich regions. Our findings highlight the importance of eddies in forming an internal wave continuum and in controlling upper ocean mixing patterns.

The meridional overturning circulation (MOC) plays a crucial role in the global distribution of heat, carbon, and other climate‐relevant tracers. Monitoring the evolution of MOC is essential for understanding climate variability, yet direct MOC observations are sparse and geographically limited. Although satellite measurements have shown potential for short‐term monitoring of the MOC, it remains unclear whether MOC variability on decadal and longer timescales can be detected remotely. In this study, we leverage machine learning to reconstruct long‐term MOC variability from satellite‐measurable quantities, using climate simulations under pre‐industrial conditions. We demonstrate that our proposed non‐local dual‐branch neural network (DBNN) effectively reconstructs both the strength and vertical structure of the Atlantic MOC (AMOC) and the Southern Ocean MOCs across sub‐annual to multi‐decadal timescales. Using a neural network interpretation technique, we identify ocean bottom pressure near the western boundary and along dense‐water export pathways as the dominant input features for MOC reconstruction. This indicates that DBNN's predictions can be interpreted as an approximation of geostrophic balance. The DBNN also effectively reconstructs the AMOC in the equatorial region, where geostrophy breaks down. This success is attributed to the capability of DBNN in utilizing latitudinally non‐local ocean bottom pressure information and the meridional coherence of AMOC variability. Additionally, the DBNN accurately reconstructs Southern Ocean MOCs using only sea surface height and zonal wind stress as inputs, thereby avoiding reliance on ocean bottom pressure, which is subject to considerable measurement uncertainty in practice. This work demonstrates the possibility of continuous, long‐term MOC monitoring using satellite measurements. Plain Language Summary The meridional overturning circulation (MOC) is a key ocean circulation system that moves heat, carbon, and other important tracers throughout the globe. Changes in the MOC, especially over decades or longer, greatly influence global climate. It is important to track these changes to better understand climate variability, but direct MOC measurements are logistically challenging and resource‐intensive. A possible solution is using satellite data, like sea surface height, to monitor the MOC remotely. Previous research has managed to track monthly‐to‐yearly changes of MOC using this indirect method, but it remains unclear if this can be done over multi‐year or multi‐decadal periods. In this study, we demonstrate the capability of “neural networks” to achieve long‐term MOC monitoring from quantities that satellites can measure, using simulations of hundreds to thousands of years of climate evolution as a test bed. Our approach also performs well near the equator, where traditional methods often fail. We additionally applied a neural network interpretation technique, which reveals that its prediction of the MOC primarily uses local and non‐local information about east‐to‐west pressure changes, consistent with physical expectations. Our results thus provide a pathway toward accurate monitoring of the MOC using satellite data over climate‐relevant timescales. Key Points We developed a non‐local dual‐branch neural network to reconstruct the long‐term variability of the meridional overturning circulation (MOC) Ocean bottom pressure near western boundaries and along dense water export pathways are identified as the dominant input features Latitudinally non‐local ocean bottom pressure information is crucial for equatorial Atlantic MOC reconstruction

Recent years have seen a surge in interest for leveraging neural networks to parameterize small-scale or fast processes in climate and turbulence models. In this short paper, we point out two fundamental issues in this endeavor. The first concerns the difficulties neural networks may experience in capturing rare events due to limitations in how data is sampled. The second arises from the inherent multiscale nature of these systems. They combine high-frequency components (like inertia-gravity waves) with slower, evolving processes (geostrophic motion). This multiscale nature creates a significant hurdle for neural network closures. To illustrate these challenges, we focus on the atmospheric 1980 Lorenz model, a simplified version of the Primitive Equations that drive climate models. This model serves as a compelling example because it captures the essence of these difficulties.