Abstract Subsurface eddies are a key component of eastern boundary upwelling systems, yet their structure and dynamics remain poorly constrained by observations. Using multichannel seismic reflection data combined with simultaneous shipboard acoustic Doppler current profiler (ADCP) measurements, we investigate two subsurface submesoscale anticyclonic eddies observed offshore of southern Chile in February 2017. Seismic imaging provides high-resolution constraints on the vertical structure and horizontal scales of the eddies, particularly their lateral boundaries. Based on the eddy geometry resolved from seismic imaging and coincident velocity observations, we conduct quantitative analyses of the eddy velocity structure and momentum balance. The estimated Rossby numbers indicate strongly ageostrophic dynamics, and a comparison of centrifugal and Coriolis terms shows that the radial momentum balance of both eddies is governed by gradient wind balance rather than geostrophic balance. The joint observations further reveal a strong poleward Peru–Chile Undercurrent (PCUC) near 44°S, with velocities of 0.1–0.2 m s −1 , characterized by a distinctive seismic reflection signature along the continental slope. The spatial relationship among the eddies, the undercurrent, and local bathymetric curvature provides new observational evidence that subsurface anticyclonic eddies in eastern boundary upwelling systems can form through flow separation of the poleward undercurrent. These results demonstrate the value of combining seismic oceanography with velocity measurements to constrain the dynamics of subsurface submesoscale eddies. Significance Statement Ocean eddies are swirling masses of water that help move heat and nutrients through the ocean. Many eddies exist below the surface, where they are difficult to observe and, therefore, poorly understood. In this study, we use a sound-based imaging method together with shipboard current measurements to examine two subsurface eddies off the coast of southern Chile. We find that these subsurface eddies have complex velocity structures and do not behave like the simple, symmetrical eddies often assumed in models. The combined observations show that the eddy’s rotation follows a more complex physical balance that accounts for both Earth’s rotation and the curvature of the swirling flow, rather than the simpler geostrophic balance. We also observe a semilens-shaped pattern along the continental slope that likely represents a persistent poleward undercurrent and may be related to how the eddies form. These results highlight that subsurface eddies are abundant and more complex than previously recognized and emphasize the need for better observations to improve our understanding of ocean circulation and its impacts on climate and marine ecosystems.
Abstract Present forecasting efforts rely on assimilation techniques that adjust the model initial state, meaning that profiles of temperature and salinity are used as measured or converted to temperature and salinity through statistical relationships. This information influences the upper ocean ( < 1000 mdepth), while minimally influencing the deep ocean. Nevertheless, development of the full water column circulation critically depends upon the dynamical interactions between upper and deep fields. We review ensemble forecasts in the Gulf of Mexico demonstrating the importance of the initial deep ocean features in the evolution of the surface field. Initial conditions throughout the full water column that agree with observations are needed to improve the forecast predictions. Here, best and worst ensemble members in two 92-day forecasts are identified and contrasted in order to determine how the deep ocean features differ between these groups. The forecasts cover the duration of the Loop Current Eddy Thor separation event, which coincides with available deep observations. Model ensemble member performance is assessed with a newly developed ranking method, demonstrated with surface variables against verifying analysis and satellite altimeter data during the forecast time-period. Deep cyclonic and anticyclonic features are reviewed, and compared against deep observations, indicating subtle differences in locations of deep eddies at relevant times. These results highlight both the importance of deep circulation dynamics of the Loop Current system and more broadly motivate efforts to assimilate deep observations to better constrain the deep initial fields and improve surface and sub-surface predictions.
Abstract Convergence of buoyant material in an estuary is important because it can facilitate interactions between particles related to predator-prey dynamics, access to nutrients, and exposure to pollutants. Convergence is often associated with lateral transport in an estuary. Traditionally viewed in a tidally-averaged framework, a common mechanism of convergence is differential advection due to lateral density gradients. Recently, a time-dependent, Lagrangian, convergence mechanism has been suggested and tested for a highly idealized estuary with constant density and Coriolis force. This mechanism found that a lateral phase shift in the lateral flows can result in a Lagrangian residual circulation and lead to lateral convergence. Here, we explore the combined effects and competition of Eulerian and Lagrangian convergence in a tidally-resolved idealized estuary model. We find that, in both high and low vertical eddy viscosity cases, the Eulerian mean flow drives convergence toward the channel center. However, the direction of the lateral phase propagation shifts from divergence under high vertical eddy viscosity to convergence under low vertical eddy viscosity, altering the overall convergence rate relative to the Eulerian flow alone. We suggest the use of a non-dimensional parameter to predict if a system will exhibit convergent or divergent Lagrangian residual circulation. We also explore sensitivity of the Lagrangian residual circulation to changing width, depth, and the inclusion of Coriolis force. Overall, Lagrangian mechanisms are important to consider because they can control buoyant particle convergence rates and potentially alter their trajectory relative to the Eulerian mean flow.
Abstract Mesoscale ocean-atmosphere coupling modulates global climate. As a major participant, sea surface temperature anomalies (SSTAs) induced by mesoscale eddies exhibit significant diversity and complexity, typically classified into monopole SSTA and various residue as dipole SSTA. However, the distinct global distribution patterns and their variance contributions remain insufficiently understood. Analysis of 29-year satellite observations reveals that dipole SSTA cyclonic (anticyclonic) eddies account for 49.3% (51.5%) of global cyclonic (anticyclonic) eddy-induced SSTA variance. Using idealized models, we show that zonal eddy relative drift plays a notable role in shaping SSTA structures. Monopole SSTAs mainly appear in the extensions of the Gulf Stream, Kuroshio, and Antarctic Circumpolar Current (ACC) with strong eastward relative drifting, while dipole SSTAs are more common in eastern ocean basins where weak zonal relative drifting favors their development. This discovery challenges the monopole-centric paradigm of mesoscale ocean–atmosphere coupling and provides a benchmark for improving eddy representation in climate models.
Abstract When a river plume encounters a coastal valley, local dynamics are modified relative to those with seawater. However, the underlying dynamical processes remain poorly understood. In this study, an idealized numerical model is employed to investigate how the presence of a river plume alters the flow behavior over a coastal valley under downwelling-favorable winds. The arrival of the plume intensifies the alongshore current, weakens the cross-shore flow, and induces another upwelling–downwelling dipole within the valley. Simultaneously, the net vertical and cross-shore transports reverse from a downward-offshore pattern under seawater conditions to an upward-onshore pattern with a plume. The river plume not only amplifies the contribution of vertical vorticity diffusion but also reshapes the spatial distribution of relative vorticity changes that govern vertical motion in the valley. Compared with the dominance of relative potential vorticity advection in the no-plume case, the primary driver of cross-shore transport within the valley shifts to the joint effect of baroclinicity and topographic relief when the plume is present. These dynamical changes are linked to the combined effects of sea level anomalies associated with valley-induced coastal trapped lee waves and plume-induced spatial density variations. After wind relaxation, mesoscale instabilities develop throughout the water column, featuring longer wavelengths on the downstream side of the valley. During this stage, eddy potential energy is converted into eddy kinetic energy, part of which is subsequently transferred to the mean kinetic energy. Significance Statement Coastal valleys are widespread along continental margins, yet their dynamical interactions with river plumes remain poorly understood. This study demonstrates that plume intrusion into a shelf valley fundamentally modifies local dynamics and net transport relative to seawater conditions. Under downwelling-favorable winds, the plume shifts the net cross-shore and vertical transports within the valley toward onshore and upward directions, opposite to that with seawater conditions. As winds relax, mesoscale instabilities develop, reshaping pathways of material exchange and energy transfer across the valley. These findings highlight the nonlinear interactions between river plumes and valley topography and suggest that valley-induced coastal trapped lee waves and spatial variations in plume density are the original forces for the dynamical variations within the valley.
Abstract Low-level radial convergent wind is an important component of tropical cyclone (TC) wind fields, typically accounting for 10%–30% of the total wind speed. However, its impact on wave characteristics remains unclear. This study investigates the influence of radial wind on TC wave fields using idealized numerical wave simulations. Results show that inclusion of radial wind significantly enhances significant wave height (SWH) near and behind the TC center. Sensitivity analyses indicate that this enhancement is primarily modulated by TC translation speed, radius of maximum winds (RMW), and intensity. As translation speed increases, the maximum relative SWH enhancement near the center shifts rearward, decreasing from 52% to 19%. As the RMW increases, this enhancement rises from 18% to 47%. Variations in radial wind fraction mostly exert a greater influence on maximum relative SWH increase (16%–36%) than those in maximum wind speed (22%–29%). Additionally, radial wind reduces azimuthal asymmetry in the wave field, particularly at higher translation speeds. Mechanism analysis reveals that radial wind alters the angle between local wind direction and spectral peak wave direction, reducing wind-sea coverage within 3RMW from approximately 47% to 40.4%. Radial wind enhances local wind energy input and whitecapping dissipation behind the TC center, suppresses net outward wave energy flux near the center, and promotes inward convergence of external swell energy, collectively leading to wave energy accumulation near and behind the TC center. These findings highlight the necessity of incorporating radial wind component in TC wave modeling and parametric wind field construction.
Abstract As the ocean tide flows over the rough seafloor it induces topographic stresses that feed back on the strength of the tide. Here we examine how these topographic stresses change as the dynamical regime transitions from barotropic to baroclinic with increasing stratification and/or decreasing topographic lengthscale, thereby bridging between previous work which studied one or other regime in isolation. Our investigation is conducted using linear theory validated by comparison with a suite of over 100 fully nonlinear numerical simulations. For super-inertial tidal flows across an isolated ridge, it is shown that the topographic stress rapidly transitions from out-of-phase with the tidal flow to in-phase with the tidal flow at ridge widths of 1-2 times the baroclinic mode-1 wavelength. This change in stress is associated with a switch from topographically-confined perturbation flows in the barotropic regime to radiating waves in the baroclinic regime. The transition becomes more complicated in the presence of multiple ridges due to the interference of the waves generated at each. These interactions lead to significant changes in both the magnitude and phase of the topographic stress as compared to the sum of the contributions from two isolated ridges. Further, particular combinations of ridges — so-called ‘invisible topographies’ — lead to exactly zero stress and therefore have no effect on the barotropic tide. These results have implications for improving models of ocean tides and tidally-driven mixing.
Abstract High-resolution numerical simulations and field efforts have revealed ubiquitous lateral buoyancy gradients around surface-intensified mesoscale eddies and emphasized the role of submesoscale turbulence in the energy cascade of geostrophic flows and vertical communication of tracers. However, active fronts and submesoscale turbulence, along with associated geostrophic energy dissipation, remain poorly understood in subsurface eddy fields, partly due to high-resolution observational limitations in the ocean interior. In this study, a field campaign observed a mesoscale intrathermocline eddy (ITE) with lens-shaped isopycnals and enhanced energy dissipation in the thermocline. The turbulent kinetic energy (TKE) dissipation rates measured by a vertical microstructure profiler are significantly elevated to 10 −7 –10 −8 W kg −1 in the ITE periphery, which are one to two orders of magnitude higher than surrounding subsurface areas (∼10 −9 W kg −1 ) and even comparable to mixed layer values. Diagnostic results from the Gregg–Henyey–Polzin fine-scale parameterization do not support internal wave activity as the primary source of observed high dissipation rates, although contributions from high-frequency nonlinear internal waves cannot be resolved here. Meanwhile, 600-m-resolution Triaxus observations across the ITE reveal submesoscale-enhanced lateral buoyancy gradients, increased geostrophic shear, and decreased potential vorticity (PV) in regions of elevated TKE dissipation, indicating conditions favorable for frontal submesoscale instability. The consistency of density fronts, negative PVs, and symmetric instability implies that elevated dissipation in the ITE periphery is highly associated with submesoscale instabilities. These direct observations emphasize active fronts and submesoscale turbulence around the ITE and highlight their key role in the forward energy cascade and dissipation of subsurface geostrophic eddies. Significance Statement Submesoscale turbulence with horizontal scales of O (1–10) km and time scales of hours to days has been widely studied in the surface mixed layer. However, these submesoscale processes below the mixed layer remain poorly understood due to observational challenges. High-resolution Triaxus profiling and microstructure measurements within an intrathermocline eddy (ITE) field reveal elevated energy dissipation rates and enhanced lateral buoyancy gradients in the ocean interior. Strong density fronts and submesoscale turbulence associated with symmetric instability help explain the forward energy cascade leading to dissipation from mesoscale toward smaller scales. Considering the widespread presence of ITEs in the ocean interior, which cannot be detected by satellites, active fronts and submesoscale turbulence may be crucial in driving the downscale energy transfer and ultimate dissipation of subsurface geostrophic eddies.
Abstract The patchy nature of thermocline turbulence is examined with seven turbulence profiling floats. All were released within 1 km over 3 h, and left to disperse over a three-week period during which separations increased to 100 km while continuously profiling the upper 180 m. Coherent patches of enhanced turbulence can be confidently matched by eye across pairs of floats separated by ∼1 km or less. For these small separations, correlation coefficients between pairs of turbulent dissipation measurements (20-m×1-h averages) are ∼0.6. Out to separations of 10 km, correlations decrease approximately linearly with the log of separation distance. We show that such a curve is consistent with past measurements of a power-law distribution of patch sizes with patch widths that are often hundreds of meters and occasionally kilometers. Correlations and other comparison metrics plateau at separations beyond 10–15 km.
Abstract Internal tides (ITs) in the northern South China Sea exhibit pronounced spatiotemporal variability modulated by complex oceanic background conditions, complicating assessments of their predictability and intrinsic regularity. Using a high-resolution numerical simulation [Massachusetts Institute of Technology General Circulation Model (MITgcm) LLC4320], I evaluate IT predictability by quantifying how IT-induced baroclinic sea surface height (SSH) accounts for observed variability in along-track satellite altimetry and assess IT regularity using both conventional stationarity and a newly developed dynamical regularity (DR) index based on the Hilbert–Huang transform. Stationary IT is reasonably captured by the model, whereas nonstationary variability substantially reduces the predictability of the total IT, highlighting the need for data assimilation strategies and improved internal wave parameterization. Stationarity diagnosed from horizontal kinetic energy and baroclinic energy flux is generally high near the Luzon Strait and along main propagation beams, but results are sensitive to the diagnostic metric and sampling window length. Further analysis of baroclinic SSH suggests that nonstationary ITs retain notable dynamical regularity, rather than behaving random or unpredicatable. By explicitly incorporating variability in instantaneous frequency and energy, DR provides a time-resolved and physically consistent characterization of IT regularity. DR confirms high IT regularity near generation sites and reveals that low-mode ITs maintain pronounced regularity far downstream within the deep basin, in contrast to the downstream decay indicated by stationarity. DR also reveals reduced diurnal IT regularity in the northern Luzon Strait, underscoring the significant role of local dynamics such as the Kuroshio intrusion. Overall, the DR index captures a broader spectrum of IT dynamical behaviors than stationarity, offering a new framework capable of characterizing IT regularity in complex oceanic environments.
Abstract Strong cross-channel shear of tidal currents through a bounded channel can lead to instabilities in the flow, causing a meandering of the mean along-channel current and potentially the spinoff of large eddies. To estimate the wavenumbers of shear instabilities within the Hampton-Seabrook Estuary, New Hampshire, a spatially lagged array consisting of seven sensors measuring bidirectional horizontal currents and pressure was deployed for 1 week during the spring tide in May 2021. Using iterative maximum likelihood estimators, wavenumber–frequency spectra are estimated during 3–4-h periods with approximately steady currents on both the flood and ebb tides. Dominant wavenumbers (±0.002–0.02 m −1 ) of the low-frequency motions (0.0006–0.01 s −1 ) are resolved and consistent with motions determined from barotropic linear stability analysis described in the companion paper. The instabilities propagate into the inlet on flood tides and out of the inlet on the ebbs, consistent with the expected propagation of unstable modes. The normalized velocity-to-pressure variance ratio at each station shows that the infragravity band is dominated by rigid-lid-like motions characteristic of instabilities. The lack of breaking wave group modulations within the inlet and the presence of the seaward propagating instabilities on the ebb flow indicate that the presence of the instabilities can be attributed to the shear of the tidal current. Significance Statement Horizontal instabilities of tidal currents flowing through bounded channels can lead to a meandering of the mean along-channel current and potentially the spinoff of large eddies. The resulting high-frequency variability of the currents and vorticities may affect navigation and the transport of organic and inorganic matter and cause lateral mixing of momentum across the inlet. Instabilities of the mean current are observed in a tidal inlet on both the ebb and flood tides propagating in the direction of the mean current, and the dominant wavelengths and periods are estimated and compared with theoretical linear stability predictions. The forcing is from the strong gradient in velocity and is not tied to breaking incident gravity wave groups that are absent in the inlet.
In the hydraulics of sheared, inviscid channel flows, where the horizontal velocity profile varies with height, the speed of long waves is governed by an integral equation with an apparent singularity that is present for wave speeds within the range of the profile. It is shown that simple linear profiles (or those composed of linear segments) do not have a singularity, but more complicated cases with curvature to the profile are singular. In singular cases, the singularity can be interpreted by analyzing the initial value problem, where it results in a so-called continuous spectrum solution with different space/time behavior than the classical wave mode solutions. This is relevant in the hydraulics of sheared flows since it affects the signal response carried by the upstream wave mode, with a rapidly decreasing flux found as the Froude number increases. SIGNIFICANCE STATEMENT: Understanding the propagation characteristics of long waves on the ocean surface is crucial for predicting the flows in channels and constrictions. However, when the flow exhibits strong shear (i.e., large changes in current speed with depth), the equations predicting the speed of these long surface waves are no longer properly defined when the wave speed lies in the range of the current speeds. This note demonstrates that in certain simple conditions, the equations can be "corrected" to remove the mathematical problem, but in general, and more realistic, oceanic flows, this is not the case. However, the mathematical problem can be overcome and has a physical explanation revealing that the upstream propagation of wave signals in sheared channel flows is highly reduced.
Ocean eddies are ubiquitous in the ocean. Characterizing and quantifying their impact on the large-scale ocean circulation is key. Here, we compute eddy-mean interactions for Conservative Temperature variance, including temperature variance transfers. This is done using the ANDRO dataset, which records mean temperature and horizontal displacement of Argo floats during their journey at parking depth (;1000 m). The analysis does not show any consistency between the sign of the turbulent heat flux and the slope of the mean isotherms, questioning the validity of traditional downgradient flux turbulent closure in the context of the temperature variance budget. The temperature variance interactions suggest the dominance of the nonlocal, redistribution term over the local, transfer term. They both have typical spatial scales ranging from 200 to 1000 km. When averaged over large regions, transfers are from the mean to the turbulence, but the northwest Atlantic remains a unique region which acts as a turbulence graveyard. Within a water-mass framework, transfers are quite consistently shrinking the mean temperature distribution except for a few extreme water masses: the Arctic Intermediate Water, the Antarctic Bottom Water, and the Red Sea-Persian Gulf Intermediate Water. This is also the case for a subset of the Mediterranean Water. However, the Mediterranean Water is the main location of the sharpening of the mean temperature distribution. These results provide observational evidence of the action of the turbulence on the mean temperature structure that could be tested in numerical ocean and climate models for validation and for the development and the implementation of ocean turbulent closures.
The physical mechanisms governing ocean swell propagation are long-standing issues in physical oceanography. One key aspect is the dissipation of swell energy across the oceans, which is constrained due to limitations in observational coverage. In this study, the trans-Pacific propagation and dissipation of swells generated by Southern Ocean storms are investigated. Data are sourced from the Chinese-French Oceanography Satellite (CFOSAT) Surface Waves Investigation and Monitoring (SWIM) instrument, buoy observations, wave hindcast, and reanalysis. A total of 1755 swell trajectories are traced to quantify spectral evolution, wavelength variation, and energy dissipation along great-circle paths. As swells propagate across the ocean, the spectral width and its distribution range narrow monotonically. This demonstrates the progressive separation of frequency components in space and time as a result of frequency dispersion, leading to a more monochromatic wave field locally. The mean dissipation rate is estimated at 2.09 +/- 0.024 3 10-7 m-1, with an attenuation rate of 5.05 +/- 0.027 3 10-7 m-1. This dissipation level is approximately twice that of previous studies and exhibits a systematic bias relative to the trackwise estimate (1.35 3 10-7 m-1), likely reflecting the sensitivity of pointwise calculations to observational noise. Beyond 4000 km from the storm source, both spectral width and its variability narrow significantly. Additionally, the spectrally weighted peak wavelength within the swell partition increases by approximately 11 m (1000 km)-1 of propagation.
A theoretically operable but unvalidated method has been presented to observe the strength of the upwelling induced by global tropical cyclones (TCs); here, it is validated using observations from the daily 2-km-resolution level-3 Surface Water and Ocean Topography (SWOTl3) satellite data. The method quantifies the upwelling strength as the change of the sea surface height (SSH) extreme within a cyclonic ocean eddy (COE) or anticyclonic ocean eddy (AOE) identified from low-resolution gridded altimetry datasets. Although the artificial smoothness segment (ASS) always exists in the time series of an observed eddy SSH extreme, the method further argued that the maximum change in the ASS theoretically equals to the upwelling strength. To evidence its reliability, the time series of swath-mean SSH and the eddy extremes of three COEs and an AOE are derived from four gridded datasets. In sharp contrast to the abrupt decreases in SWOTl3-observed data, all the time series from the gridded datasets show the slow decrease near the typhoon's passage and thus directly verify the existing ASSs. Using the method, the quantified upwelling strengths near 17 degrees N are very consistent with the SWOTl3 observations, confirming its reliability. The quantified upwelling strengths in the Kuroshio near 27 degrees N seem to be enhanced with the increasing quality of the gridded datasets. However, even in the Kuroshio, the upwelling strength quantified from the best available gridded dataset in recent years should still be reliable. The validated method will provide an effective tool to quantify global TC-induced upwelling. SIGNIFICANCE STATEMENT: The upwelling induced by a tropical cyclone plays a key role in the effects of global tropical cyclones on ocean. However, a feasible method to quantify the upwelling strength is still absent for global tropical cyclones. A theoretically operable but unvalidated method has been presented. Here, this method is validated to be reliable using observations from the daily 2-km-resolution level-3 Surface Water and Ocean Topography satellite data.
Abstract The Atlantic meridional overturning circulation (AMOC) is sustained by changes in seawater density, but the link between those local density changes and the global-scale overturning circulation has not been fully resolved, in part due to ambiguity in the barotropic component of the flow. We define a new depth coordinate that compensates for the barotropic vortex stretching that balances planetary vorticity changes associated with meridional motion. In this framework, the divergence of barotropic flow is identically zero, and geostrophic divergence is determined solely by zonal density gradients. As a result, the geostrophic component of the Eulerian overturning circulation can be diagnosed directly from the density field without the need for a barotropic reference velocity or assumed level of no motion. We apply this framework to diagnose AMOC structure in a high-resolution numerical model. This application provides a direct link between density structure and overturning, clarifying how diapycnal processes at high latitudes influence Eulerian overturning at lower latitudes.
Abstract Using a 1/20° ocean general circulation model, this study investigates eddies generated along the Irminger Current west of the Reykjanes Ridge and their impacts on upper-layer (100–1000 m) restratification of the interior Irminger Sea following wintertime convection. From 2008 to 2018, 647 cyclones and 403 anticyclones are generated in the Irminger Current in the model, both carrying relatively warm waters compared to the convective interior and thus are potential buoyancy sources. However, trajectories of these coherent eddies reveal that they rarely reach the deep convection site, precluding a direct contribution to restratification therein. A heat budget analysis in the convection region indicates that the mean-state heat gain during the restratification period (April–November) is mostly accomplished by locally generated eddies. On interannual time scale, however, the variability in heat gain is modulated by seasonal and interannual fluctuations in local circulation and temperature. Although the Irminger Current eddies do not penetrate the convection site, they play an important, though indirect, role in restratification. Specifically, they facilitate substantial heat transport from the boundary current into a transition zone—the general area between the boundary current and the convective interior—where heat is subsequently advected into the deep convection site by locally generated eddies (in the long-term mean) or circulation (on interannual time scale). This study thus elucidates the heat pathway from an eddy-rich buoyant boundary current to the deep convection region in the Irminger Sea, highlighting the interplay between remote and local processes in restratification.
This paper considers coastal-trapped waves and instabilities in the nonhydrostatic Boussinesq equations in the presence of a background flow and complicated coastal topography, using a spectral method to discretize the twodimensional eigenvalue problem and solve the resulting discrete problem by standard methods. Our approach is applied to several examples and demonstrated to be consistent with previous numerical and analytical results. Further, we are able to reliably identify previously unseen coastal-trapped wave modes using a realistic coastal geometry, thereby confirming predictions made by Gelderloos et al. based on recent simulations of the southeast Greenland shelf.
Abstract In eddy-permitting models, only mixing induced by unresolved subgrid-scale eddies needs to be parameterized. Therefore, it is essential to study the diffusivity induced by eddies with spatial scales smaller than a separation scale L * , i.e., scale-specific eddy diffusivity. Using Lagrangian particle trajectories from a high-resolution model solution [Massachusetts Institute of Technology General Circulation Model (MITgcm) latitude–longitude–polar cap (LLC4320) configuration], we estimate full-depth and scale-dependent eddy diffusivities in the Kuroshio Extension region, and then develop a novel empirical formula to accurately represent their variations. Our results reveal significant variations in both the magnitude and spatial structure of diffusivity with L * and depth. We find that Eady scale–based mixing length parameterization excels in the upper ocean, while GEOMETRIC and topographic GEOMETRIC parameterizations better capture scale-dependent particle-based diffusivity in the depth range away from the ocean surface. At middepths and for L * ranging from 0.8° to 1.8°, the parameterization based on eddy size effectively represents both the spatial structure and magnitude of diffusivities. By combining the strengths of these parameterizations, our empirical formula provides an accurate representation of eddy diffusivity across the entire ocean depth. This study offers a promising approach for improving subgrid-scale eddy mixing parameterizations in eddy-permitting climate models. Significance Statement Eddy-permitting climate models require scale-specific eddy mixing coefficients to parameterize mixing processes induced by eddies smaller than the smallest resolvable scale. In this study, we show that the eddy mixing rate has significant spatial variability in the Kuroshio Extension region, varying with separation scale (the resolvable scale; the cutoff between resolved and unresolved eddies) and depth. By extending total eddy mixing parameterizations to the scale-dependent case and evaluating their performance, we develop a novel empirical formula. Our findings reveal that this empirical formula, which combines the advantages of scale-dependent GEOMETRIC, topographic GEOMETRIC, Eady scale–based, and eddy size–based schemes, captures both the magnitude and spatial variability of scale-specific eddy mixing rates well. These insights provide a promising foundation for improving climate model performance by using full-depth, scale-dependent eddy mixing coefficients inferred from parameterization schemes.
Abstract Tidal rectification over sloping bathymetry is a key mechanism for generating alongshore currents in the coastal ocean, shaping heat, salt, and material exchanges across continental margins. Yet, existing theoretical frameworks on tidal rectification often rely on a simplified continuity equation that neglects sea surface height variations—an assumption appropriate for the deep ocean without lateral boundaries but not for shallower coastal environments. Here, we derive analytical expressions for the strength of tidally rectified currents in a two-dimensional, homogeneous coastal ocean. Introducing an onshore closed boundary weakens the local cross-shore tidal current and, in turn, produces rectified currents that are substantially weaker than those predicted by previous open ocean formulations. We validate our solutions using idealized numerical simulations and discuss the underlying physical processes and parameter dependencies governing tidal rectification in coastal settings.
