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The fact that ocean currents must flow parallel to the coast leads to the dynamics of coastal sea level being quite different from the dynamics in the open ocean. The coastal influence of open-ocean dynamics (dynamics associated with forcing which occurs in deep water, beyond the continental slope) therefore involves a hand-over between the predominantly geostrophic dynamics of the interior ocean and the ageostrophic dynamics which must occur at the coast. An understanding of how this hand-over occurs can be obtained by considering the combined role of coastal trapped waves and bottom friction. We here review understanding of coastal trapped waves, which propagate cyclonically around ocean basins along the continental shelf and slope, at speeds which are fast compared to those of baroclinic planetary waves and currents in the open ocean (excluding the large-scale barotropic mode). We show that this results in coastal sea-level signals on western boundaries which, compared to the nearby open-ocean signals, are spatially smoothed, reduced in amplitude, and displaced along the coast in the direction of propagation of coastal trapped waves. The open-ocean influence on eastern boundaries is limited to signals propagating polewards from the equatorial waveguide (although a large-scale diffusive influence may also play a role). This body of work is based on linearised equations, but we also discuss the nonlinear case. We suggest that a proper consideration of nonlinear terms may be very important on western boundaries, as the competition between advection by western boundary currents and a counter-propagating influence of coastal trapped waves has the potential to lead to sharp gradients in coastal sea level where the two effects come into balance.

The wide and highly productive Patagonian Shelf (PS) hosts a variety of waves. The study of Coastal Trapped Waves with periods smaller than 20 days has been limited by the temporal resolution of satellite altimetric data. The fast sampling phase of the recently launched Surface Water and Ocean Topography (SWOT) satellite revisits specific areas once a day and provides an unprecedented opportunity to examine rapidly changing signals over the PS. SWOT provides evidence of waves with wavelengths larger than 4,000 km and periods between 8 and 10 days which propagate with speeds of 5–6 m/s over the Pacific side and 10–13 m/s over the PS. They represent a major feature of the 20‐day high‐pass filtered sea surface height anomaly variability of the fast sampling phase. Wind bursts along the Pacific side probably contribute to their generation.

The roles of equatorial trapped waves (EQWs) and internal inertia–gravity waves in driving the quasi-biennial oscillation (QBO) are investigated using a high-resolution atmospheric general circulation model with T213L256 resolution (60-km horizontal and 300-m vertical resolution) integrated for three years. The model, which does not use a gravity wave drag parameterization, simulates a QBO. Although the simulated QBO has a shorter period than that of the real atmosphere, its amplitudes and structure in the lower stratosphere are fairly realistic. The zonal wavenumber/frequency spectra of simulated outgoing longwave radiation represent realistic signals of convectively coupled EQWs. Clear signals of EQWs are also seen in the stratospheric wind components. In the eastward wind shear of the QBO, eastward EQWs including Kelvin waves contribute up to ∼25%–50% to the driving of the QBO. The peaks of eastward wave forcing associated with EQWs and internal inertia–gravity waves occur at nearly the same time at the same altitude. On the other hand, westward EQWs contribute up to ∼10% to driving the QBO during the weak westward wind phase but make almost zero contribution during the relatively strong westward wind phase. Extratropical Rossby waves propagating into the equatorial region contribute ∼10%–25%, whereas internal inertia–gravity waves with zonal wavelength ≲1000 km are the main contributors to the westward wind shear phase of the simulated QBO.

Velocity data from a mooring array deployed northeast of the Campeche Bank (CB) show the presence of subinertial, high-frequency (below 15 days) velocity fluctuations within the core of the northward flowing Loop Current. These fluctuations are associated with the presence of surface-intensified Loop Current frontal eddies (LCFEs), with cyclonic vorticity and diameter < 100 km. These eddies are well reproduced by a high-resolution numerical simulation of the Gulf of Mexico, and the model analysis suggests that they originate along and north of the CB, their main energy source being the mixed baroclinic–barotropic instability of the northward flow along the shelf break. There is no indication that these high-frequency LCFEs contribute to the LC eddy detachment in contrast to the low-frequency LCFEs (periods > 30 days) that have been linked to Caribbean eddies and the LC separation process. Model results show that wind variability associated with winter cold surges are responsible for the emergence of high-frequency LCFEs in a narrow band of periods (6–10 day) in the region of the CB. The dynamical link between the formation of these LCFEs and the wind variability is not direct: (i) the large-scale wind perturbations generate sea level anomalies on the CB as well as first baroclinic mode, coastally trapped waves in the western Gulf of Mexico; (ii) these waves propagate cyclonically along the coast; and (iii) the interaction of these anomalies with the Loop Current triggers cyclonic vorticity perturbations that grow in intensity as they propagate downstream and develop into cyclonic eddies when they flow north of the Yucatan shelf.

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 present study analyzes novel observations of vertical wind (w)$(w)$in the tropical upper troposphere‐lower stratosphere obtained from a radar wind profiler in Cochin, India. Between December 2022 and April 2023, 63 consecutive 4 hr curtains of w$w$were measured with a vertical spacing of 180 m and a sampling time step of 44 s, thus resolving almost the whole spectrum of vertical motions. Spectra of w$w$strongly vary with altitude. They are generally flat up to the local Brunt‐Väisälä frequency (BVF), but sometimes exhibit a peak of w$w$variance closer to BVF, a feature which may be attributed to trapped gravity waves. At other times and locations, the w$w$profiles reveal Kelvin‐Helmholtz billows. Finally, the variability of w$w$variance over the 4 month campaign period is investigated. Using brightness temperature from geostationary satellites as a convective proxy, it is found that w$w$variance is highly correlated with fluctuations in convective activity. Plain Language Summary Vertical wind is a key meteorological parameter. In the tropical Upper Troposphere Lower Stratosphere (UTLS, the atmospheric layer between 14 and 20 km altitude above sea level), it crucially affects the formation of clouds and the transport of trace gases, such as water vapor, ozone and radiatively active constituents. The ensuing impacts on stratospheric composition and the Earth radiative budget have consequences for surface weather and climate. However, only a few instruments are capable of measuring vertical wind accurately in clear air, and these include VHF radars. In this study, we analyze radar measurements of UTLS vertical wind over Cochin, India taken at a 44 s sampling rate and with a vertical resolution of 180 m. Thanks to its high quality and temporal resolution, the data resolves the full spectrum of vertical motions and provides invaluable insights into the complex dynamics of the UTLS. In particular, it suggests a frequent occurrence of trapped gravity waves in this region. Trapped waves are confined vertically due to a specific vertical structure of wind and stability, but propagate long distances horizontally. The study also finds a clear relationship between vertical wind magnitude in the UTLS and convective clouds in the troposphere. Key Points Measurements of the vertical wind throughout the upper troposphere and lower stratosphere (UTLS) from a recently built radar Observations of Kelvin‐Helmholtz billows and trapped gravity waves in the tropical UTLS Impact of convection on clear‐sky vertical wind variance in the tropical UTLS

The effect of equatorially trapped waves on the movement of tropical cyclones (TC) is studied numerically based on a two-dimensional barotropic model in a beta-plane approximation. According to recent studies, equatorially trapped waves contribute to the genesis of TCs. It is thus natural to assume that these waves affect also the movement of the TC. The effect of three types of equatorially trapped waves, namely Kelvin, Rossby, and n = 0 eastward inertio-Gravity (EIG) waves, on the TC trajectory is investigated with a focus on the sensitivity on some key physical parameters such as the wavenumber and wavespeed. Using a simple barotropic model forced by a prescribed baroclinic flow, the barotropic response to equatorially trapped waves is simulated for a period of 50 days, under various wave parameter configurations. This response is then used as a background flow where TC’s can evolve and propagate. TC-like flows are injected into this wavefield background at arbitrary times during the simulation, and the TC trajectories are tracked and recorded for 48h after the injection time. The resulting TC trajectory patterns with respect to the injection times and wave parameters appear to be stochastic and the mean paths and the associated standard deviations are calculated and reported here. The statistics are different for different wave types. Kelvin waves make shorter length of TC trajectories and small divergence of direction. On the contrary, Rossby waves cause rather dramatic changes in the TC path and yield longer trajectories. Meanwhile, TCs in EIG waves maintain fairly the same direction and typically have longer trajectories though less dramatic. A robustness test using a random forcing instead has also been conducted.

In this study, we investigated diurnal coastal trapped waves in the eastern coastal area of the Shimokita Peninsula near the Tsugaru Strait. The coastal trapped waves in this area have not yet been observed. We observed current velocities at three sites on the coast to clarify the propagation and seasonal features. We also used an ocean general circulation model to determine the detailed structure and the causes underlying the seasonal characteristics of the waves. The coastal trapped waves propagated southward along the coast from the strait, where significant tidal currents exist. Coastal trapped waves depend on cross-shelf length and stratification strength. The coastal trapped waves propagate as internal Kelvin waves from summer to early winter in the northern part of the peninsula (where the shelf is narrow) and as shelf waves in the southern part (where the shelf is wide). From late winter to spring, the coastal trapped waves practically disappear in the northern part of the peninsula owing to the vertical uniform density off the east coast and the small cross-shelf width in the northern part. In autumn, the tidal current flows north of the sill near Cape Shiriya at the eastern mouth of the straits owing to the northward shift of the Tsugaru Warm Current in the strait; thus, the coastal trapped waves along the Shimokita coast weaken.

Unusually high sea level (UHSL) in early September 1971, which caused coastal flooding around the southern coasts of Japan despite no severe weather conditions, is examined using a coastal assimilation system with 2-km resolution. The observed duration of high sea-level anomalies (SLAs) for the UHSL was successfully represented by assimilation results. Through sensitivity experiments, we investigated the contribution of two factors, the wind and the Kuroshio effects, as suggested by previous research. The northeasterly winds associated with Typhoon 7123 induced coastal-trapped waves (CTWs) along the Kashima-nada Sea. The CTWs propagated clockwise along the coast at a speed of about 2.3 m/s and caused the sea level to increase by about 15 cm in Sagami and Tokyo Bays. A cold eddy associated with a Kuroshio meander was formed, and as a result, the warm Kuroshio water intruded into the Enshu-nada Sea due to the northward flow in the eastern flank of the eddy. The warm water intrusion significantly contributed to the duration of SLAs of about 30 cm around the Enshu-nada and Kumano-nada Seas. It was also shown that the high SLAs for the UHSL were quantitatively explained by the sum of the two factors. Thus, we conclude that the UHSL event was caused by the superposition of the wind-induced CTWs and the Kuroshio-induced warm water intrusions.

Three winter storms struck the Bohai and Yellow seas in succession during February 16–25, 2017. Periodic fluctuations of sea level, currents, temperature, and salinity were recorded at a moored station deployed in the Bohai Strait. Observations also captured significant synoptic fluctuations of inflow and outflow through the Bohai Strait with maximum magnitude exceeding 50 cm s−1. The sea level dropped by > 1 m and the bottom temperature decreased by 2.5 °C in < 30 h during these winter storms. A regional ocean model was used to investigate the prominent fluctuations of synoptic exchange flow through the Bohai Strait. The model results indicated that the Bohai and Yellow seas in their entirety responded strongly to the storm bursts and subsequent relaxation at the synoptic scale. The periodic winter storm bursts and relaxation excited the cyclonic propagation of coastal-trapped waves around the Bohai and Yellow seas. Strong periodic inflow and outflow during the passage of the three successive storms promoted water exchange between the Bohai Sea and the northern Yellow Sea. Successive winter storms might also affect the mean current structure through the Bohai Strait. The mean currents through the Bohai Strait during the studied storm period were characterized by inflow in both northern and southern parts of the strait and outflow through the middle of the strait. This arrangement is different from the traditional view of inflow via the northern channel and outflow through the southern channel.