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In this work, we consider a Shallow‐Water Quasi Geostrophic equation on the sphere, as a model for global large‐scale atmospheric dynamics. This equation, previously studied by Verkley (2009, https://doi.org/10.1175/2008jas2837.1) and Schubert et al. (2009, https://doi.org/10.3894/james.2009.1.2), possesses a rich geometric structure, called Lie‐Poisson, and admits an infinite number of conserved quantities, called Casimirs. In this paper, we develop a Casimir preserving numerical method for long‐time simulations of this equation. The method develops in two steps: first, we construct an N‐dimensional Lie‐Poisson system that converges to the continuous one in the limit N → ∞; second, we integrate in time the finite‐dimensional system using an isospectral time integrator, developed by Modin and Viviani (2020, https://doi.org/10.1017/jfm.2019.944). We demonstrate the efficacy of this computational method by simulating a flow on the entire sphere for different values of the Lamb parameter. We particularly focus on rotation‐induced effects, such as the formation of jets. In agreement with shallow water models of the atmosphere, we observe the formation of robust latitudinal jets and a decrease in the zonal wind amplitude with latitude. Furthermore, spectra of the kinetic energy are computed as a point of reference for future studies. Plain Language Summary: We conducted a study on a model that represents the movements of planetary flows. This model has important physical and mathematical properties that are related to its long‐term behavior, which is essential for understanding geophysical turbulence. In this work, we developed a numerical method for simulation that preserves the key mathematical structure of the model through a two‐step process. We applied our method to simulate global atmospheric flow and investigate the impact of varying strengths of planetary rotation. Our findings demonstrate the expected formation of wind patterns known as zonal jets, where stronger winds occur near the equator and weaker winds near the poles. We also present energy spectra that illustrate the influence of planetary rotation on the transfer of turbulent energy, which aligns with existing theoretical predictions found in literature. These results highlight the potential of our numerical method for studying fundamental problems in geophysical fluid dynamics. Key Points: We develop a numerical method preserving Casimirs to simulate balanced shallow water flow on the sphereWe perform global high‐resolution simulations while accurately accounting for latitude‐dependent effectsOur simulations show the formation of robust zonal jets and provide key insights into quasi‐geostrophic turbulence [ABSTRACT FROM AUTHOR]

In contrast to physical processes, biogeochemical processes are inherently patchy in the ocean, which affects both the observational sampling strategy and the representativeness of sparse measurements in data assimilating models. In situ observations from multiple glider deployments are analyzed to characterize spatial scales of variability in both physical and biogeochemical properties, using an empirical statistical model. We find that decorrelation ranges are strongly dependent on the balance between local dynamics and mesoscale forcing. The shortest horizontal (5-10 km) and vertical (45 m) decorrelation ranges are for chlorophyll $a$ fluorescence. Whereas those variables that are a function of regional ocean and atmosphere dynamics (temperature and dissolved oxygen) result in anisotropic patterns with longer ranges along (28-37 km) than across the shelf (8-19 km). Variables affected by coastal processes (salinity and colored dissolved organic matter) have an isotropic range similar to the baroclinic Rossby radius (10-15 km). [ABSTRACT FROM AUTHOR]

The article presents a study which explored the improvement of the variability of Atlantic subpolar gyre (SPG), considering baroclinic threshold with coarse resolution model. The study perturbed the model system with freshwater forcing. Results showed the important role which can be played by North Atlantic ocean's baroclinic self-amplification in observed SPG variability.

This paper investigates the evolution of global eddies and various types of eddies originating from baroclinic instability (BCI) by utilizing satellite altimetry, Argo profiles, and climatology datasets. The structure of global eddies with regard to potential temperature anomalies experiences downward propagation and spreading from the periods of eddy growth to stabilization. However, from the eddy's stabilization to the decay period, the process of spreading primarily occurs horizontally, and this process is usually accompanied by weakening. By comparing the evolution of eddies in three typical regions dominated by distinct types of BCI, we found that the basic properties of eddies related to different BCI types evolve similarly; however, there are notable differences in their vertical structures and evolution. Eddies associated with Phillips + Charney_s-type, Charney_s-type, and Eady-type BCIs exhibit dual-core, single-core, and dual-core structures, respectively. In particular, the intrusion of the Okhotsk cold water mass into the Northwest Pacific region forms cold-core anticyclonic eddies, resulting in AEs that are significantly distinct from the rest of the ocean. The evolution of surface-layer cores closely resembles that of the global eddies, while the decay of subsurface and bottom-layer cores is comparably sluggish. Additionally, we examine the impact of local oceanic stratification conditions on eddy decay and determine that stronger vertical gradients result in more vigorous eddy decay, accounting for the concentration of eddies at depths where vertical gradients are weaker during their evolution. [ABSTRACT FROM AUTHOR]

The availability of remote sensing imagery at high spatiotemporal resolutions presents the opportunity to monitor the surface motion of rock glaciers, a key constraint for characterizing the dynamics of their evolution. In this paper, we investigate four North American rock glaciers by automatically measuring their horizontal surface displacement using photogrammetric data acquired with crewed and uncrewed aircraft along with orbital spacecraft over monitoring periods of up to eight years. We estimate vertical surface changes on these rock glaciers with photogrammetrically generated digital elevation models (DEM) and digitized topographic maps. Uncertainty analysis shows that the imagery with the highest resolution and most precise positioning have the best performance when used with the automated change detection algorithm. This investigation produces gridded velocity fields over the entire surface area of each study site, from which we estimate the age of rock glacier formation using along-flow velocity integration. Though the age estimates vary, the ice within the modern extent of these landforms began flowing between 3000 and 7000 years before present, postdating the last glacial maximum. Surface elevation change maps indicate present-day thinning at the lower latitude/higher elevation sites in Wyoming, while the higher latitude/lower elevation sites in Alaska exhibit relatively stable surface elevations. [ABSTRACT FROM AUTHOR]

The Earth's weather and climate are strongly influenced by synoptic-scale systems such as extratropical cyclones. From this point of view, extratropical cyclones are very important for Equator–Pole heat exchange, and their positions are relevant to the understanding of the behavior of this system under current conditions and in the context of climate change. Baroclinic instability (BI), meridional heat flux (MHF), and kinetic energy (KE) are among the ways of calculating storm tracks (the regions in which extratropical cyclones most often occur). Forecasting is important for predicting the evolution of these phenomena and preparing future political decisions. In this study, we used ERA5 reanalysis data and BESM model forecasts to calculate BI, MHF, and KE. Overestimation of the BESM BI at lower and higher latitudes and underestimation of BI at medium latitudes were observed. In general, KE and MHF were underestimated and were displaced southward in the BESM. The analyses show a tendency towards poleward displacement of these tracks for all variables studied in in this paper. The scenarios show the same bias, with RCP8.5 having more extreme changes in all situations. [ABSTRACT FROM AUTHOR]

The large-scale flows of the oceans and the atmosphere are driven by a non-uniform surface heating over latitude, and rotation. For many years scientists try to understand these flows by doing laboratory experiments. In the present paper we discuss two rather new laboratory experiments designed to study certain aspects of the atmospheric circulation. One of the experiments, the differentially heated rotating annulus at the Brandenburg University of Technology (BTU) Cottbus, has a cooled inner cylinder and a heated outer wall. However, the structure of the atmospheric meridional circulation motivates a variation of this "classical" design. In the second experiment described, operational at the Institute of Continuous Media Mechanics (ICMM) in Perm, heating and cooling is performed at different vertical levels that resembles more the atmospheric situation. Recent results of both experiments are presented and discussed. Differences and consistencies are highlighted. Though many issues are still open we conclude that both setups have their merits. The variation with heating and cooling at different levels might be more suited to study processes in the transition zone between pure rotating convection and the zone of westerly winds. On the other hand, the simpler boundary conditions of the BTU experiment make this experiment easier to control. [ABSTRACT FROM AUTHOR]

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Finally, with respect to the inclusion of a contribution regarding the river hydrological system, Campuzano et al. [[11]] aim to explore the potential impacts on the ocean system that can be obtained by using sophisticated land boundary conditions based on the capacities of state-of-the-art hydrologic models combined with observation networks. Improving Operational Ocean Models for the Spanish Port Authorities: Assessment of the SAMOA Coastal Forecasting Service Upgrades. The paper assesses the potential impacts that newly available river discharge datasets can have on regional ocean model solutions delivered by the Copernicus Marine IBI-MFC regional service when used as part of the freshwater land forcing. [Extracted from the article]

A recent paper by Mak et al. grants the opportunity to discuss two different definitions of the frontogenetical function proposed in the literature to study the formation and evolution of upper-level fronts. This comment exposes some problems that, in this author's opinion, are related to the use of the Lagrangian tendency of the 3D (in place of horizontal) gradient of potential temperature, as adopted in the Mak et al. paper. [ABSTRACT FROM AUTHOR]

This paper introduces wavetrisk-2.1 (i.e. wavetrisk-ocean), an incompressible version of the atmosphere model wavetrisk-1.x with free surface. This new model is built on the same wavelet-based dynamically adaptive core as wavetrisk, which itself uses dynamico's mimetic vector-invariant multilayer rotating shallow water formulation. Both codes use a Lagrangian vertical coordinate with conservative remapping. The ocean variant solves the incompressible multilayer shallow water equations with inhomogeneous density layers. Time integration uses barotropic–baroclinic mode splitting via an semi-implicit free surface formulation, which is about 34–44 times faster than an unsplit explicit time-stepping. The barotropic and baroclinic estimates of the free surface are reconciled at each time step using layer dilation. No slip boundary conditions at coastlines are approximated using volume penalization. The vertical eddy viscosity and diffusivity coefficients are computed from a closure model based on turbulent kinetic energy (TKE). Results are presented for a standard set of ocean model test cases adapted to the sphere (seamount, upwelling and baroclinic turbulence). An innovative feature of wavetrisk-ocean is that it could be coupled easily to the wavetrisk atmosphere model, thus providing a first building block toward an integrated Earth system model using a consistent modelling framework with dynamic mesh adaptivity and mimetic properties. [ABSTRACT FROM AUTHOR]

The use of machine learning to build subgrid parametrizations for climate models is receiving growing attention. State‐of‐the‐art strategies address the problem as a supervised learning task and optimize algorithms that predict subgrid fluxes based on information from coarse resolution models. In practice, training data are generated from higher resolution numerical simulations transformed in order to mimic coarse resolution simulations. By essence, these strategies optimize subgrid parametrizations to meet so‐called a priori criteria. But the actual purpose of a subgrid parametrization is to obtain good performance in terms of a posteriori metrics which imply computing entire model trajectories. In this paper, we focus on the representation of energy backscatter in two‐dimensional quasi‐geostrophic turbulence and compare parametrizations obtained with different learning strategies at fixed computational complexity. We show that strategies based on a priori criteria yield parametrizations that tend to be unstable in direct simulations and describe how subgrid parametrizations can alternatively be trained end‐to‐end in order to meet a posteriori criteria. We illustrate that end‐to‐end learning strategies yield parametrizations that outperform known empirical and data‐driven schemes in terms of performance, stability, and ability to apply to different flow configurations. These results support the relevance of differentiable programming paradigms for climate models in the future. Plain Language Summary: Climate projection and weather forecast heavily rely on computer simulations. But, if the physical laws governing the evolution of the climate system are well known, their simulation is still rather challenging. Fluid flows being essentially turbulent, small details at fine scales can have a tremendous impact on larger scales. Still, because of the limitations in computing power, all these interactions across scales cannot be explicitly resolved in computer simulations. Some of these interactions can only be represented approximately, and the design of these approximations is an active research area. Here, we describe a new method which leverages recent advances in machine learning. We propose to train an approximate representation of unresolved scales of motions that optimizes the quality of the climate model over some temporal horizon. This results in more accurate and stable predictions. Our method shows very promising results in toy example flow simulations, but its deployment at scale may seriously challenge the overall design of legacy climate models. Key Points: Subgrid parametrizations can be learned end‐to‐end with a posteriori criteria involving model integration over several time‐stepsA posteriori learning for quasi‐geostrophic turbulent flows can solve numerical stability issues related to energy backscatterLearned parametrizations outperform existing baselines for various evaluation metrics and apply to different flow configurations [ABSTRACT FROM AUTHOR]

This paper investigates the impact of combined axial through flow and radial mass flux on Taylor–Couette flow in a counter-rotating configuration, in which different branches of nontrivial solutions appear via Hopf bifurcations. Using direct numerical simulation, we elucidate flow structures, dynamics, and bifurcation behavior in qualitative and quantitative detail as a function of axial Reynolds numbers ( R e ) and radial mass flux (α) spanning a parameter space with a very rich variety of solutions. We have determined nonlinear properties such as anharmonicity, asymmetry, flow rates (axial and radial) and torque for toroidally closed Taylor vortices and helical spiral vortices. Small to moderate radial flow α initially decreases the symmetry of the different flows, before for larger values, α , the symmetry eventually increases, which appears to be congruent with the degree of anharmonicity. Enhancement in the total torque with α are elucidated whereby the strength varies for different flow structures, which allows for potential better selection and control. Further, depending on control parameters, heteroclinic connections (and cycles) of oscillatory type in between unstable and topological different flow structures are detected. The research results provide a theoretical basis for simple modification the conventional Taylor flow reactor with a combination of additional mass flux to enhance the mass transfer mechanism. [ABSTRACT FROM AUTHOR]

This paper investigates the gas flow and the mass transport in simplified axial-symmetric vertical HVPE reactors for the growth of GaN bulk crystals through numerical simulations. We evaluate the relative significance of different flow and transport phenomena in dependence on the direction of gravity. The performed simulations show that buoyancy effects due to density differences between neighboring gas lines are the main factor causing the deformation of laminar flow patterns and the formation of recirculation cells within the growth zone. Baroclinic instabilities have been identified as the source for these phenomena. In contrast, typical vertical temperature gradients show only a minor impact on the stability of the gas flow within the growth zone in the vicinity of the growing crystal. Based on these results, major differences of the species transport in vertical HVPE reactors, where the flow is parallel or anti-parallel to the direction of gravity, referred to as down-flow and up-flow, respectively, are summarized. The performed analysis of the interplay and relative significance of different flow effects in the HVPE environment allows a general recommendation for reactor design and scaling with respect to stable gas flow conditions within the growth zone. [ABSTRACT FROM AUTHOR]

Ocean circulation receives its energy input at basin scales while dissipates at microscopic mixing scale. How this energy is transferred across different lengthscales is of paramount importance for understanding the ocean circulation equilibration and variability. Advancement in high‐resolution numerical simulations in recent years has significantly improved our understanding of kinetic energy (KE) cascades from basin to kilometer scales, although observational evidence to verify the simulated processes remains limited. Using repeat ship‐board velocity measurements along 165°E across the equatorial, subtropical and subarctic Pacific Ocean, we show that the length scale separating the inverse and forward cascades, LS, falls in the 8 ∼ 300 km range and it does not scale straightforwardly with the baroclinic deformation radius. Balanced and unbalanced oceanic motions co‐exist in this range but contribute oppositely to the directional energy cascades. LS is observed to depend on the relative strengths of these motions, as well as by their interaction. Plain Language Summary: This paper investigates how nonlinear interactions in the turbulent upper ocean transport kinetic energy (KE) across different spatial scales. This investigation is important because the energy input that drives the ocean circulation has scales at tens of thousand kilometers, whereas the oceanic mixing and dissipation take place below the centimeter scales. How oceanic KE is transported from one scale to another is neither fully understood nor adequately observed, and this is particularly true in the oceanic meso‐submesoscales in the 1 ∼ 300 km range. By using repeat shipboard Acoustic Doppler Current Profiler surveys from 2004 to 2020 in the western Pacific Ocean, we examined the cross‐scale KE transfers in dynamically different regimes of tropics, subtropics and high latitudes. We found that the KE can transfer both up‐scales and down‐scales due to the co‐existence of balanced geostrophic motions and unbalanced wave motions. The length scale that separates the bi‐directional KE transfers is geographically dependent. It is controlled by the relative strengths of co‐existing balanced and unbalanced motions, as well as by how the unbalanced wave motions are dynamically generated. Key Points: Nonlinear interaction in upper ocean transfers kinetic energy both up‐ and down‐scalesUpper ocean balance and unbalanced motions contribute oppositely to energy cascadeBi‐directional energy cascade depends on relative importance of balanced versus unbalanced motions and characteristics of the unbalanced motions [ABSTRACT FROM AUTHOR]

Vortices are readily produced by hydrodynamical instabilities, such as the Rossby wave instability, in protoplanetary disks. However, large-scale asymmetries indicative of dust-trapping vortices are uncommon in submillimeter continuum observations. One possible explanation is that vortices have short lifetimes. In this paper, we explore how radiative cooling can lead to vortex decay. Elliptical vortices in Keplerian disks go through adiabatic heating and cooling cycles. Radiative cooling modifies these cycles and generates baroclinicity that changes the potential vorticity of the vortex. We show that the net effect is typically a spin down, or decay, of the vortex for a subadiabatic radial stratification. We perform a series of two-dimensional shearing box simulations, varying the gas cooling (or relaxation) time, t cool, and initial vortex strength. We measure the vortex decay half-life, t half, and find that it can be roughly predicted by the timescale ratio t cool/ t turn, where t turn is the vortex turnaround time. Decay is slow in both the isothermal (t cool ≪ t turn) and adiabatic (t cool ≫ t turn) limits; it is fastest when t cool ∼ 0.1 t turn, where t half is as short as ∼300 orbits. At tens of astronomical units where disk rings are typically found, t turn is likely much longer than t cool, potentially placing vortices in the fast decay regime. [ABSTRACT FROM AUTHOR]

Rossby wave packets (RWPs) are Rossby waves for which the amplitude has a local maximum and decays to smaller values at larger distances. This review focuses on upper-tropospheric transient RWPs along the midlatitude jet stream. Their central characteristic is the propagation in the zonal direction as well as the transfer of wave energy from one individual trough or ridge to its downstream neighbor, a process called "downstream development." These RWPs sometimes act as long-range precursors to extreme weather and presumably have an influence on the predictability of midlatitude weather systems. The paper reviews research progress in this area with an emphasis on developments during the last 15 years. The current state of knowledge is summarized including a discussion of the RWP life cycle as well as Rossby waveguides. Recent progress in the dynamical understanding of RWPs has been based, in part, on the development of diagnostic methods. These methods include algorithms to identify and track RWPs in an automated manner, which can be used to extract the climatological properties of RWPs. RWP dynamics have traditionally been investigated using the eddy kinetic energy framework; alternative approaches based on potential vorticity and wave activity fluxes are discussed and put into perspective with the more traditional approach. The different diagnostics are compared to each other and the strengths and weaknesses of individual methods are highlighted. A recurrent theme is the role of diabatic processes, which can be a source for forecast errors. Finally, the paper points to important open research questions and suggests avenues for future research. [ABSTRACT FROM AUTHOR]

Holistic simulation approaches are often required to assess human impacts on a river-estuary-coastal system, due to the intrinsically linked processes of contrasting spatial scales. In this paper, a Semi-implicit Cross-scale Hydroscience Integrated System Model (SCHISM) is applied in quantifying the impact of a proposed hydraulic engineering project on the estuarine hydrodynamics. The project involves channel dredging and land expansion that traverse several spatial scales on an ocean-estuary-river-tributary axis. SCHISM is suitable for this undertaking due to its flexible horizontal and vertical grid design and, more importantly, its efficient high-order implicit schemes applied in both the momentum and transport calculations. These techniques and their advantages are briefly described along with the model setup. The model features a mixed horizontal grid with quadrangles following the shipping channels and triangles resolving complex geometries elsewhere. The grid resolution ranges from ~6.3 km in the coastal ocean to 15 m in the project area. Even with this kind of extreme scale contrast, the baroclinic model still runs stably and accurately at a time step of 2 min, courtesy of the implicit schemes. We highlight that the implicit transport solver alone reduces the total computational cost by 82%, as compared to its explicit counterpart. The base model is shown to be well calibrated, then it is applied in simulating the proposed project scenario. The project-induced modifications on salinity intrusion, gravitational circulation, and transient events are quantified and analyzed. [ABSTRACT FROM AUTHOR]

Envelope gravity solitary waves are an important research hot spot in the field of solitary wave. And the weakly nonlinear model equations system is a part of the research of envelope gravity solitary waves. Because of the lack of technology and theory, previous studies tried hard to reduce the variable numbers and constructed the two-dimensional model in barotropic atmosphere and could only describe the propagation feature in a direction. But for the propagation of envelope gravity solitary waves in real ocean ridges and atmospheric mountains, the three-dimensional model is more appropriate. Meanwhile, the baroclinic problem of atmosphere is also an inevitable topic. In the paper, the three-dimensional coupled nonlinear Schrödinger (CNLS) equations are presented to describe the evolution of envelope gravity solitary waves in baroclinic atmosphere, which are derived from the basic dynamic equations by employing perturbation and multiscale methods. The model overcomes two disadvantages: (1) baroclinic problem and (2) propagation path problem. Then, based on trial function method, we deduce the solution of the CNLS equations. Finally, modulational instability of wave trains is also discussed. [ABSTRACT FROM AUTHOR]

This paper reports a comprehensive instability analysis of a 3D Charney-like model with an observationally compatible generic stratosphere. It is found that the values of a single nondimensional parameter Γ =   λ f o 2 / (β D N 1 2 ) (detailed definition in text), in conjunction with representative values of four other nondimensional parameters, would dictate the existence of multiple branches of unstable modes as a function of the zonal wavenumber. Prototype Charney mode, Green mode, and two additional structurally distinct modes (Charney+ mode and tropopause mode) are identified. The latter result from the additional strong influence of the tropopause. The dynamical nature of all modes is delineated in terms of their meridional fluxes of heat and potential vorticity. The three-dimensional structure of the ageostrophic velocity field in each mode is presented to identify its potential of inducing frontogenesis. Optimal-mode analyses are also performed to ascertain how a disturbance with a predisposed structure would explosively develop toward each type of normal mode. In view of the pivotal role of Γ in baroclinic instability and for historical reason, we name it the Charney number. It is most instructive to think of Γ as a ratio of the meridional gradient of PV associated with the basic flow in the troposphere,   λ f o 2 / (D N 1 2) , to that associated with Earth's rotation, β. [ABSTRACT FROM AUTHOR]

Fast-moving synoptic-scale atmospheric disturbances produce large-scale near-inertial waves in the ocean mixed layer. In this paper, we analyze the distortion of such waves by smaller-scale barotropic eddies, with a focus on the evolution of the horizontal wavevector k under the effects of straining and refraction. The model is initialized with a horizontally uniform (k = 0) surface-confined near-inertial wave, which then evolves according to the phase-averaged model of Young and Ben Jelloul. A steady barotropic vortex dipole is first considered. Shear bands appear in the jet region as wave energy propagates downward and toward the anticyclone. When measured at a fixed location, both horizontal and vertical wavenumbers grow linearly with the time t elapsed since generation such that their ratio, the slope of wave bands, is time independent. Analogy with passive scalar dynamics suggests that straining should result in the exponential growth of jkj. Here instead, straining is ineffective, not only at the jet center, but also in its confluent and diffluent regions. Low modes rapidly escape below the anticyclonic core such that weakly dispersive high modes dominate in the surface layer. In the weakly dispersive limit, k = -t∇ζ(x, y, t)/2 provided that (i) the eddy vertical vorticity z evolves according to the barotropic quasigeostrophic equation and (ii) k50 initially. In steady flows, straining is ineffective because k is always perpendicular to the flow. In unsteady flows, straining modifies the vorticity gradient and hence k, and may account for significant wave--eddy energy transfers. [ABSTRACT FROM AUTHOR]

With both hunting cooperation and Allee effects in predators, a predator–prey system was modeled as a planar cubic differential system with three parameters. The known work numerically plots the horizontal isocline and the vertical one with appropriately chosen parameter values to show the cases of two, one and no coexisting equilibria. Transitions among those cases with the rise of limit cycle and homoclinic loop were exhibited by numerical simulations. Although it is hard to obtain the explicit expression of coordinates, in this paper, we give the distribution of equilibria qualitatively, discuss all cases of coexisting equilibria, and obtain the Bogdanov–Takens bifurcation diagram to show analytical parameter conditions for those transitions. Our results give analytical conditions for not only the observed saddle-node bifurcation, Hopf bifurcation and homoclinic bifurcation but also the transcritical and pitchfork bifurcations at the predator-extinction equilibrium, which were not considered in the known work. Our analytic conditions provide a quantitative instruction to reduce the risk of predator extinction and promote the ecosystem diversity. [ABSTRACT FROM AUTHOR]

This paper presents a method for detecting the ensemble means, spreads, and occurrence probabilities for each of the multiple Kuroshio states. This is accomplished by classifying the forecasts of the ensemble members with a Gaussian mixture distribution model, a machine learning method. Ensemble simulations with 80 members are conducted to reproduce possible occurrences of the multiple Kuroshio states, targeting the large meander event in 2017. To test its performance, first, the method is applied for the southernmost latitude, a conventional index that represents meander intensity. The results show that the Kuroshio initially taking the nearshore nonlarge meander state bifurcates into the large meander and offshore nonlarge meander states, which occur with similar probabilities. Both developments are accompanied by positive potential energy extraction rates, consistent with baroclinic instability. As a more objective approach, the method is then applied for the dominant modes derived from empirical orthogonal function (EOF) analysis of the sea surface height field in the entire Kuroshio region. Importantly, almost identical results can be achieved. In particular, the bimodality between the large meander and nonlarge meander is shown to appear on the axis of the first EOF mode. From a mathematical perspective, this mode can be interpreted as the singular vector which grows most rapidly following the timeevolution operator. Finally, the multimodality of the Kuroshio is reinterpreted as a phase transition phenomenon where the nearshore nonlarge meander constitutes the basic state. [ABSTRACT FROM AUTHOR]

In this paper, the Richtmyer–Meshkov (RM) instability in spherical and cylindrical converging geometries with a Mach number of about 1.5 is investigated by using the direct numerical simulation method. The heavy fluid is sulfur hexafluoride, and the light fluid is nitrogen. The shock wave converges from the heavy fluid into the light fluid. The main focus is on the energy transport characteristics in the mixing layer during the entire development process from early instability to late-time turbulent mixing. First, the turbulence kinetic energy transport equation is analyzed, and it is found that the production and dissipation mechanisms of the turbulence induced by the spherical and cylindrical converging RM instabilities in the mixing layer are the same. The turbulent diffusion terms are crucial in the whole development processes of the mixing layers. Before the reflected shock waves transit the interfaces, the dissipation terms can be ignored relative to other terms, and after that, the dissipation terms are close to the production terms and play an important role. The compressibility terms are approximate to the production terms and promote the production of turbulence kinetic energy in the later stage. The viscous diffusion terms can be ignored throughout the process. Then, the enstrophy transport equation is researched, and it is found that, in the mixing layers, the baroclinicity terms play a leading role in the early stage, while the vortex stretching terms play a leading role in the later stage, and the vortex stretching term of the spherical converging geometry develops faster than that of the cylindrical converging geometry. The compressibility terms are positive in the early stage, which promote the production of enstrophy. After the reflected shock waves transit the interfaces, the compressibility terms become negative, which inhibit the production of enstrophy. In addition, the results of the present direct numerical simulation also show that the density fluctuation spectra in the centers of the mixing layers of the spherical and cylindrical converging RM instabilities present the obvious −5/3 scaling law. [ABSTRACT FROM AUTHOR]

Background There is limited evidence on association between air pollutants and hospital admissions, hospital cost and length of stay (LOS) among patients with diabetes mellitus (DM) and comorbid respiratory diseases (RD), especially in low- and middle-income countries (LMICs) with low levels of air pollution. Methods Daily data on RD-DM patients were collected in Panzhihua from 2016 to 2020. A generalised additive model (GAM) was used to explore the effect of air pollutants on daily hospital admissions, LOS and hospital cost. Attributable risk was employed to estimate RD-DM's burden due to exceeding air pollution exposure, using both 0 microgrammes per cubic metre (μg/m3) and WHO's 2021 air quality guidelines as reference. Results For each 10 ug/m3 increase of particles with an aerodynamic diameter <2.5 micron (≥m) (PM2.5), particles with an aerodynamic diameter <10 ≥m (PM10), sulfur dioxide (SO2), nitrogen dioxide (NO2) and ozone (O3), the admissions of RD-DM patients increased by 7.25% (95% CI = 4.26 to 10.33), 5.59% (95% CI = 3.79 to 7.42), 10.10% (95% CI = 7.29 to 12.98), 12.33% (95% CI = 8.82 to 15.95) and -2.99% (95% CI = -4.08 to -1.90); per 1 milligramme per cubic metre (mg/m3) increase of carbon monoxide (CO) corresponded to a 25.77% (95% CI = 17.88 to 34.19) increment for admissions of RD-DM patients. For LOS and hospital cost, the six air pollutants showed similar effect. Given 0 μg/m3 as the reference, NO2 showed the maximum attributable fraction of 32.68% (95% CI = 25.12 to 39.42%), corresponding to an avoidable burden of 5661 (95% CI = 3611 to 5860) patients with RD-DM. Conclusions There is an association between PM2.5, PM10, SO2, NO2, and CO with increased hospital admissions, LOS and hospital cost in patients with RD-DM. Disease burden of RD-DM may be improved by formulating policies related to air pollutants exposure reduction, especially in LMICs with low levels of air pollution. [ABSTRACT FROM AUTHOR]

In this paper, an extended nonlinear multiscale interaction model is proposed to examine nonlinear behavior of eddy-driven blocking as a Rossby wave packet in a three-dimensional background flow by dividing the background meridional potential vorticity gradient (PVy) into dynamical PVy (PVD y) related to the horizontal (mainly meridional) shear of background westerly wind (BWW) and thermodynamic PVy (PVT y) associated with the meridional temperature gradient (MTG). It is found that eddy-driven baroclinic blocking with large amplitude in the midtroposphere tends to have a longer lifetime (;20 days) in a baroclinic atmosphere with stratification than eddy-driven barotropic blocking without vertical variation (less than 15 days). It is shown that barotropic blocking shows a northwest-southeast orientation and has long lifetime, large retrogression, and slow decay only for weaker barotropic BWW and PVD y in higher latitudes. In a baroclinic atmosphere with stratification, baroclinic blocking shows long lifetime, strong eastward movement, slow decay, weak strength, and less local persistence for large barotropic BWW and PVD y under PVT y 50, but becomes less slow decay, weak retrogression, and large local persistence for small barotropicBWWand PVD y. Such a blocking with a north-south antisymmetric dipole, large amplitude, and long local persistence, characterized by a persistent large meander of westerly jet streams, is easily seen when baroclinic BWWand PVT y are small in the lower tomidtroposphere. Comparatively, themagnitude of PVT y plays a larger role in the blocking change than that of PVD y, whereas the vertical variation of MTG is more important for the blocking change than the MTG itself for some cases. [ABSTRACT FROM AUTHOR]

Atmospheric stochastic forcing associated with the North Atlantic Oscillation (NAO) and intrinsic ocean modes associated with the large-scale baroclinic instability of the North Atlantic Current (NAC) are recognized as two strong paradigms for the existence of the Atlantic multidecadal oscillation (AMO). The degree to which each of these factors contribute to the low-frequency variability of the North Atlantic is the central question in this paper. This issue is addressed here using an ocean general circulation model run under a wide range of background conditions extending from a supercritical regime where the oceanic variability spontaneously develops in the absence of any atmospheric noise forcing to a damped regime where the variability requires some noise to appear. The answer to the question is captured by a single dimensionless number Γ measuring the ratio between the oceanic and atmospheric contributions, as inferred from the buoyancy variance budget of the western subpolar region. Using this diagnostic, about two-thirds of the sea surface temperature (SST) variance in the damped regime is shown to originate from atmospheric stochastic forcing whereas heat content is dominated by internal ocean dynamics. Stochastic wind stress forcing is shown to substantially increase the role played by damped ocean modes in the variability. The thermal structure of the variability is shown to differ fundamentally between the supercritical and damped regimes, with abrupt modifications around the transition between the two regimes. Ocean circulation changes are further shown to be unimportant for setting the pattern of SST variability in the damped regime but are fundamental for a preferred time scale to emerge. [ABSTRACT FROM AUTHOR]

Research findings suggest that water (hydrological) cycle of the earth intensifies in response to climate change, since the amount of water that evaporates from the ocean and land to the atmosphere and the total water content in the air will increase with temperature. In addition, climate change affects the large-scale atmospheric circulation by, for example, altering the characteristics of extratropical transient eddies (cyclones), which play a dominant role in the meridional transport of heat, moisture, and momentum from tropical to polar latitudes. Thus, climate change also affects the planetary hydrological cycle by redistributing atmospheric moisture around the globe. Baroclinic instability, a specific type of dynamical instability of the zonal atmospheric flow, is the principal mechanism by which extratropical cyclones form and evolve. It is expected that, due to global warming, the two most fundamental dynamical quantities that control the development of baroclinic instability and the overall global atmospheric dynamics—the parameter of static stability and the meridional temperature gradient (MTG)—will undergo certain changes. As a result, climate change can affect the formation and evolution of transient extratropical eddies and, therefore, macro-exchange of heat and moisture between low and high latitudes and the global water cycle as a whole. In this paper, we explore the effect of changes in the static stability parameter and MTG caused by climate change on the annual-mean eddy meridional moisture flux (AMEMF), using the two classical atmospheric models: the mid-latitude f-plane model and the two-layer β-plane model. These models are represented in two versions: "dry," which considers the static stability of dry air alone, and "moist," in which effective static stability is considered as a combination of stability of dry and moist air together. Sensitivity functions were derived for these models that enable estimating the influence of infinitesimal perturbations in the parameter of static stability and MTG on the AMEMF and on large-scale eddy dynamics characterized by the growth rate of unstable baroclinic waves of various wavelengths. For the base climate change scenario, in which the surface temperature increases by 1 °C and warming of the upper troposphere outpaces warming of the lower troposphere by 2 °C (this scenario corresponds to the observed warming trend), the response of the mass-weighted vertically averaged annual mean MTG is − 0.2   ° C per 1000 km. The dry static stability increases insignificantly relative to the reference climate state, while on the other hand, the effective static stability decreases by more than 5.4%. Assuming that static stability of the atmosphere and the MTG are independent of each other (using One-factor-at-a-time approach), we estimate that the increase in AMEMF caused by change in MTG is about 4%. Change in dry static stability has little effect on AMEMF, while change in effective static stability leads to an increase in AMEMF of about 5%. Thus, neglecting atmospheric moisture in calculations of the atmospheric static stability leads to tangible differences between the results obtained using the dry and moist models. Moist models predict ~9% increase in AMEMF due to global warming. Dry models predict ~4% increase in AMEMF solely because of the change in MTG. For the base climate change scenario, the average temperature of the lower troposphere (up to ~4 km), in which the atmospheric moisture is concentrated, increases by ~ 1.5   ° C . This leads to an increase in specific humidity of about 10.5%. Thus, since both AMEMF and atmospheric water vapor content increase due to the influence of climate change, a rather noticeable restructuring of the global water cycle is expected. [ABSTRACT FROM AUTHOR]

Persian Gulf Water and Red Sea Water are salty and dense waters flowing at intermediate depths in the Gulf of Oman and the Gulf of Aden, respectively. Their spreading pathways are influence by mesoscale eddies that dominate the surface flow in both semi-enclosed basins. In situ measurements combined with altimetry indicate that Persian Gulf Water is stirred in the form of filaments and submesoscale structures by mesoscale eddies. In this paper, we study the formation and the life cycle of intense submesoscale vortices and their potential impact on the spreading of Persian Gulf Water and Red Sea Water. We use a primitive-equation three-dimensional hydrostatic model at a submesoscale-resolving resolution to study the evolution of submesoscale vortices. Our configuration idealistically mimics the dynamics in the Gulf of Oman and the Gulf of Aden: a zonal row of mesoscale vortices interacting with north and south topographic slopes. Intense submesoscale vortices are generated in the simulations along the continental slopes due to two different mechanisms. First, intense vorticity filaments are generated over the continental slope due to frictional interactions of the background flow with the sloping topography. These filaments are shed into the ocean interior and undergo horizontal shear instability that leads to the formation of submesoscale coherent vortices. The second mechanism is inviscid and features baroclinic instabilities arising at depth due to the weak stratification. Submesoscale vortices subsequently drift away, merge and form larger vortices. They can also pair with opposite-signed vortices and travel across the domain. They eventually dissipate their energy via several mechanisms, in particular fusion into the larger eddies or erosion on the topography. Since no submesoscale flow clearly associated with the fragments of Persian Gulf Water was observed in situ, we modeled Persian Gulf Water as Lagrangian particles. Particle patches are advected and sheared by vortices and are entrained into filaments. Their size first grows as the square root of time: a signature of the merging processes. Then, it increases linearly with time, corresponding to their ballistic advection by submesoscale eddies. On the contrary, without intense submesoscale eddies, particles are mainly advected by mesoscale eddies; this implies a weaker dispersion of particles than in the previous case. This shows the potentially important role of submesoscale eddies in spreading Persian Gulf Water and Red Sea Water. [ABSTRACT FROM AUTHOR]

This paper presents the new adaptive dynamical core wavetrisk. The fundamental features of the wavelet-based adaptivity were developed for the shallow water equation on the β plane and extended to the icosahedral grid on the sphere in previous work by the authors. The three-dimensional dynamical core solves the compressible hydrostatic multilayer rotating shallow water equations on a multiscale dynamically adapted grid. The equations are discretized using a Lagrangian vertical coordinate version of the dynamico model. The horizontal computational grid is adapted at each time step to ensure a user-specified relative error in either the tendencies or the solution. The Lagrangian vertical grid is remapped using an arbitrary Lagrangian–Eulerian (ALE) algorithm onto the initial hybrid σ -pressure-based coordinates as necessary. The resulting grid is adapted horizontally but uniform over all vertical layers. Thus, the three-dimensional grid is a set of columns of varying sizes. The code is parallelized by domain decomposition using mpi, and the variables are stored in a hybrid data structure of dyadic quad trees and patches. A low-storage explicit fourth-order Runge–Kutta scheme is used for time integration. Validation results are presented for three standard dynamical core test cases: mountain-induced Rossby wave train, baroclinic instability of a jet stream and the Held and Suarez simplified general circulation model. The results confirm good strong parallel scaling and demonstrate that wavetrisk can achieve grid compression ratios of several hundred times compared with an equivalent static grid model. [ABSTRACT FROM AUTHOR]

The investigation on the fluctuations of nonlinear Rossby waves is of great importance for the understanding of atmospheric or oceanic motions. The present paper mainly deals with the well-known atmospheric blocking phenomena through the nonlinear Rossby wave theories and the corresponding methods. Based on the equivalent barotropic potential vorticity model in the β-plane approximation underlying a weak time-dependent mean flow, the multiscale technique and perturbation approximated methods are adopted to derive a new forced Korteweg-de Vries model equation with varied coefficients (vfKdV) for the Rossby wave amplitude. For a further analytical treatment of the obtained model problem, a special kind of basic flow is adopted. The evolution processes of atmospheric blocking are well discussed according to the given parameters according to the dipole blocking theory. The effects of some physical factors, especially the mean flow, on the propagation of atmospheric blocking are analyzed. [ABSTRACT FROM AUTHOR]

Mesoscale eddies modulate the stratification, mixing, tracer transport, and dissipation pathways of oceanic flows over a wide range of spatiotemporal scales. The parameterization of buoyancy and momentum fluxes associated with mesoscale eddies thus presents an evolving challenge for ocean modelers, particularly as modern climate models approach eddy‐permitting resolutions. Here we present a parameterization targeting such resolutions through the use of a subgrid mesoscale eddy kinetic energy budget (MEKE) framework. Our study presents two novel insights: (a) both the potential and kinetic energy effects of eddies may be parameterized via a kinetic energy backscatter, with no Gent‐McWilliams along‐isopycnal transport; (b) a dominant factor in ensuring a physically‐accurate backscatter is the vertical structure of the parameterized momentum fluxes. We present simulations of 1/2° and 1/4° resolution idealized models with backscatter applied to the equivalent barotropic mode. Remarkably, the global kinetic and potential energies, isopycnal structure, and vertical energy partitioning show significantly improved agreement with a 1/32° reference solution. Our work provides guidance on how to parameterize mesoscale eddy effects in the challenging eddy‐permitting regime. Plain Language Summary: Ocean eddies evolving on horizontal lengthscales of order 10–100 km are not sufficiently resolved in modern global ocean models that have horizontal resolutions of about 25–100 km. The under‐representation of such eddies leads to inaccuracies in the modeled ocean state, including weakened current systems, incorrect stratification, and erroneous distributions of physical and biological ocean tracers. Here we develop a novel approach to mimicking the unresolved eddy effects by artificially energizing the flow in a way that is consistent with eddy dynamics, specifically their vertical structure. We find that our approach is able to correct for a variety of unresolved eddy effects when employed in a coarse‐resolution ocean model and compared against a high‐resolution reference case. Our work provides new insights on how to account for unresolved eddies in the next generation of climate models. Key Points: We propose a parameterization for mesoscale eddies targeting ocean models at eddy‐permitting resolutionsWe find that both the potential and kinetic energy effects of eddies on the flow may be parameterized via a kinetic energy backscatterThe novel approach of our backscatter scheme is its use of vertical structure, that is, backscattering onto the equivalent barotropic mode [ABSTRACT FROM AUTHOR]

Cut-off lows (COLs) exhibit diverse structures and lifecycles, ranging from confined upper-tropospheric systems to deep, multi-level vortex structures. While COL climatologies are well documented, the mechanisms driving their deepening remain unclear. To bridge this gap, a novel track matching algorithm applied to ERA-Interim reanalysis investigates the vertical extent of Southern Hemisphere COLs. Composite analysis based on structure and eddy kinetic energy budget differentiates four COL categories: shallow, deep, weak, and strong, revealing similarities and disparities. Deep, strong COLs concentrate around Australia and the southwestern Pacific, peaking in autumn and spring, while shallow, weak COLs are more common in summer and closer to the Equator. Despite their differences, both contrasting types evolve energetically via anticyclonic Rossby wave breaking. The distinct roles of jet streams in affecting COL types are addressed: intense polar front jets correlate with more deep COLs, whereas stronger subtropical jets relate to fewer shallow COLs. The COL deepening typically occurs in the presence of a robust upstream polar front jet, which enhances ageostrophic flux convergence and baroclinic processes. The subtropical jet positively correlates with COL intensity but weakens when considering the seasonality, suggesting uncertainties in this relationship. Additionally, we highlight the significance of diabatic processes in COL deepening, addressing their misrepresentation in reanalysis and emphasizing the need for more observational and modelling studies to refine the energetic framework. [ABSTRACT FROM AUTHOR]

Along with the familiar Rossby–Haurwitz waves, two-dimensional flows on the surface of a rotating sphere in the regime of zonostrophic turbulence harbor another class of waves known as zonons. Zonons are wave packets produced by energetic large-scale Rossby–Haurwitz wave modes 'enslaving' other wave modes. They propagate westward with the phase speed of the enslaving modes. Zonons can be visualized as enslaving modes' 'ringing' in the enslaved ones with the frequencies of the former, the property that renders zonons non-dispersive. Zonons reside in high-shear regions confined between the opposing zonal jets yet they are mainly attached to westward jets and sustained by the ensuing barotropic instability. They exchange energy with the mean flow while preserving their identity in a fully turbulent environment, a feature characteristic of solitary waves. The goal of this study is to deepen our understanding of zonons' physics using direct numerical simulations, a weakly non-linear theory, and asymptotic analysis, and ascertain that zonons are indeed isomorphic to solitary waves in the Korteweg–de Vries framework. Having this isomorphism established, the analysis is extended to eddies detected in the atmospheres of Jupiter and Saturn based upon the observed mean zonal velocity profiles and earlier findings that circulations on both planets obey the regime of zonostrophic macroturbulence. Not only the analysis confirms that many eddies and eddy trains on both giant planets indeed possess properties of zonons, but the theory also correctly predicts latitudinal bands that confine zonal trajectories of the eddies. [ABSTRACT FROM AUTHOR]

A wide range of environments that prevail over the globe generate various types of cyclones such as tropical, extratropical, and hybrid cyclones. In this paper, idealized numerical experiments are used to explore a spectrum of cyclones ranging from the diabatic type to the baroclinic type in a parameter space consisting of three environmental factors: temperature, vertical shear, and planetary vorticity. The experiments reproduce not only typical dynamics of tropical and extratropical cyclones but also their modified dynamics, which are consistent with theoretical studies; tropical cyclones are suppressed by vertical shear, while extratropical cyclones are intensified by condensational heating. The experiments also reproduce hybrid cyclones in environments with high temperature and large baroclinicity. The hybrid cyclones show multiscale dynamics in which synoptic-scale baroclinic systems spawn smaller-scale tropical cyclone–like convective cores. The spectrum of cyclones is found to be nonmonotonic in the parameter space because of a two-sided effect of the vertical shear: moderate shear weakens a tropical cyclone by tilting the small-scale vortex to the downshear, while strong shear develops a large-scale vortex of an extratropical cyclone or a hybrid cyclone through warm-air advection from the south. The indices based on the energetics and the symmetric and asymmetric structures overview the different types of cyclones in the parameter space. These parameter sweep experiments provide useful information on what environment is favorable for cyclones, particularly for intermediate environments where cyclone mechanisms are yet to be fully defined. [ABSTRACT FROM AUTHOR]

This paper investigates the effects of baroclinic pressure gradients on mean flow and turbulence in the diabatic atmospheric boundary layer (ABL). Large-eddy simulations are conducted where the direction of the baroclinicity, its strength, and the surface buoyancy flux are systematically varied to examine their interacting effects. The thermal wind vector, which represents the vertical change in the geostrophic wind vector resulting from horizontal temperature gradients, significantly influences the velocity profiles, the Ekman turning, and the strength and location of the low-level jet (LLJ). For instance, cold advection and positive (negative) geostrophic shear increased (decreased) friction velocity and changed the LLJ elevation. Given the baroclinicity strength and direction under neutral conditions, a simple reduced model is proposed and validated here to predict the general trends of baroclinic mean winds. The baroclinic effects on turbulence intensity and structure are even more intricate, with turbulent kinetic energy (TKE) profiles displaying an increase of TKE magnitude with height for some cases. When a fixed destabilizing surface heat flux is added, a positive geostrophic shear favors streamwise aligned roll-type structures, which are typical of neutral ABLs. Conversely, a negative geostrophic shear promotes cell-type structures, which are typical of strongly unstable ABLs. Furthermore, baroclinicity increases shear in the outer ABL and tends to make the outer flow more neutral by decreasing the Richardson flux number. These findings are consequential for meteorological measurements and the wind-energy industry, among others: baroclinicity alters the mean wind profiles, the TKE, coherent structures, and the stability of the ABL, and its effects need to be considered. [ABSTRACT FROM AUTHOR]

A weak planetary vorticity gradient and weak density stratification in the northern North Atlantic and Nordic seas lead to time-mean currents that are strongly guided by bottom topography. The topographic steering sets up distinct boundary currents with strong property fronts that are prone to both baroclinic and barotropic instability. These instability processes generate a macroturbulent eddy field that spreads buoyancy and other tracers out from the boundary currents and into the deep basins. In this paper we investigate the particular role played by baroclinic instability in generating the observed eddy field, comparing predictions from linear stability calculations with diagnostics from a nonlinear eddy-permitting ocean model hindcast. We also look into how the bottom topography impacts instability itself. The calculations suggest that baroclinic instability is a consistent source of the eddy field but that topographic potential vorticity gradients impact unstable growth significantly. We also observe systematic topographic effects on finite-amplitude eddy characteristics, including a general suppression of length scales over the continental slopes. Investigation of the vertical structure of unstable modes reveal that Eady theory, even when modified to account for a bottom slope, is unfit as a lowest-order model for the dynamics taking place in these ocean regions. [ABSTRACT FROM AUTHOR]

The research of gravity solitary waves movement is of great significance to the study of ocean and atmosphere. Baroclinic atmosphere is a complex atmosphere, and it is closer to the real atmosphere. Thus, the study of gravity waves in complex atmosphere motion is becoming increasingly essential. Deriving fractional partial differential equation models to describe various waves in the atmosphere and ocean can open up a new window for us to understand the fluid movement more deeply. Generally, the time fractional equations are obtained to reflect the nonlinear waves and few space-time fractional equations are involved. In this paper, using multiscale analysis and perturbation method, from the basic dynamic multivariable equations under the baroclinic atmosphere, the integer order mKdV equation is derived to describe the gravity solitary waves which occur in the baroclinic atmosphere. Next, employing the semi-inverse and variational method, we get a new model under the Riemann-Liouville derivative definition, i.e., space-time fractional mKdV (STFmKdV) equation. Furthermore, the symmetry analysis and the nonlinear self-adjointness of STFmKdV equation are carried out and the conservation laws are analyzed. Finally, adopting the exp(-Φ(ξ)) method, we obtain five different solutions of STFmKdV equation by considering the different cases of the parameters (η,σ). Particularly, we study the formation and evolution of gravity solitary waves by considering the fractional derivatives of nonlinear terms. [ABSTRACT FROM AUTHOR]

Protoplanetary discs should exhibit a weak vertical variation in their rotation profiles. Typically, this 'vertical shear' issues from a baroclinic effect driven by the central star's radiation field, but it might also arise during the launching of a magnetocentrifugal wind. As a consequence, protoplanetary discs are subject to a hydrodynamical instability, the 'vertical shear instability' (VSI), whose breakdown into turbulence could transport a moderate amount of angular momentum and facilitate, or interfere with, the process of planet formation. Magnetic fields may suppress the VSI, however, either directly via magnetic tension or indirectly through magnetorotational turbulence. On the other hand, protoplanetary discs exhibit notoriously low ionization fractions, and non-ideal effects, if sufficiently dominant, may come to the VSI's rescue. In this paper, we develop a local linear theory that explores how non-ideal magnetohydrodynamics influences the VSI, while exciting additional diffusive shear instabilities. We derive a set of analytical criteria that establish when the VSI prevails, and then show how it can be applied to a representative global model of a protoplanetary disc. Our calculations suggest that within ∼10 au the VSI should have little trouble emerging in the main body of the disc, but beyond that, and in the upper regions of the disc, its onset depends sensitively on the size of the preponderant dust grains. [ABSTRACT FROM AUTHOR]

This paper revisits how the restratifying buoyancy flux w0b0 generated by baroclinic mixed layer instabilities depends on environmental conditions. The frontal spindown is shown to produce buoyancy fluxes that increase significantly beyond the previously proposed and widely used scaling w0b0~fʌ2H2 (f is the Coriolis parameter, ʌ is the geostrophic shear, and His the mixed layer depth), irrespective of whether the initial front is broad or narrow. This increase occurs after the initial phase of the nonlinear evolution, when the baroclinic eddies grow in size and develop velocities significantly in excess of the scaling assumption V ~ üH. Implications for parameterizing the restratification caused by baroclinic mixed layer instabilities in coarseresolution models are discussed. [ABSTRACT FROM AUTHOR]

The evidence for, baroclinic energetics of, and geographic distribution of parametric subharmonic instability (PSI) arising from both diurnal and semidiurnal tides in a global ocean general circulation model is investigated using 1/12.5° and 1/25° simulations that are forced by both atmospheric analysis fields and the astronomical tidal potential. The paper examines whether PSI occurs in the model, and whether it accounts for a significant fraction of the tidal baroclinic energy loss. Using energy transfer calculations and bispectral analyses, evidence is found for PSI around the critical latitudes of the tides. The intensity of both diurnal and semidiurnal PSI in the simulations is greatest in the upper ocean, consistent with previous results from idealized simulations, and quickly drops off about 5° from the critical latitudes. The sign of energy transfer depends on location; the transfer is positive (from the tides to subharmonic waves) in some locations and negative in others. The net globally integrated energy transfer is positive in all simulations and is 0.5%–10% of the amount of energy required to close the baroclinic energy budget in the model. The net amount of energy transfer is about an order of magnitude larger in the 1/25° semidiurnal simulation than the 1/12.5° one, implying the dependence of the rate of energy transfer on model resolution. [ABSTRACT FROM AUTHOR]

This paper reviews the current understanding of moist orographic convection and its regulation by surface-exchange processes. Such convection tends to develop when and where moist instability coincides with sufficient terrain-induced ascent to locally overcome convective inhibition. The terrain-induced ascent can be owing to mechanical (airflow over or around an obstacle) and/or thermal (differential heating over sloping terrain) forcing. For the former, the location of convective initiation depends on the dynamical flow regime. In "unblocked" flows that ascend the barrier, the convection tends to initiate over the windward slopes, while in "blocked" flows that detour around the barrier, the convection tends to initiate upstream and/or downstream of the high terrain where impinging flows split and rejoin, respectively. Processes that destabilize the upstream flow for mechanically forced moist convection include large-scale moistening and ascent, positive surface sensible and latent heat fluxes, and differential advection in baroclinic zones. For thermally forced flows, convective initiation is driven by thermally direct circulations with sharp updrafts over or downwind of the mountain crest (daytime) or foot (nighttime). Along with the larger-scale background flow, local evapotranspiration and transport of moisture, as well as thermodynamic heterogeneities over the complex terrain, regulate moist instability in such events. Longstanding limitations in the quantitative understanding of related processes, including both convective preconditioning and initiation, must be overcome to improve the prediction of this convection, and its collective effects, in weather and climate models. [ABSTRACT FROM AUTHOR]

The stability properties of intermediate-order climate models are investigated by computing their Lyapunov exponents (LEs). The two models considered are PUMA (Portable University Model of the Atmosphere), a primitive-equation simple general circulation model, and MAOOAM (Modular Arbitrary -Order Ocean-Atmosphere Model), a quasi-geostrophic coupled ocean– atmosphere model on a β -plane. We wish to investigate the effect of the different levels of filtering on the instabilities and dynamics of the atmospheric flows. Moreover, we assess the impact of the oceanic coupling, the dissipation scheme, and the resolution on the spectra of LEs. The PUMA Lyapunov spectrum is computed for two different values of the meridional temperature gradient defining the Newtonian forcing to the temperature field. The increase in the gradient gives rise to a higher baroclinicity and stronger instabilities, corresponding to a larger dimension of the unstable manifold and a larger first LE. The Kaplan–Yorke dimension of the attractor increases as well. The convergence rate of the rate function for the large deviation law of the finite-time Lyapunov exponents (FTLEs) is fast for all exponents, which can be interpreted as resulting from the absence of a clear-cut atmospheric timescale separation in such a model. The MAOOAM spectra show that the dominant atmospheric instability is correctly represented even at low resolutions. However, the dynamics of the central manifold, which is mostly associated with the ocean dynamics, is not fully resolved because of its associated long timescales, even at intermediate orders. As expected, increasing the mechanical atmosphere–ocean coupling coefficient or introducing a turbulent diffusion parametrisation reduces the Kaplan–Yorke dimension and Kolmogorov–Sinai entropy. In all considered configurations, we are not yet in the regime in which one can robustly define large deviation laws describing the statistics of the FTLEs. This paper highlights the need to investigate the natural variability of the atmosphere–ocean coupled dynamics by associating rate of growth and decay of perturbations with the physical modes described using the formalism of the covariant Lyapunov vectors and considering long integrations in order to disentangle the dynamical processes occurring at all timescales. [ABSTRACT FROM AUTHOR]

We are concerned about the barotropic compressible Navier-Stokes equations with density-dependent viscosities which may degenerate in vacuum. We show that any classical solution to barotropic compressible Navier-Stokes equations in bounded domains will blow up, when the initial density admits an isolated mass group and the viscosity coefficients satisfy some conditions. A new condition on viscosities is first put forward in this paper. [ABSTRACT FROM AUTHOR]

This paper introduces WAVETRISK-2.1 (i.e. WAVETRISK-OCEAN), an incompressible version of the atmosphere model wavetrisk-1.x with free-surface. This new model is built on the same wavelet-based dynamically adaptive core as wavetrisk, which itself uses DYNANICO's mimetic vector-invariant multilayer rotating shallow water formulation. Both codes use a Lagrangian vertical coordinate with conservative remapping. The ocean variant solves the incompressible multilayer shallow water equations with inhomogeneous density layers. Time integration uses barotropic--baroclinic mode splitting via an semi-implicit free surface formulation, which is about 34-44 times faster than an unsplit explicit time-stepping. The barotropic and baroclinic estimates of the free surface are reconciled at each time step using layer dilation. No slip boundary conditions at coastlines are approximated using volume penalization. The vertical eddy viscosity and diffusivity coefficients are computed from a closure model based on turbulent kinetic energy (TKE). Results are presented for a standard set of ocean model test cases adapted to the sphere (seamount, upwelling and baroclinic turbulence). An innovative feature of wavetrisk-ocean is that it could be coupled easily to the wavetrisk atmosphere model, thus providing a first building block toward an integrated Earth-system model using a consistent modelling framework with dynamic mesh adaptivity and mimetic properties. [ABSTRACT FROM AUTHOR]

Introduction: Statistical methods such as empirical orthogonal functions (EOFs) are often used to model the sound speed profile (SSP). However, their statistical nature often leads to the sample dependence and physical fuzziness. Method: This study proposes a technique for modeling the SSP from the perspective of ocean dynamics. It employs the ocean normal mode, which is the mode of fluid particles motion, to deduce perturbations in the SSP, which is called the ocean mode basis (OMB). Result: The results of SSP reconstruction of in-situ samples showed that a few leading orders of the OMB can provide a compact representation of the SSP. Oscillations of the contours and gradient of the sound speed in thermocline were analyzed by using the first two orders of the projection coefficients of the relationship between the OMB and the baroclinic mode. As a physical model, this technique can also be used to characterize the dynamics of internal solitary waves. Furthermore, the OMB derived from archival date was used for SSP inversion. The results showed that the OMB can reconstruct SSP of a reasonable resolution without requiring in-situ samples. Discussion: Compared with statistical models, the OMB can better explain the ocean dynamics underlying variations in the SSP while requiring fewer samples. [ABSTRACT FROM AUTHOR]

Sea level and its horizontal gradient are an expression of oceanic volume, heat content, and currents. Large‐scale currents have historically been viewed as mostly "baroclinic," and tides as "barotropic," respectively, in the loose sense of being strongly related to the oceanic density distribution or not. In particular, the evolution of the barotropic velocity is influenced by a horizontal pressure‐gradient force that depends on the gradient of a particular depth‐weighting of the density field as well as on the gradient of the sea‐surface elevation ζ; hence, even the tides must be viewed as a product of the coupled interaction of barotropic and baroclinic fields. The purpose of this note is to give dynamical precision to the distinction between barotropic and baroclinic contributions to ζ and the surface pressure‐gradient force −g∇ζ, and, in the particular case of the tides, demonstrate their combined barotropic‐baroclinic interactions with a realistically forced, high‐resolution simulation of the Pacific Ocean circulation. While the different tidal sea‐level contributions manifest a horizontal scale separation (e.g., more barotropic at larger scales; more baroclinic surface pressure‐gradient force at smaller scales), there are cross‐mode corrections in both at the level of tens of percent. The proposed barotropic‐baroclinic decomposition is generally relevant to the sea‐level expression of oceanic currents. Plain Language Summary: Sea‐level variations at tidal frequencies occur because of the "astronomical" gravitational force acting nearly uniformly over the oceanic depth. Thus, they are commonly associated with the depth‐averaged velocity, that is, the barotropic current. However, due to oceanic density stratification and variable bathymetry, the resulting barotropic currents also generate vertically varying (baroclinic) tidal currents that also have an expression in the sea level and surface pressure‐gradient force. A prescription is given for how to decompose sea level and its gradient into its barotropic and baroclinic parts for both tides and currents, and the answers are illustrated using a tide‐resolving simulation of the Pacific Ocean. Key Points: Sea level, measured relative to a geopotential iso‐surface, is the surface dynamic pressure for the oceanic momentum balanceBarotropic and baroclinic dynamics combine in determining the sea levelA decomposition of tidal sea level and pressure‐gradient force in a Pacific Ocean simulation shows barotropic‐baroclinic coupling [ABSTRACT FROM AUTHOR]

Seasonal variation in westward-propagating quasi-10 d waves (Q10DWs) in the mesosphere and lower thermosphere of the Southern Hemisphere (SH) high-latitude regions is investigated using meteor radar (MR) observations for the period of 2012–2016 and using the Specified Dynamics (SD) version of the Whole Atmosphere Community Climate Model (WACCM). The phase difference in meridional winds measured by two MRs located in Antarctica gives observational estimates of the amplitude and phase of the Q10DW with zonal wavenumber 1 (W1). The amplitude of the observed Q10DW-W1 is large around equinoxes. In order to elucidate the variations in the observed Q10DW-W1 and its possible amplification mechanism, we carry out two SD-WACCM experiments nudged towards the MERRA-2 reanalysis from the surface up to ∼ 60 km (EXP60) and ∼ 75 km (EXP75). Results of the EXP75 indicate that the observed Q10DW-W1 can be amplified around regions of barotropic and/or baroclinic instability in the middle mesosphere around 60–70° S. In the EXP60 experiment, it was also found that the Q10DW-W1 is amplified around the regions of instability, but the amplitude is too large compared to MR observations. The large-scale instability in the EXP60 in the SH summer mesosphere is stronger than that in the EXP75 and Microwave Limb Sounder observations. The larger instability in the EXP60 is related to the large meridional and vertical variations in polar mesospheric zonal winds in association with gravity wave parameterization (GWP). Given uncertainties inherent in GWP, these results can suggest that it is possible for models to spuriously generate traveling planetary waves such as the Q10DW, especially in summer, due to excessively strong large-scale instability in the SH high-latitude mesosphere. [ABSTRACT FROM AUTHOR]

Earth system models suffer from various structural and parametric errors in their representation of nonlinear, multi‐scale processes, leading to uncertainties in their long‐term projections. The effects of many of these errors (particularly those due to fast physics) can be quantified in short‐term simulations, for example, as differences between the predicted and observed states (analysis increments). With the increase in the availability of high‐quality observations and simulations, learning nudging from these increments to correct model errors has become an active research area. However, most studies focus on using neural networks, which while powerful, are hard to interpret, are data‐hungry, and poorly generalize out‐of‐distribution. Here, we show the capabilities of Model Error Discovery with Interpretability and Data Assimilation (MEDIDA), a general, data‐efficient framework that uses sparsity‐promoting equation‐discovery techniques to learn model errors from analysis increments. Using two‐layer quasi‐geostrophic turbulence as the test case, MEDIDA is shown to successfully discover various linear and nonlinear structural/parametric errors when full observations are available. Discovery from spatially sparse observations is found to require highly accurate interpolation schemes. While NNs have shown success as interpolators in recent studies, here, they are found inadequate due to their inability to accurately represent small scales, a phenomenon known as spectral bias. We show that a general remedy, adding a random Fourier feature layer to the NN, resolves this issue enabling MEDIDA to successfully discover model errors from sparse observations. These promising results suggest that with further development, MEDIDA could be scaled up to models of the Earth system and real observations. Plain Language Summary: Numerical models are used to predict the Earth system, for example, from daily weather to the next‐century climate. These models have been developed and validated against observations over decades, however, they still have shortcomings (errors) in their representations of many complex processes, particularly those that are nonlinear and span many scales in time and space. The rapid improvements in the quality and quantity of observational data from the Earth system and advances in machine learning (ML) algorithms provide an opportunity to try to reduce these errors. However, the challenge is that many ML methods require a lot of training data, and it is also often difficult to explain how they are reducing the error. Here, we show the capabilities of a framework called MEDIDA (Model Error Discovery with Interpretability and Data Assimilation), which uses a class of ML methods that provide closed‐form (thus interpretable) equations for what they are learning from the differences between observations and model predictions. We show the success of MEDIDA when applied to a model of atmospheric turbulent circulation. Even when observations are only sparsely (not at every location) available, we show that MEDIDA works accurately once we leverage more recent advances in ML. Key Points: Model error discovery with interpretability and data assimilation is scaled up to geostrophic turbulence and sparse observationsNaive use of neural nets (NNs) as interpolator does not capture small scales due to spectral bias, failing discoveries of closed‐form errorsReducing this bias using random Fourier features enables NNs to represent the full range of scales, leading to successful error discoveries [ABSTRACT FROM AUTHOR]

This paper investigates the factors that determine the equilibrium state, and in particular the height and structure of the tropopause, in an idealized primitive equation model forced by Newtonian cooling in which the eddies can determine their own depth. Previous work has suggested that the midlatitude tropopause height may be understood as the intersection between a radiative and a dynamical constraint. The dynamical constraint relates to the lateral transfer of energy, which in midlatitudes is largely effected by baroclinic eddies, and its representation in terms of mean-flow properties. Various theories have been proposed and investigated for the representation of the eddy transport in terms of the mean flow, including a number of diffusive closures and the notion that the flow evolves to a state marginally supercritical to baroclinic instability. The radiative constraint expresses conservation of energy and so must be satisfied, although it need not necessarily be useful in providing a tight constraint on tropopause height. This paper explores whether and how the marginal criticality and radiative constraints work together to produce an equilibrated flow and a tropopause that is internal to the fluid. The paper investigates whether these two constraints are consistent with simulated variations in the tropopause height and in the mean state when the external parameters of an idealized primitive equation model are changed. It is found that when the vertical redistribution of heat is important, the radiative constraint tightly constrains the tropopause height and prevents an adjustment to marginal criticality. In contrast, when the stratification adjustment is small, the radiative constraint is only loosely satisfied and there is a tendency for the flow to adjust to marginal criticality. In those cases an alternative dynamical constraint would be needed in order to close the problem and determine the eddy transport and tropopause height in terms of forcing and mean flow. [ABSTRACT FROM AUTHOR]