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This study investigates the impact of eddy viscosity on equatorially trapped waves and the instability of the background shear in a simple barotropic–baroclinic model. It is the first study to include eddy viscosity in the study of tropical wave dynamics. This study also unifies the study of baroclinic and barotropic instabilities by using a coupled barotopic and baroclinic model of the tropical atmosphere. Linear wave theory is combined with a systematic Galerkin projection of the baroclinic dynamical fields onto parabolic cylinder functions. This study investigates varying shear strengths, eddy viscosities, and their combined effects. In the absence of shear, baroclinic and barotropic waves decouple. The baroclinic waves themselves separate into triads, forming the equatorially trapped wave modes known as Matsuno waves. However, when a strong eddy viscosity is included, the structure and propagation characteristics of these equatorial waves are significantly altered. Different wave types interact, leading to strong mixing in the meridional direction and coupling between meridional modes. This coupling destroys the Matsuno mode separation and offers pathways for these waves to couple and interact with one another. These results suggest that viscosity does not simply suppress growth; it may also reshape the propagation characteristics of unstable modes. In the presence of a background shear, some wave modes become unstable, and barotropic and baroclinic waves are coupled. Without eddy viscosity, instability begins with small scale and slowly propagating modes, at arbitrary small shear strengths. This instability manifests as an ultra-violet catastrophe. As the shear strength increases, the catastrophic instability at small scales expands to high-frequency waves. Meanwhile, instability peaks emerge at synoptic and planetary scales along several Rossby mode branches. When a small eddy viscosity is reintroduced, the catastrophic small-scale instabilities disappear, while the large-scale Rossby wave instabilities persist. These westward-moving modes exhibit a mixed barotropic–baroclinic structure with signature vortices straddling the equator. Some vortices are centered close to the equator, while others are far away. Some waves resemble synoptic-scale monsoon depressions and tropical easterly waves, while others operate on the planetary scale and present elongated shapes reminiscent of atmospheric-river flow patterns.

The driving mechanisms of mesoscale processes and associated heat transport in the Japan/East Sea (JES) from 1990 to 2010 were examined using eddy-resolving ocean model simulations. The simulated circulation showed correctly reproduced JES major basin-scale currents and mesoscale dynamics features. We show that mesoscale eddies can deepen isotherms/isohalines up to several hundred meters and transport warm and low salinity waters along the western and eastern JES boundaries. The analysis of eddy kinetic energy (EKE) showed that the mesoscale dynamics reaches a maximum intensity in the upper 300 m layer. Throughout the year, the EKE maximum is observed in the southeastern JES, and a pronounced seasonal variability is observed in the southwestern and northwestern JES. The comparison of the EKE budget components confirmed that various mechanisms can be responsible for the generation of mesoscale dynamics during the year. From winter to spring, the baroclinic instability of basin-scale currents is the leading mechanism of the JES mesoscale dynamics’ generation. In summer, the leading role in the generation of the mesoscale dynamics is played by the barotropic instability of basin-scale currents, which are responsible for the emergence of mesoscale eddies, and in autumn, the leading role is played by instabilities and the eddy wind work. We show that the meridional heat transport (MHT) is mainly polewards. Furthermore, we reveal two paths of eddy heat transport across the Subpolar Front: along the western and eastern (along 138∘ E) JES boundaries. Near the Tsugaru Strait, we describe the detected intensive westward eddy heat transport reaching its maximum in the first half of the year and decreasing to the minimum by summer.

Based on an eddy-permitting numerical model, the mesoscale variability in the East-Sakhalin Current is investigated during the winter-spring period. Analysis of necessary conditions for the development of baroclinic instability showed that the nearshore component of the East-Sakhalin Current is potentially baroclinic unstable in the first half-year. The simulated circulation uncovered a generation of anticyclonic eddies on the eastern Sakhalin shelf. It was established that a spatial scale of these eddies and the first baroclinic Rossby radius of deformation are values of the same order; a lifetime of these eddies varies from 4 to 6 weeks, given the Rossby number varies from 0.05 to 0.2. Analysis of the rate of eddy energy conversion on the eastern Sakhalin shelf showed that the generation of the revealed mesoscale eddies results from, mainly, baroclinic instability, whereas barotropic instability can be both favoring and preventing to the generation of these eddies.

This research investigated the eddy–mean flow interactions in the Agulhas leakage region by utilizing the Ocean General Circulation Model for the Earth Simulator (OFES) output and an energetic analysis tool called the multiscale energetics and vorticity analysis tool (MS-EVA). MS-EVA relies on multiscale window transform (MWT) functional analysis and canonical transfer. It is found that the climatological characteristics of the nonlinear interactions between the eddy and mean flow exhibit mixed canonical transfers, including both barotropic and baroclinic canonical transfers. These canonical transfers are related to barotropic and baroclinic instabilities, respectively. These transfers are highly inhomogeneous in space, reaching their maxima around 18°–22° E and 36°–42° S, where the Agulhas Ring forms. Besides, the barotropic canonical transfers from the mean flow to the eddy tend to dominate the entire Agulhas leakage region, with a contribution ratio of 1.55 between the barotropic and baroclinic canonical transfers. These results suggest that barotropic instability plays a more important role in producing eddy activities in this region.

A recently developed tool, the multiscale window transform, along with the theory of canonical energy transfer is used to investigate the roles of multiscale interactions and instabilities in the Gulf of Mexico Loop Current (LC) eddy shedding. A three-scale energetics framework is employed, in which the LC system is reconstructed onto a background flow window, a mesoscale eddy window, and a high-frequency eddy window. The canonical energy transfer between the background flow and the mesoscale windows plays an important role in LC eddy shedding. Barotropic instability contributes to the generation/intensification of the mesoscale eddies over the eastern continental slope of the Campeche Bank. Baroclinic instability favors the growth of the mesoscale eddies that propagate downstream to the northeastern portion of the well-extended LC, eventually causing the shedding by cutting through the neck of the LC. These upper-layer mesoscale eddies lose their kinetic energy back to the background LC through inverse cascade processes in the neck region. The deep eddies obtain energy primarily from the upper layer through vertical pressure work and secondarily from baroclinic instability in the deep layer. In contrast, the canonical energy transfer between the mesoscale and the high-frequency frontal eddy windows accounts for only a small fraction in the mesoscale eddy energy balance, and this generally acts as a damping mechanism for the mesoscale eddies. A budget analysis reveals that the mesoscale eddy energy gained through the instabilities is balanced by horizontal advection, pressure work, and dissipation.

Sheddings of Kuroshio Loop Current (KLC) eddies in the northeastern South China Sea (SCS) are investigated using mooring arrays, multiple satellite data, and data-assimilative HYCOM products. Based on altimeter sea surface heights between 1992 and 2014, a total of 19 prominent KLC eddy shedding (KLCES) events were identified, among which four events were confirmed by the concurrent moored and satellite observations. Compared to the leaping behavior of Kuroshio, KLCES is a relatively short-duration phenomenon that primarily occurs in boreal autumn and winter. The KLC and its shedding anticyclonic eddy (AE) trap a large amount of Pacific water with high temperature–salinity and low chlorophyll concentration in the upper layer. The corresponding annual-mean transport caused by KLCES reaches 0.24–0.38 Sv (1 Sv ≡ 10 6 m 3 s −1 ), accounting for 6.8%–10.8% of the upper-layer Luzon Strait transport. Altimeter-based statistics show that among ~90% of the historical KLCES events, a cyclonic eddy (CE) is immediately generated behind the AE southwest of Taiwan. Both energetics and stability analyses reveal that because of its large horizontal velocity shear southwest of Taiwan, the northern branch of KLC is strongly unstable and the barotropic instability of KLC constitutes the primary generation mechanism for the CE. After CE is generated, it quickly grows and gradually migrates southward, which in turn facilitates the detachment of AE from KLC. The intrinsic relationship between KLC and CE explains well why eddy pairs are commonly observed in the region southwest of Taiwan.

This study identified four patterns of regional extreme precipitation events (REPEs) in Central Asia (CA) and their crucial synoptic systems and multiscale interactions. Four patterns with distinct spatial distributions were identified in: northern Kazakhstan, southern Xinjiang, western CA, and the Tianshan Mountains. Focusing on the three most frequent REPEs, the kinetic energy (KE) cross‐scale transfer from the basic‐to synoptic‐scale windows exhibited a zonal dipole, resulting in the development and enhancement of REPEs in northern Kazakhstan. The available potential energy (APE) cross‐scale transfer exhibited opposing patterns between the upper and lower troposphere, indicating baroclinic instability in the lower troposphere and barotropic instability of the basic flow in the upper troposphere. Both mechanisms enhanced the Central Asian vortices (CAVs) in southern Xinjiang and induced REPEs. Conversely, the energy budgets exhibited baroclinic instability of the basic flow throughout the entire region when the Tianshan Mountains REPEs occurred, providing energy for prevalent CAVs. Plain Language Summary A self‐organizing map was employed to classify the regional extreme precipitation events (REPEs) in Central Asia (CA) into four patterns with unique spatial distributions (northern Kazakhstan: P1, southern Xinjiang: P2, western CA: P3, and Tianshan Mountains: P4). This study further illuminated the multiscale interaction mechanisms for the development of key synoptic systems that generate REPEs for the three most frequent patterns (P1, P2, and P4). A zonal dipolar kinetic energy (KE) cross‐scale transfer occurred throughout the region in P1, resulting in the development of a long‐wave trough and the enhancement of REPEs. P2 is characterized by a negative eastward shift of the North Atlantic Oscillation‐like in the original field and the reconstructed intraseasonal‐scale field, which promotes the development of Central Asian vortices (CAVs) over southern Xinjiang. The available potential energy (APE) and KE cross‐scale transfer from the basic‐to synoptic‐scale windows indicate that baroclinic and barotropic instability occur in the lower and upper troposphere, respectively. Thus, providing sufficient energy and dynamic conditions for CAVs enhances REPEs. Furthermore, the Silk Road pattern‐like dominates over Eurasia, and CAVs occur over the northwestern Tianshan Mountains, as observed in P4. APE cross‐scale transfer induces strong baroclinic instability throughout the troposphere and provides energy for more prevalent CAVs that intensify the REPEs. Key Points The long‐wave trough and Central Asia (CA) vortex are the crucial synoptic systems of summer regional extreme precipitation in CA The crucial synoptic systems are powered by the basic‐ and intraseasonal‐scale baroclinic instability The spatial inconsistency of local multiscale interactions affects the formation of the crucial synoptic systems and extreme precipitation

Two prognostic experiments taking into account real atmospheric forcing for 2006 and 2011 were carried out based on the eddy-resolving numerical model with a horizontal resolution of 1.6 km for the Black Sea. The main dynamic features such as the Rim Current, the Sevastopol, and Batumi anticyclones are reproduced in both experiments. The model results are confirmed via observation data. We accomplished the analysis of simulated circulation and energetics. The results demonstrate that both the vertical viscosity and vertical diffusion along with the energy inflow from the wind have been the main contributors to the annual and seasonal budgets of kinetic and potential energies of the Black Sea circulation. It is shown that two regimes of the Black Sea general circulation are implemented depending on a magnitude of wind contribution to the kinetic energy in winter. Intensive mesoscale eddy formation was observed along the Anatolian, Caucasian, and Crimean coasts. The analysis of the Black Sea circulation and eddy energetics allowed us to conclude that the generation and development of the mesoscale coastal eddies is associated with the barotropic instability in case of intensive coastal currents and is associated with both the barotropic and baroclinic instability in case of weak coastal currents.

The western boundary current system off southeastern Brazil is composed of the poleward-flowing Brazil Current (BC) in the upper 300 m and the equatorward flowing Intermediate Western Boundary Current (IWBC) underneath it, forming a first-baroclinic mode structure in the mean. Between 22° and 23°S, the BC-IWBC jet develops recurrent cyclonic meanders that grow quasi-stationarily via baroclinic instability, though their triggering mechanisms are not yet well understood. Our study, thus, aims to propose a mechanism that could initiate the formation of these mesoscale eddies by adding the submesoscale component to the hydrodynamic scenario. To address this, we perform a regional 1/50° (∼2 km) resolution numerical simulation using CROCO (Coastal and Regional Ocean Community model). Our results indicate that incoming anticyclones reach the slope upstream of separation regions and generate barotropic instability that can trigger the meanders’ formation. Subsequently, this process generates submesoscale cyclones that contribute, along with baroclinic instability, to the meanders’ growth, resulting in a submesoscale-to-mesoscale inverse cascade. Last, as the mesoscale cyclones grow, they interact with the slope, generating inertially and symmetrically unstable anticyclonic submesoscale vortices and filaments.

The Lorenz energy cycle was often used to analyze energy conversions related to instabilities in planetary atmospheres using zonal means as basic states. Alternatively, the bred vector (BV) energy equations use the control run as basic states and detect longitudinal dependency of the energy conversions. Additionally, it quantifies contributions from baroclinic and barotropic instabilities separately. We apply this method to understand energy conversions of the Venus atmosphere. BVs are obtained from breeding cycles emphasizing perturbation growths in the cloud layer. The BV potential energy in the pressure coordinate is newly derived. Energy conversions at different latitudes in the cloud layer are examined. Results show that baroclinic conversions are stronger at higher latitudes and exceed barotropic conversions at mid‐ to high‐latitudes. Thermal tides increase energy conversions in the morning hemisphere at mid‐latitudes. This study offers new insights into energy conversions of the Venus atmosphere, with potential applications to other planetary atmospheres. Plain Language Summary The atmospheres of planets such as Earth, Mars, and Venus, have various instabilities. Energy conversions occur when instabilities are triggered. The Lorenz energy cycle was typically used to understand energy conversions. However, this method considers zonal averages as basic flow, which works better for Earth's atmosphere than for Venus’s, where longitudinal dependency due to planetary‐scale disturbances is important. We applied an alternative approach, the Bred Vector (BV) energy equations, to analyze energy conversions of the Venusian atmosphere. This method has been used to study Earth’s ocean and the Martian atmosphere but has never been applied to the Venusian atmosphere. The advantage of this method is that it can detect longitudinal dependency of the energy conversion and quantify contributions of instabilities from meridional temperature gradient (baroclinic instability) and from horizontal wind shear (barotropic instability). Our findings show that the energy conversion related to baroclinic instability is stronger at higher latitudes and exceeds those related to barotropic instability in mid‐ to high‐latitude regions. We also found that thermal tides, excited by solar heating, increase energy conversions related to both instabilities in the morning hemisphere at mid‐latitudes. This study provides new insights into understanding energy conversions related to instabilities in the Venusian atmosphere. Key Points Energy conversions of the Venus atmosphere were examined for the first time using bred vector kinetic and potential energy equations Baroclinic energy conversion is stronger than barotropic energy conversion in the cloud layer at the mid‐ and high‐latitudes Thermal tide increases the baroclinic and barotropic energy conversions in the morning hemisphere at the mid‐latitudes