Instabilities of internal gravity waves have been studied widely in an effort to shed light on how internal tidal energy is transferred to smaller-scale disturbances and eventually gets dissipated in oceans.  Among various mechanisms, considerable attention has been paid to triad resonance instabilities, particularly  parametric subharmonic instability (PSI), where the two unstable perturbations that form resonant triads with the basic wave state are fine-scale disturbances at half the basic-wave frequency.  Another approach to possible small-scale instabilities is via the so-called local stability analysis, which assumes disturbances in the form of WKB modes.  In this presentation, rather than postulating a particular instability mechanism, we use formal stability analysis based on Floquet theory.  Studying the Floquet stability eigenvalue problem asymptotically in the limit of short-scale disturbances reveals a novel, broadband instability mechanism, where instability modes comprise multiple frequency components, due to the advection of the perturbation by the underlying wave.  Applications to finite-width wave beams in an unbounded fluid and to propagating wave modes in a layer of finite depth are discussed.

Internal tides are generated in the stratified ocean interior by the interaction of barotropic tidal currents with rough bathymetry. Low-vertical-mode internal tides can transport energy far from their generation site, but it remains unclear how and where this energy is eventually dissipated at small scales. A potential mechanism for the transfer of energy from low-mode internal tides to smaller scales in equatorial regions is superharmonic generation, whereby nonlinear self-interaction of internal tides in non-uniform stratification excites waves with shorter wavelengths and higher frequencies. Here, we use a realistically-forced global configuration of the  Massachusetts Institute of Technology general circulation model to investigate an enhanced superharmonic signal in the equatorial Pacific Ocean. Using existing theory, we demonstrate that the superharmonic amplitude is consistent with nonlinear self-interaction of the original baroclinic tide, providing strong evidence for an energy pathway from the mode-1 semidiurnal internal tide to smaller horizontal scales.

The decay of the internal tide contributes to watermass mixing in the global ocean, which is relevant for the overturning circulation and the dispersal of biogeochemial tracers. In this study, we report on an understudied decay mechanism due to near-resonant interactions between low-mode internal tides. We diagnose a 30-day forward global ocean model simulation with a 4-km grid spacing and 41 layers. This simulation is forced with realistic tides and atmospheric fields. We decompose the 3D fields into tidal and supertidal (>2.5 cycles per day) vertical modes and quantify their energetics. Diurnal modes are resolved beyond mode 6, semidiurnal modes are resolved up to mode 4, and supertidal modes are resolved up to mode 2, in agreement with a canonical horizontal resolution criterion. The meridional trends in the kinetic to available potential energy ratios of these resolved modes agree with an internal wave consistency relation. The supertidal band is dominated by the higher harmonics of the diurnal and semidiurnal tides. Its higher harmonic energy projects on the internal wave dispersion curves in frequency-wavenumber spectra and is captured mostly by the terdiurnal and quarterdiurnal mode-1 waves. Terdiurnal modes are mostly generated in the west Pacific, where diurnal internal tides are strong. In contrast, quarterdiurnal modes occur at all longitudes near strong semidiurnal generation sites. The globally integrated energy in the supertidal band is about one order of magnitude smaller than the energy in the tidal band. The supertidal energy as a fraction of the tidal energy is elevated along semidiurnal internal wave beams in the tropics. We attribute this to near-resonant mode-mode interactions, which are enhanced for low f. These interactions drive cross-scale energy transfers, which we quantify with a coarse-graining method. The transfers agree with the supertidal flux divergence in spatial patterns and magnitude. 

Disturbances to a free water surface in a channel take the form of surface gravity waves that propagate to the left and right, and in so doing, communicate information along the channel according to the dispersion relation.  When current, constant with depth, is present, the dispersion relation shows that surface gravity waves propagate as before with a simple advection of the current and equal amplitudes.  However, if the current is sheared with depth, a new type of evolution of the water surface is present that corresponds to the "continuous spectrum".  It does not satisfy a dispersion relation, but is damped in time as it spreads in space.  The continuous spectrum arises as an important part of the solution of the (forced) initial value problem for a free surface flow with vertically sheared horizontal currents.  I show that for Froude numbers of order one, the continuous spectrum can have a greater amplitude than the upstream surface gravity wave mode, which loses its significance as the shear is increased, and can contribute up to a third of the total signal amplitude.  General analytical solutions are presented for long waves, including a similarity solution for the evolution of the continuous spectrum in space and time.

Observations of subsurface turbulent kinetic energy (TKE) dissipation rates under moderate to strong wind forcing on the western North Atlantic shelf show a clear enhancement relative to the classic law-of-the-wall scaling in the upper water column, with convergence toward rigid-wall behavior at greater depths. The data suggests a two-layer structure: a near-surface region characterized by approximately constant TKE dissipation rates, followed by a transitional zone where dissipation decays as ~z^-2, eventually converging to the canonical scaling associated with the law-of-the-wall (i.e. z^-1). We propose that the near-surface region of uniform dissipation defines the depth of energy injection, denoted l_o , which can be interpreted as the macro length scale representative of local turbulence driven by wave breaking. Based on the classic cascading relationship, observational estimates indicate that the depth of injection l_o is O(10^-2) - O(10^-1) meters. This depth can be scaled using either the significant wave height (​H_s) or the mean wave height (​H_m), both of which are directly derivable from the wave energy spectrum. Therefore, we propose that H_s and H_m can be used to constrain the depth of injection and inform roughness length parameterizations.  Finally, we interpret the depth at which dissipation transitions to law-of-the-wall scaling as the penetration depth (​p_d). This depth appears to coincide with a penetration depth defined solely by the presence of small air bubbles, supporting its use as a dynamically defined boundary for the wave-affected layer and its relevance for air-sea exchange studies. The penetration depth is larger than l_o, extending 5-6 times H_s from the surface. As such, we propose ​p_d serves as a physically meaningful length scale that captures the entirety of the wave affected layer.  

Most ocean boundary layers invoke an eddy diffusivity to parameterize fluxes and/or other high order covariances. To be valid, this requires that the eddy size is smaller than the boundary layer scale. We test this hypothesis by finding the top and bottom turning points of measured Lagrangian trajectories in a variety of ocean boundary layer forced by wind, wind-wave, convection and symmetric instability.  Downward trajectories mostly start near the surface and end within the boundary layer with a nearly equal probability at all depths. Upward trajectories return to the surface. This is inconsistent with eddy diffusivity models.  However, the trajectory statistics scaled by the layer depth are similar regardless of the forcing mechanism, while the energetics varies.  This suggests that a nonlocal mixing model with prescribed geometry and variable energetics might be both efficient and accurate.  Progress toward such a model will be presented.

Ocean mixing plays a fundamental role in shaping the distribution of temperature, salinity and other tracers –such as oxygen, nutrients and greenhouse gases– in the ocean interior. Quantification of turbulent mixing and associated fluxes requires measurement of small-scale velocity and/or scalar fluctuations at fast rates. These observations have traditionally been resource-intensive and, consequentially, mostly local and intermittent. Due to the sparsity of mixing observations, the spatial and temporal variability of the mixing rates and drivers are largely unknown, and so is their role in modulating heat and tracer distributions in the ocean. In recent years, progress is being made on the integration of microstructure turbulence sensors on Argo-class profiling floats. This is achieved through the integration of rudimentary sensor packages and low-power data loggers. The development includes onboard processing of the otherwise voluminous microstructure data, to make it suitable for satellite transmission. Experiments with such integrations have been done by progressive adopters of the technology. Here, we present results from two turbulence float deployments in two contrasting mixing regimes: a weakly stratified regime in the Iceland Basin, where tracer mixing is mainly driven by mesoscale isopycnal stirring, and an energetic internal-wave site over the South Atlantic, with more vigorous diapycnal mixing. We compare float observations with concomitant measurements using traditional microstructure profilers, and assess the potential of microstructure floats to expand our capacity to observe ocean mixing across a range of turbulence regimes.

We investigate the turbulence kinetic energy (TKE) budget of the upper ocean and its response to wind and wave forcing in the Southern Ocean using realistically forced Large Eddy Simulations (LES) and in situ microstructure shear observations. The widely used law-of-the-wall similarity scaling assumes that shear production of TKE is balanced by its dissipation. However, in the presence of waves, this assumption is violated: dissipation is primarily balanced by local Stokes shear production, augmented by almost equal contributions from local Eulerian shear production and non-local convergence of TKE transport. Current similarity scalings that include waves effects predict dissipation through the addition of a Stokes shear component, typically through the turbulent Langmuir number. Through a systematic interrogation of similarity scalings relative to resolved turbulence in the LES and measured dissipation, we present an empirically derived augmentation to the existing suite of similarity scalings that takes into account the role of the turbulent transport term in addition to Stokes shear. We further use these results to reason why the canonical law-of-the-wall scaling appears to predict measured dissipation under wave forcing, even though the underlying physical reasoning does not hold. These insights have important implications for interpreting turbulence dissipation rate observations.

Langmuir turbulence in shallow-water coastal environments can sometimes evolve into full-column Langmuir supercells, enhancing eddy sizes and vertical mixing in the entire column. However, their generation requires suitable coupling between near-surface wind-wave and the near-bottom current-shear forcings. We use large-eddy simulations (LES) to investigate how wind, waves, and current shear modulate the coherent structure, energetics, and resulting mixing of coastal Langmuir turbulence under different circumstances. The main focus of this study is to explore the effects of longitudinal alignment, namely the aligned or opposite wind-wave and current. Results show that Langmuir supercells, which emerged with aligned forcings, possess an intense full-column, narrow-band energetic mode. This energy spectrum is distinct from and coexists with that of Langmuir turbulence. Under this circumstance, the momentum exchange at the column scale is highly asymmetric between upwelling and downwelling limbs. Strong connections between surface and bottom turbulence, as indicated by the vortex-tube connections, can only be found in upwelling regions. As a result, the upwelling motions contribute considerably more momentum flux than the downwelling motions. When wind-wave and current oppose, only Langmuir and shear turbulence exist near the surface and bottom boundaries. Moreover, despite no stratification in simulations, their structures are split by a mid-layer barrier that limits surface-bottom interaction. All these results indicate that, despite the windrow pattern on the ocean surface from near-surface wind-wave interaction, different scales and intensities of mixing below the surface could happen, depending on different wind-wave-current interactions.

The Ogasawara subregion of the Izu-Ogasawara-Mariana arc system in the western North Pacific is recognized as one of the most notable hotspots for thermocline turbulent mixing. While parametric subharmonic instability (PSI) is generally considered a primary driver of enhanced turbulence by facilitating energy transfer from low-mode semidiurnal internal tides to high-mode near-inertial waves (NIWs), recent observations suggest that NIWs remotely induced by winds also contribute to significant seasonal variations in thermocline turbulence in this region. Here, three-day velocity and density yo-yo measurements, conducted near the PSI critical latitude of 28.8°N opportunistically after several storm passages, reveal the coexistence of PSI-induced high-mode NIWs and wind-induced low-mode NIWs. Two distinct pairs of upward- and downward-propagating NIWs are identified, each forming a phase-locked triad with locally generated upward-propagating semidiurnal internal tides. In a mid-depth layer, a pair of high-mode upward- and downward-propagating NIWs form a scale-separated PSI triad with the internal tides, whereas in an overlying layer, a pair of low-mode downward-propagating NIWs and intermediate-mode upward-propagating NIWs form a distinct non-scale-separated triad. Consequently, turbulent dissipation is enhanced at the boundary between these distinct near-inertial velocity layers. These findings are not inconsistent with the view that wind-induced low-mode NIWs interact with internal tides, promoting the growth of intermediate-mode NIWs and eventually contributing to the enhanced thermocline turbulence, thus suggesting an overlooked pathway to turbulence in the ocean interior.

Planning and adapting to future coastal ocean conditions requires accurate coastal ocean predictions of the nutrient, pollutant, heat and sediment transport. In regions with an energetic internal wave field, turbulent mixing can be dominated by nonlinear internal waves which can steepen and break in the coastal ocean, generating bursts of intense turbulence that can drive nutrients into the euphotic zone. Here, I will present data from both process-based field campaigns and long-term monitoring efforts to demonstrate the role of internal waves in mixing the coastal ocean.  Our observations demonstrate that overall the diapycnal mixing is dominated by relatively rare but energetic mixing events, driven by high-frequency internal waves and steepened internal bores. Long-term records reveal that the semi-diurnal barotropic tide, the spring-neap tidal variability, and the seasonal variability in stratification all affect the magnitude of diapycnal mixing and its vertical distribution. Finally, I will share detailed near-seabed observations that reveal the role of internal waves and boundary layer turbulence in resuspending and transporting sediment.

Vortices in the ocean interact with near-inertial waves (NIWs), leading to mutual modifications in wave propagation and vortex dynamics. In the case of idealized mesoscale vortices with single-sign vorticity, NIW energy tends to concentrate and become trapped within anticyclones, while being repelled from cyclones. This energy trapping in anticyclones occurs periodically in time, at a frequency much lower than the local inertial frequency.

We demonstrate that this behavior arises from the excitation of trapped near-inertial eigenmodes, which are naturally supported by the vortex structure and can be efficiently excited by an initial wave field with a horizontal scale much larger than the vortex radius. Using the reduced model for NIW dynamics developed by Young and Ben Jelloul (YBJ), we investigate this mechanism and validate the theoretical predictions against high-resolution numerical simulations of the three-dimensional Boussinesq equations.

Extending our analysis to submesoscale vortices, we modify the YBJ model to incorporate cyclostrophic effects, allowing us to study vortices in cyclogeostrophic balance. We explore how these additional effects modify the eigenmodes and the characteristics of wave trapping. Finally, we examine shielded vortices, where the interaction with NIWs gives rise to more complex wave structures due to the radial structure of the vorticity field.

In estuaries, cross-channel (lateral) flow can be generated through differential salt advection due to faster tidal currents in the deeper channel, resulting in the formation of two counter rotating flow cells across the estuary (axial convergence). This study examines flow interactions between estuarine axial convergence flows and wave-driven Langmuir turbulence (LT) in an idealized estuary. LT is characterized by wind-aligned roll vortices (Langmuir cells) which enhance mixing and may couple the surface and bottom boundary layers in shallow coastal oceans. Utilizing a shallow water large eddy simulation (LES), lateral circulation is driven by an oscillating tidal pressure gradient force and an along-channel density gradient. LT is generated through the Craik-Leibovich (CL) vortex force which includes the Stokes drift due to wind-driven surface gravity waves. Over the course of a tidal cycle, the estuary transitions between channel- wide pairs of axial cells on flood and ebb tides and developing LT fields during slack tides. Langmuir cells on low and high tides generate enhanced vertical overturning and inhibit density stratification, resulting in the development of axial cells up to three hours earlier on flood tides compared to the case without LT. Axial cells develop vertically sheared lateral currents that distort and inhibit the formation of coherent Langmuir cells. Both Langmuir cells and axial cells receive vorticity from lateral shear of along-channel tidal currents via vortex tilting by wave induced Stokes drift. Overall, LT and axial flow interactions display complex two-way feedbacks, which may significantly impact the estuarine circulation.

We examine the life cycle of wind-generated, near-inertial internal waves with a suite of nested high resolution simulations spanning a range of scales from hundreds of kilometers  to a few meters. The outer domain encompasses a region that includes the  Sidra Gyre, a semi-permanent anticyclone located off the coast of Libya, while the innermost domain moves with the eddy core and is limited to the region at the base of Sidra.

The coordinated nested simulations produce a dynamically-coupled flow field consisting of mesoscale eddies, submesoscale filaments, near-inertial and higher frequency internal waves, shear-driven instabilities, and nearly isotropic turbulent motions down to the Ozmidov scale, allowing for a comprehensive detailed study of dynamical processes from the meso- to turbulent scales in a realistic ocean setting. Our one-way nesting approach reproduces energy cascades tracked from wind-forced near-inertial waves in the surface mixed layer, through refraction and trapping in a baroclinic anticyclone, downward propagation into the pycnocline, critical-layer amplification and ultimately to shear instability, yielding insight unattainable with stand-alone simulations.

In this talk, we will address the fundamental question of how near-inertial internal waves are connected to diapycnal mixing: Do near-inertial waves break and directly produce small scale,  isotropic turbulence or is there an intermediate transition to large-scale anisotropic turbulence on the path to isotropy and dissipation?

Ocean surface waves strongly modulate vertical turbulent mixing in the ocean surface boundary layer. When they are aligned with wind-driven shear, Craik-Leibovich instability occurs, resulting in the formation of Langmuir turbulence that strongly enhances vertical mixing. By the same mechanism, ocean surface waves can also stabilize the water column and suppress boundary layer turbulence when they are in opposite direction as the Eulerian current. Here, we demonstrate this stabilizing effect induced by opposing Eulerian current and Stokes drift in large eddy simulations (LES) under idealized homogeneous surface cooling and no wind conditions. Rolls of convection form under the competing effects of destabilizing surface cooling and stabilizing wave-induced stratification. The latter depends on the alignment of Eulerian shear and Stokes drift shear, resulting in roll structures aligned perpendicular to Stokes drift. In addition, the intensity of turbulence is significantly reduced as compared to the case of pure convection. Such stabilizing effect of wave-induced stratification has yet to be incorporated in wave-driven mixing parameterizations and may leads to potential improvements. Using this idealized test case, we also demonstrate the effect of assuming down-Eulerian shear mixing versus down-Lagrangian shear mixing in the sub-grid scale scheme by comparing two LES models. While such effect may be hidden in strongly wind-forced cases, it results in completely different solutions in this idealized case by changing the boundary condition for the mean flow. Therefore, care should be taken when designing and interpreting LES with misaligned currents and waves.

Over the last decades there has been significant progress on both submesoscale physical oceanography observations (km to tends of km in horizontal scale) and turbulent microscope observations (cm to m scales).  The physical processes in between those scales (meters to km horizontally and ~1-10 meters vertically) are less well understood.  Some of this ‘finescale’ range consists of breaking internal waves, moving energy through anisotropic processes towards fully three-dimensional turbulence. Some of instead appears to consist of fronts, filaments, wisps, billows, braids, and other things for which we yet have no names. Here I’ll show examples from a decade of observations using novel high resolution lateral and vertical measurements to start to explore the underlying phenomenology and physics. 

The ocean is not in a steady state. Deep ocean waters (2000-4000 m) are warming at a rate of O(1) m^oC/year, with significant regional variability in the sign and magnitude of the observed change. Identifying these signals has required 50 years of concerted observational efforts. We re-evaluate the classical `Abyssal recipes' framework of Munk 1966, i.e. a 1D advection-diffusion balance, by accounting for a lack of steady state. We find that the rate of change of temperature is comparable to the divergence in heat flux from upwelling and mixing. Our analysis shows that a simple double-exponential solution, fit to individual ocean temperature profiles, can be used to derive the ratio between the rate of change of temperature and the vertical effective diffusivity. Using the turbulent diffusivity, inferred from the finescale internal wave parameterization, we can predict the rate of change of temperature, which matches the magnitude of observed trends. Inverting this calculation, we use observed changes in temperature to create a global map of vertical effective diffusivity and vertical velocity. Our analysis demonstrates that the vertical structure of ocean tracers contains valuable information coupling the rates of warming to the magnitude of turbulence, and provides an independent method to estimate temperature trends, diffusivities and vertical velocities.

Tides are a key source of energy for ocean mixing, particularly in the quiescent deep ocean where alternative energy sources are limited. Though much is qualitatively understood about the mechanisms by which tidal energy is dissipated, knowledge gaps remain in our ability to quantitatively predict when and where tidal mixing will occur, hindering our ability to accurately model ocean circulation on global scales. This is especially true for low-mode internal tides that can transfer energy across ocean basins away from their generation sites.

In this talk, I will discuss the role of coastally trapped waves (CTWs) in tidal energy pathways, with a particular focus on their superinertial variants. Unlike subinertial CTWs—which are well documented—superinertial CTWs have received comparatively little attention. These waves travel along coastlines while radiating energy into the ocean interior as freely propagating internal tides. Recent work has shown that superinertial CTWs can be generated through scattering processes when along-shelf topographic corrugations satisfy a triad resonance condition with incoming waves. In this way, superinertial CTWs may serve as a key mechanism linking low-mode internal tides to turbulent dissipation near coastal boundaries.

The use of the Lagrangian form of the equations of motion in theoretical oceanography is rare. Surprisingly, many studies of wave-wave interactions of internal gravity waves have used coupling coefficients derived from a Lagrangian formulation. We revisit the Lagrangian framework, including rotation and non-hydrostatic conditions, derive a Hamiltonian and show how coupling coefficients of the Lagrangian/Hamiltonian frame and the Eulerian frame are related. A major difference of the Lagrangian and Eulerian formulations concerns how energy is expressed in terms of the field variables (for the Boussinesq system: velocities and buoyancy) and the normal mode amplitudes of the respective systems. While energy (local or integrated over the system's domain) of the Eulerian system is strictly quadratic in physical and in Fourier space, the Lagrangian one is quadratic only in physical space but a non-linear functional of its normal mode amplitudes. The consequence for energy conservation and the scattering integral (Boltzmann integral) for wave-wave interactions, derived by wave-turbulence theory, is investigated in detail. Emphasis is put here also on non-resonant interactions which so far have entirely been neglected in internal wave research. 

We assess a prognostic formulation of triple coherence relating to energy exchange between mesoscale eddies and the internal wavefield and compare with observations from the Sargasso Sea. 

We break new ground in the following ways:  

(1) We utilize concepts from Open Quantum Systems to arrive at the essential results presented in Muller (1976, JFM), where eddy induced internal wave-stress perturbations are damped using a nonlinear relaxation time scale approximation. The broad brush take on Open Quantum Systems is that there is a system (ray tracing), a bath (a background internal wavefield) and a system-bath interaction (nonlinear relaxation).  We avoid the asymptotic expansion involving small perturbations to wave phase speed that is the basis of Muller.  

(2) We define the background internal wave spectrum based upon a regional characterization of the wavefield in the Sargasso Sea.  This differs from the canonical description referred to as GM76 in crucial respects.  

(3) We use recent theoretical work on both extreme scale separated interactions and the internal wave kinetic equation to properly define relaxation time scales.  

Agreement of the prognostic formulation with data is remarkable and is consistent with eddy-wave coupling dominating the regional internal wave energy budget, as in the diagnostic study of Polzin (2010, JPO) using data from the Local Dynamics Experiment of PolyMode III.  Extraction of eddy energy happens at the horizontal and vertical scales that characterize baroclinic instability and potential vorticity fluxes.  The goodness of this effort reinforces a prior hypothesis (Polzin and Lvov, 2011 RoG) that the character of the internal wavefield in the Sargasso Sea is set by this interaction, which, in turn, serves as an amplifier of tertiary energy inputs from larger vertical scales that characterize internal swell.  With this knowledge and confidence, we then speculate on the role that this coupling plays in mesoscale eddy dynamics in the Southern Recirculation Gyre of the Gulf Stream.  We argue that this nonlinear relaxation effectively provides a local eddy enstrophy damping consistent with potential vorticity flux observations from the Local Dynamics Experiment.  This happens at spatial scales somewhat smaller than the energy extraction scale and locates the end of the potential enstrophy cascade in the spectral domain as the energy containing scale of the internal wavefield.  We offer insight into how speculation might acquire firmer ground by showing how modulation of the lower bound of the internal wavefield by eddy relative vorticity and thickness gradients can be incorporated into the existing formulation.  In the context of a formal WKB approximation, the current formulation stands as a 'geometric optics' approximation whereas modulations of the waveguide are 'physical optics'.  

Regardless, the dynamical consequence is that wave-eddy coupling is responsible for the maintenance of gyre scale potential vorticity gradients.

Fram Strait is a key gateway between the North Atlantic and the Arctic Ocean, where mixing processes drive sea ice melt, primary production, and water mass transformations. The region features a pronounced seasonal cycle of upper-ocean stratification – shaped by sea ice meltwater release in summer and convective mixing in winter – and strong tidal currents on the nearby Yermak Plateau. Since buoyant meltwater accumulates close to the surface, shallow observations are required for understanding momentum transfer, turbulence generation, and subsequent mixing in this regime.

Combining near-surface measurements from autonomous instruments on drifting sea ice floes with data from moorings and crewed ice stations, we show that internal waves generated from tide-topography interactions influence the meltwater-stratified boundary layer. In particular, they enhance boundary stress at the ice-ocean interface and interact with the near-surface mesoscale currents, which catalyzes wave-driven turbulence. Notably, these upward-propagating waves exhibit energetic resonant frequencies of the semidiurnal and diurnal tides at approximately 3 and 4 cycles per day. We further link internal tides to episodically enhanced (“spiking”) velocity shear in the upper ocean (<25 m depth).

We hypothesize that internal wave-driven mixing prolongs plankton blooms and weakens the meltwater stratification in summer, entrains heat into the convective mixed layer in winter, and facilitates cross-scale energy transfers below the ice. This highlights the role of internal waves and subsequent turbulent mixing for energy transfers and ecosystem dynamics in a changing Arctic Ocean.

We report on direct measurements of ocean turbulence collected by a Slocum glider equipped with a Rockland Scientific MicroRider turbulence package, alongside yearlong mooring observations and results from a high-resolution, three-dimensional regional tidal model. These data were acquired as part of the Northern Ocean Rapid Surface Evolution (NORSE) project. The study site is located on a ridge in the Norwegian Sea near Jan Mayen (71˚N, 7˚W), in close proximity to a branch of the Norwegian Atlantic Current that interacts with the local Jan Mayen Spur topography.

The group velocity of linear internal waves depends on their intrinsic frequency, as well as the Coriolis and buoyancy (Brunt–Väisälä) frequencies. At this latitude (71°N), semidiurnal ("D2") internal waves can radiate energy, whereas diurnal ("D1") tidally forced baroclinic motions are subinertial, possess evanescent group velocities, and remain confined to topographic features. When subinertial motions become trapped over isolated topography, energy can propagate azimuthally along closed isobaths. Dissipation is enhanced by bottom-intensified processes such as shear instabilities and hydraulic jumps, which may be sufficient to balance both the local tidal energy input and any nonlinear energy leakage. This energy trapping results in elevated effective diffusivities near topography, supporting enhanced diapycnal fluxes of heat, salt, and buoyancy.

Our observations reveal enhanced dissipation, elevated mixing rates, and increased diapycnal heat fluxes throughout the water column at the ridge site. Model results further suggest that the mooring and glider sampling fortuitously captured one of several regional hotspots of intensified dissipation located along closed topographic contours encircling Jan Mayen.

Regional deviations of ocean internal-wave (IW) spectra from the empirical Garrett-Munk (1976) model have been widely documented and are thought to depend in part on variations in forcing mechanisms, including from interactions with mesoscale eddy fields, through parametric-subharmonic-instability decay of low-mode tides, and through wind forcing of near-inertial waves.  We present vertical profiles of internal-wave dissipation from high-resolution simulations in three regions corresponding to these different forcing regimes.  The numerical model has frequently updated wind stresses, astronomical forcing, and nested boundary conditions from an IW-permitting global ocean model.  Potential and kinetic-energy spectra are characterized for both eddy and IW fields.  Comparisons are made with fine-scale-based IW dissipation estimates.  We evaluate the relative importance of different numerical schemes by region.  Previous work from a single region north of Hawaii showed favorable comparisons with finescale-based observations if suitable numerical dissipation schemes were used, namely, that the horizontal viscosity scheme be restricted to not act on horizontally divergent modes.  Building on this work, the prospects of restricting the horizontal (Leith) viscosity scheme to improve internal wave representations across regions and IW forcing regimes are evaluated.

Oceanic mesoscale eddy mixing plays a crucial role in the Earth’s climate system by redistributing heat, salt and carbon. Eddy mixing, typically parameterised by an eddy diffusivity, is impacted by various physical factors, one of which is the oceanic bottom slope. Within a barotropic framework, it can be shown analytically that bottom slopes suppress the cross-slope eddy diffusivity. Unfortunately, adding baroclinic effects greatly increases the complexity of the problem. To understand how bottom slopes influence eddy diffusivity in a baroclinic framework, we study eddy fields in a quasi-geostrophic two-layer model with a linear bottom slope. We investigate the eddy diffusivity by releasing and tracking virtual particles in the flow fields and analysing how they spread in the cross-slope direction. This is done for a range of bottom slope magnitudes and for prograde as well as retrograde slopes. We find that for steep bottom slopes, the baroclinic instability is suppressed, the eddy field gets weaker, and the spreading of particles in the cross-slope direction decreases. This suppression is observed not only in the bottom layer, where the slope is located, but also in the upper layer. We investigate how the eddy diffusivity depends on the eddy kinetic energy and the Lagrangian integral timescale. Notably, both of these factors behave asymmetrically for prograde and retrograde slopes. Furthermore, we compare the Lagrangian diffusivities with Eulerian potential vorticity (PV) diffusivities as computed by the flux-gradient relation. Whereas the two measures agree in the upper layer, the Eulerian diffusivities are higher than the Lagrangian diffusivities in the lower layer, but the bottom slope does not affect the differences; the discrepancy is already seen for a flat bottom case. These results raise questions about the meaning of either type of diffusivity and the true meaning of "suppression" by bottom slopes.

Recent work—both numerical and observational—indicate that bottom boundary layers along sloping bathymetry can support a range of submesoscale, balanced flows characterized by order one Rossby and Richardson numbers. Such flows can significantly alter the dispersion and polarization relations of internal waves, resulting in wave-mean flow interactions that can facilitate energy transfers between the two types of motions, trigger wave breaking, and generate turbulence. In addition, the presence of submesoscale currents can greatly modify internal wave reflection off bathymetry by redefining the criterion for critical reflection and preventing internal waves from reaching the seafloor through wave evanescence. In this presentation, the theory behind these internal wave-mean flow interactions will be described and their mechanisms will be demonstrated using numerical simulations. Potential impacts on mixing, water mass transformation, and energy budgets of the circulation and internal wave field will be discussed, and observational evidence of internal wave-submesoscale current interactions in bottom boundary layers will be presented.

The break-up of internal gravity waves (GWs) renders an important mechanism for depositing energy from remote regions to the mean flow. Where the mean velocity equals the wave’s phase speed, linear theory predicts a divergent amplitude growth (critical levels). Consequently, GWs break and, depending on the background properties, lead to turbulence. This transition to a turbulent state includes wave dissipation, but also secondary GW emissions. These secondary emissions represent a mechanism of energy flux through critical levels.
We perform 2D direct numerical simulations of GWs in Boussinesq theory.
Under varying initial background conditions we investigate the appropriate turbulent break-up and re-emission. Results show that the modulation of the gradient Richardson number by the growing wave amplitude can cause overturning instabilities right in front of a critical level. Wave stress can adjust the background conditions so that in the initial absence of a critical level such can be realized after a while, leading to wave break-up, as well.

As the Kuroshio encounters a small-scale island, a forward energy cascade is generated, modifying local and far-field water mass properties and nutrient supplies in a region with economically significant fisheries. Green Island (~10 km diameter) is located in the main path of the strong Kuroshio off the SE coast of Taiwan. Its pronounced wake and associated instabilities have been captured persistently in satellite images, with highly variable properties. We identify and characterize turbulent mixing hotspots and governing mixing mechanisms in the Green Island wake using data collected from four repeated deployments of 7-9 EM-APEX profiling floats clusters.

EM-APEX profiling floats were equipped with two pairs of electromagnetic (EM) sensors, SeaBird Electronics SBE41 CTD and two FP07 temperature microstructure probes (Sanford et al., 1985, 2005; Lien et al., 2016). Floats measured temperature, salinity and pressure with vertical resolution Dz ~ 2-3 m, temperature variance dissipation rate with Dz ~ 3 m and horizontal velocity components with Dz ~ 7 m, at vertical profiling rate ~ 0.15 m/s. Float trajectories were strongly modulated by tidal currents and wake vortex shedding.

Enhanced turbulent kinetic energy dissipation rate ∼10⁻⁷−10⁻⁶ W/kg coincides with the Kuroshio high salinity core (50-200 m), suggesting that mixing by wake eddies results in erosion of typical Kuroshio properties, and implying significant impact on water mass transformations downstream.

Large dissipation rates occur at Richardson number Ri < 1, suggesting strong mixing is driven by vertical shear instabilities. Vertical wavenumber spectra for vertical shear and vertical strain have variance larger by a factor of ~10 than GM for vertical wavelengths ~100 m, and shear-to-strain ratios larger by a factor of ~2 than GM, pointing to the presence of other dynamics in addition to internal waves. Polarization ratios of vertical wavenumber spectra for counterclockwise and clockwise rotating vertical shear suggest net downward energy propagation, assuming internal waves.

Horizontal divergence and relative vertical vorticity distributions are negatively skewed, with values spanning ~0.03-30 f.  Absolute values of relative vertical vorticity are on average greater by a factor of ~2 for negative compared to positive values, suggesting preferential entrapment of floats on the anticyclonic side of the wake.  Large dissipation rates occur at high Froude numbers, as well as high Rossby numbers, particularly for negative relative vorticity and negative potential vorticity anomaly, possibly indicating strong mixing driven by symmetric instabilities.

Internal gravity waves are a well-known mechanism of energy transport in stratified fluids such as the atmosphere and the ocean. Their abundance and importance for various geophysical processes like ocean mixing and momentum deposition in atmospheric jets are widely accepted. While resonant wave-wave interactions of monochromatic disturbances have received intensive study, little work has been done on triad interactions between wave trains that are modulated by a variable mean flow.
Voelker, Achatz, and Akylas (2020) showed that in Boussinesq dynamics, modulation through wind shear can partially suppress resonant interactions between wave triads. Here, we extend the underlying multiscale WKB theory to compressible dynamics and include both wave-mean-flow and wave-wave interactions. As one might expect, the wave propagation prior and after wave-wave interactions, as well as the interaction amplitudes, are sensitive to the direction of wave vectors due to the anelastic amplification effect. Using the method of an effective near-resonant interaction window, we furthermore find that the exchanged energy between triads depends on both the varying stratification and the wind shear. As a consequence, there are three regimes for the interaction. The first, reminiscent of the analysis of Voelker, Achatz and Akylas (2020), is a modulated interaction dominated by wind shear. A second regime, where the modulation is dominated by a changing stratification, similarly acts as a suppression mechanism for the near-resonant triadic energy exchange. Finally, the combination of both may lead to a third regime where the two modulation mechanisms can partially cancel out, such that the near-resonant triad interaction yields an energy exchange comparable to quiescent conditions.
In this contribution, we demonstrate the above-mentioned effects on the generation of a third wave by two incident waves, using idealized 1.5-dimensional LES with pseudo-incompressible dynamics. In neutral conditions, the meaning of upward scattered energy versus downward scattered energy is emphasized. Furthermore, we show the three interaction regimes and relate the results to the effective interaction windows resulting from the multiscale analysis.

Accurate knowledge of ocean surface currents is essential for forecasting weather and climate, marine ecosystems, and navigation at sea. Traditional approaches are limited to point measurements, typically from ships, or snapshots in time from space. In this talk I will introduce Geostationary Ocean Flow (GOFLOW), a novel product that employs existing high spatio-temporal resolution broad banded geo-stationary satellite data of the sea surface temperature together with machine learning techniques trained on state-of-the-art ocean models, to provide hourly ocean surface velocities from spatial scales of kilometers to entire basin scales.

Compared with existing operational ocean products (AVISO) and state-of-the-art satellites (SWOT), GOFLOW provides unparalleled temporal and spatial velocity resolution over a wide range of space and time scales without the need to assume geostrophic balance. I will specifically present GOFLOW’s ability to capture submesoscale turbulence statistics in the Gulf Stream Region, as well as to provide observational estimates of cross-scale kinetic energy fluxes at an unprecedently high spatial resolution.

Straits are conduits for the exchange of physical and biogeochemical properties of water masses, between large water bodies. Local changes in mixing along narrow and shallow straits have significant impact on the exchange flow. As a non-tidal, narrow and shallow strait, the Strait of Istanbul (a.k.a, Bosphorus) carries the brackish surface waters of the Black Sea and the salty deep Mediterranean Sea waters that are partially mixed in the Sea of Marmara via two-layered exchange with a striking salinity contrast of ~20 psu and a density interface that separates the distinct water masses. Past field-observations are collectively used for the first time to analyze (1) the seasonal entrainment rates across the interfacial layer, (2) the mixing processes along the strait. The interface shallows, stratifies and thins in spring with accelerating runoff (via major rivers of the Black Sea) accompanied by suppressed detrainment near its northern-end and enhanced entrainment near its southern-end. In spring, the observations show complex mixing patterns near the topographic controls with signatures of both Holmboe and Kelvin-Helmholtz instabilities, occurring along the upper and lower bounds of the interface and within the interface. In both along and cross-strait directions internal waves are accompanied by isopycnal displacements. Sholing of the interface due to supercritical regime switch causes upward energy cascade from the interface to the surface layer (coupled interfacial and surface stresses), whereas the opposite occurs with subcritical regime switch causing downward energy cascade (coupled interfacial and bed stresses) enhancing the lower-layer mixing. Hot spots for stratified turbulence and shear-driven turbulence are identified by analyzing the spectral content, anisotropy, temporal patterns, and energy transfer signatures in the backscatter data (i.e., layered, wave-dominated, and anisotropic features that favor diapycnal mixing differed from vortex-rich, isotropic patterns). The key parameters that control the local mixing in stratified and sheared strait-flows are identified as the relative depth and strength of shear and stratification in the water column, the interface thickness scaled by length of constriction, and the interfacial stress scaled by surface and bottom stresses.

With its freshwater input and low surface salinity, strong stratification and associated complex thermal structure, the Bay of Bengal is of great importance for monsoon dynamics but also represents a unique mixing environment. The shallow mixed layers in the Bay of Bengal dictate large energy fluxes under wind forcing, but the strong stratification can also limit the turbulent cascade, increase the intermittency of mixing, and suppress the translation of this energy into near-inertial internal waves at depth.

The 2024 EKAMSAT/ASTraL (funded by the Office of Naval Research) project cruise took place in the Bay of Bengal in May-June last year and utilized a wide array of oceanic and atmospheric instruments to investigate air-sea interactions at multiple scales. In particular, two drifting wave-powered profilers (Wirewalkers) were deployed. These were equipped with CTDs and ADCPs (as well as Chl and optical backscatter sensors), profiling the upper 100m and 500m of the ocean respectively. In addition, a custom fast-CTD and microstructure profiling system (with both shear and temperature fast response sensors) was deployed off the R/V Thompson doing transects in the vicinity of the drifting Wirewalkers. The ADCP-derived velocities reveal an environment of strong stratification and complex shear in the upper ~200 meters, despite limited wind forcing. 

During the cruise, tropical cyclone Remal formed over the Bay of Bengal at about 10° north of the equator and passed right over the sampling area on its way north. Remal deposited large amounts of precipitation and momentum in the area, which affords an excellent opportunity to study processes at multiple scales. Here we focus in particular on the generation of near-inertial internal waves, their interaction with strong stratification and shear, and associated patterns of elevated turbulent mixing. About 14 days after the passage of the storm, a coherent wave package appears below 400m. Measured turbulent dissipation is elevated, but interestingly, the buoyancy Reynolds number (the bandwidth available for the classic turbulent energy cascade) is small due to the extremely high stratification. The potential path of the cyclone energy from the surface to depth can shed light on how wind-driven motions penetrate strongly stratified interiors, and the role of fine-scale processes in enabling deep ocean mixing.

Sharp fronts with temperature differences of approximately 0.5°C across a remarkably small lateral scale of order 10 m were observed in a subtropical region with strong mesoscale and submesoscale activity in the southeast Atlantic at 34°S, 6.5°E, far away from any coastal freshwater sources. These fronts were formed at the leading edge of a buoyant gravity current of 20-40 m thickness that propagated at a speed of order 0.1 m/s relative to the colder and thus denser surrounding waters. High-resolution turbulence microstructure observations revealed strongly enhanced turbulence inside the nose of the gravity current, while turbulence in the trailing bulk region was mainly wind- and convectively-driven and showed a strong diurnal modulation. Satellite and meteorological data suggest that the gravity current was triggered by the mesoscale strain-induced sharpening and final collapse of a larger-scale front at the edge of a mesoscale eddy during a period with decaying winds. In contrast to previous studies that have identified similar buoyant gravity currents in the equatorial ocean at the edge of Tropical Instability Waves, our data suggest that they can also form at a mid-latitude location where rotational effects are strong. This suggests that even balanced fronts can decay into gravity currents under certain conditions, indicating a potentially relevant pathway for mesoscale energy dissipation and mixing.

The surface mixed layer (ML) mediates fluxes of momentum, heat, nutrients, and gases between the surface and subsurface ocean, influencing weather, climate, and marine ecosystems. The Labrador Sea, with strong winds and a highly variable deep ML, is ideal for studying turbulence under different atmospheric and oceanic forcing conditions. We analyze vertical water velocity sampled by oceanic gliders from December 2021 to May 2022 to quantify the turbulence response in a deep convective environment.

For one-third of the wintertime and springtime profiles, vertical velocity variance is elevated in the upper part of the ML (as determined by a density threshold) and does not reach the ML depth. During winter, the ML vertical velocity variance responds to wind and surface buoyancy forcing with a delay of half a day or less. The effect of buoyancy loss on ML mixing strength outweighs the contributions of wind shear and Langmuir turbulence in terms of relative importance. In mid-spring, however, the relative importance of buoyancy loss decreases, with no single time lag dominating the relationship between vertical velocity variance and atmospheric forcing. The decrease in buoyancy loss allows for a more diverse forcing regime, with increasing relative contributions from wind shear, geostrophic shear, and Langmuir turbulence to mixing strength. These findings suggest that in winter and early spring in the Labrador Sea, only part of the ML may be treated as actively forced by buoyancy, raising the question of whether conventional scaling approaches to turbulence are valid for deep ML.

Extratropical cyclones (ETs) are the primary source of oceanic near-inertial waves (NIWs) whose turbulent mixing helps sustain climate. Despite mounting evidence showing that the properties of ETs are shifting under climate change, it is unclear whether NIWs and their energy fluxes are subject to the same trends. To address this, we use a modified slab model and reanalysis winds to reconstruct historical patterns of inertial pumping and NIW energy fluxes into the ocean interior. Significant trends exist in all ocean basins but differ in sign and origin. Inertial pumping appears to intensify and shift to higher latitudes in the North Atlantic and Southern Oceans, following known changes in the ET storm tracks. Internal variability appears to dominate changes in the North Pacific. Changes in the morphology of ETs are also related to multidecadal trends in the horizontal wavelength of NIWs. Preliminary analyses use altimetry data to discern whether aforementioned trends are intensified or dampened by mesoscale eddies. Overall, these results suggest large scale changes in the spatial distributions of NIWs and their mixing. Lastly, they emphasize the importance of understanding NIWs as actors in the coupled ocean-atmosphere system, as storm-resolving coupled climate models are increasingly used in long-term projections.

In this presentation, I will briefly review estuarine mixing principles, ranging from the local variance decay of salinity variance due to molecular mixing on the micro-scale all the way to bulk estimates of entire estuarine systems. Some real estuaries will be used as examples, but focus will mainly be on the Elbe estuary in northern Germany.

While surface submesoscale processes have been extensively studied, their counterparts within the bottom boundary layer (BBL) remain largely unexplored. However, a few recent investigations have suggested that these subsurface structures—emerging primarily through flow-topography interactions—play a critical role not only in turbulent boundary mixing but also in the forward cascade of mesoscale energy toward dissipation and in facilitating lateral exchanges between boundary waters and the ocean interior. To date, most studies have focused on the emergence of submesoscales in the open ocean, particularly near strong, persistent current systems, coastal jets, or dense water outflows. This study uses the Baltic Sea as a natural laboratory to show that interior submesoscale structures can also arise in semi-enclosed, strongly stratified basins, far from major current systems, in regions where transient wind-driven currents typically dominate. Using realistic, high-resolution numerical simulations, we demonstrate that submesoscale vortices and filamentary features are widespread beneath the mixed layer, particularly during storms when the winds intensify the currents. Reversal of winds reverses the currents, significantly affecting the submesoscale generation sites and the mixing hotspots that exhibit, consequently, transient behavior. The intense winds also induce coastal upwelling and downwelling with the up-and downwelling sites evolving into pronounced mixing hotspots with enhanced dissipation rates as submesoscale overturning instabilities arise in the BBL. Interestingly, symmetric instability dominates even under upwelling-favorable winds —when limited mixing and increased stratification are typically expected—likely as a result of boundary friction and the development of a bottom Ekman layer within the upwelling tongue. These findings highlight the broader significance of storm-forced submesoscale dynamics in wind-driven marine and limnic systems, extending their relevance beyond the Baltic Sea context.

Across the stable density stratification of the abyssal ocean, deep dense water is slowly propelled upward by sustained, though irregular, turbulent mixing. The resulting mean upwelling determines large-scale oceanic circulation properties like heat and carbon transport. In the ocean interior, this turbulent mixing is caused mainly by breaking internal waves: generated predominantly by winds and tides, these waves interact nonlinearly, transferring energy downscale, and finally become unstable, break and mix the water column. This paradigm, long parameterized heuristically, still lacks full theoretical explanation. Here, we close this gap using wave-wave interaction theory with input from both localized (see Figure 1) and global observations. We find near-ubiquitous agreement between first-principle predictions and observed mixing patterns in the global ocean interior. Our findings lay the foundations for a wave-driven mixing parameterization for ocean general circulation models that is entirely physics-based, which is key to reliably represent future climate states that could differ substantially from today’s.

Implications of a novel approach to more accurately predict dissipation and anisotropy near an unforced free surface with second moment closures, are considered for more general flows with surface forcing. Boundary conditions that rely on variants of the law of the wall, and which thereby enforce isotropy at an unforced surface, are modified to be gradient-free at the surface, in concert with an anisotropic redistribution of transport divergence that is nonlocal. Introducing surface forcing into this modified second moment closure requires reformulation of the source terms at or adjacent to the boundary for solving the dynamic equation for turbulence dissipation, its length or its time scale. 

The diurnal variability of the atmospheric forcing in the equatorial ocean is known to periodically form thin diurnal warm layers (DWLs) in the upper few meters during daytime, and trigger "deep cycle turbulence" (DCT) inside the upper flank of the equatorial undercurrent during nighttime. In numerical models, quantifying the vertical heat flux associated with DCT is essential to correctly predict the tropical sea surface temperature and the air-sea heat exchange. Here, by comparison with large eddy simulations (LES), we evaluate the performance of a number of statistical turbulence models commonly used in ocean modelling with respect to their ability to reproduce and correctly quantify  DCT in an idealised, one-dimensional configuration. Advanced second-order turbulence closure models were shown to reproduce the occurrence and timing of DCT, and accurately predict the time-averaged turbulent heat fluxes and dissipation rates across a wide range of scenarios. This suggests that, provided the vertical model resolution is sufficient to resolve the thin DWLs near the surface, both the timing and the effect of DCT can be reliably represented in numerical ocean models.

Oceanic diapycnal mixing strongly influences the mean climate state and transient climate response, with implications on ocean heat uptake, sea level rise, and sea surface temperature (SST), among other aspects of the climate system. Since the mid-20^th century, the upper ocean has become more stratified while deep ocean stratification is weakening. This will impact the behavior of internal wave breaking, which is the main source of turbulent diapycnal mixing in the ocean interior. The sensitivity of the ocean state to diapycnal mixing has been analyzed extensively using ocean-only general circulation models and Earth System Models of Intermediate Complexity, but few studies have employed fully coupled models. Our study aims to identify the depth range in which diapycnal mixing has the largest climate impacts, and how the effects of mixing compare to those of radiative forcing. We performed a suite of 200-yr experiments using a global coupled climate model with an isopycnal ocean component under three radiative forcing scenarios in which diffusivity is enhanced in different portions of the water column. The spatial distribution is prescribed based on potential density and the magnitude is determined by a specified global input of additional mixing energy. We find that the global mean mixing-induced temperature changes are approximately independent of radiative forcing. The volume mean ocean temperature and mean SST are highly sensitive to the distribution of added diffusivity. We estimate that by year 200, instantaneously increasing the mixing energy input to the depth range of approximately 200 to 1500 m by 0.2 TW (about 50% of global depth-integrated diapycnal mixing energy consumption) would lead to an increase in volume mean temperature equal to that induced by increasing CO₂ by 1% per year until doubling, while an increase of 0.02 TW would produce warming on the order of 10% of the radiative effect.

Lagrangian time averaging, where averages are taken along particle trajectories rather than at fixed spatial locations (Eulerian averaging), has long been recognised as a useful tool for understanding fluid behaviour with multiple timescales, especially in oceanic and atmospheric flows. Using a recently derived method, it is possible to solve for Lagrangian mean fields online (that is, simultaneously with governing equations). We apply this to find Lagrangian mean velocity fields, and use these to study particle advection and tracer transport with coarse-in-time velocity data. Very good agreement is found when comparing our results to the `truth' obtained directly from model output. Using instantaneous velocity fields for the same purpose demands much smaller timesteps in order to resolve fast wave motions. This problem is avoided because the slowly varying Stokes drift associated with fast waves is accounted for in a Lagrangian mean, while the same cannot be said for Eulerian means. Our results demonstrate the potential for using memory-light output in the form of Lagrangian mean data, and supports their wider use in the field.

We revisit observations from September 2018 of warm Pacific-origin Alaskan Coastal Water (ACW) subducting over the continental slope downstream of Barrow Canyon via submesoscale unstable jets. Turbulence structure during subduction is compared across three instrument platforms: a WireWalker profiler (χ) and two free-falling profilers—a fast CTD (FCTD) with microconductivity-derived χ, and a microstructure profiler resolving ε (and occasionally χ). Mixing between ACW and near-freezing Canada Basin water is consistently elevated, particularly across a range of fine-structure intrusions, though estimates vary in magnitude between instruments. Strong background gradients in the ACW layer sometimes enable estimation of vertical diffusivities and heat fluxes using Osborn and Osborn–Cox methods. Frequent double-diffusive staircases above the ACW core transport heat upward, occasionally reaching the base of the mixed layer. Below the subducting water, thin, low-intensity thermohaline intrusions susceptible to double-diffusive convection are observed, though weak vertical temperature gradients prevent reliable diffusivity and heat flux estimates. These results highlight both the capabilities and limitations of different turbulence sensors in resolving mixing, and point to multiple pathways for heat redistribution at the confluence of Chukchi and Canada Basin waters.

Long Island Sound is a large estuary in southern New England. The western end of the Sound is connected to the estuary of the Hudson River by a tidal strait. This area is the site of several major discharges of effluent from waste-water treatment plants. Observations have demonstrated that large areas of the bottom waters are hypoxic in the summer. Though mitigation measures have reduced the extent of hypoxia over the last decade, the spatial and interannual variability remains unexplained. To better understand the interplay between vertical mixing, gas transfer, production and respiration in the water column and seabed, we developed a mathematical model for the vertical structure of the ratio of the 18O and 16O isotope concentrations (δ18O) of dissolved oxygen (DO). The major terms in LIS’s oxygen budget are 1) local air-sea gas exchange, 2) ventilation through vertical mixing, 3) near-surface photosynthetic production, 4) water column respiration, and 5) respiration in the bottom sediments. Photosynthesis produces O2 with a δ18O 24‰ lower than the atmosphere, respiration in the water column increases δ18O with a fractionation factor of about 20‰, whereas sedimentary respiration creates little isotope fractionation.
Using model parameter choices that are based on a field program we conducted in 2021 and 2022 in which we measured shear and turbulent dissipation rate, the δ18O distribution, and DO concentrations, and an array of other sources, we estimated vertical eddy fluxes using GOTM, and solved for the evolution of the DO and a δ18O ratio profile evolution. We show that the results of the model are generally consistent with the conditions observed in the late summer. Using the model, we examined how the relative importance of the various mechanisms impacted the distributions of DO and δ18O during the height of hypoxia. We conclude that for the model to be consistent with observations, it is the water column respiration that is the overwhelming sink of DO being mixed downwards. However, it may be that during the transition to hypoxia benthic respiration plays an important role.

We model a curved front as a baroclinic vortex in cyclo-geostrophic balance and examine how such structures trap NIWs. The idealized vortex includes a core and a surrounding shield of opposite vorticity, consistent with observations. Both anticyclonic cores (with cyclonic shields) and cyclonic cores (with anticyclonic shields) are studied. We introduce a non-dimensional "curvature number", representing the relative importance of centrifugal vs. Coriolis forces—effectively quantifying how tightly wound the vortex is.

Using WKB and ray-tracing methods, we find that increasing the curvature number: (i) Expands the depth and horizontal extent of NIW trapping zones, (ii) Reduces NIW energy in the center of anticyclonic cores while enhancing it in their surrounding cyclonic shields, (iii) Enables NIW trapping in anticyclonic shields around cyclonic cores, and (iv) Broadens the frequency band of trapped NIWs.

Numerical solutions of the linearized governing equations support these findings. These results are particularly relevant to high latitude (e.g. Arctic eddies), which often exhibit high curvature numbers.

Internal gravity waves propagate within the ocean's stratified interior and play a key role in the forward cascade of energy from large scale balanced motions, like mesoscale eddies, to the smallest dissipative scales. Balanced flow can directly transfer energy to internal gravity waves by nonlinear generation via two lesser understood mechanisms: spontaneous emission and stimulated emission.  Spontaneous emission involves the generation of internal waves from balanced flows without external forcing, but is inefficient at low to moderate Rossby numbers. In contrast, stimulated emission, where balanced flow transfers energy to internal waves under the influence of a pre-existing wave field, can remain effective even at low Rossby numbers. As major sources of internal wave energy in the ocean, winds and tides generate a widely present wave field, thus suggesting that stimulated emission could be an important mechanism in internal wave generation. Despite its potential significance, diagnosing and quantifying this mechanism is tricky due to nonlinear interactions between wave and balanced components and the difficulty in separating them.

Here we present stimulated wave emission with nonlinear flow decomposition in the full Boussinesq system of equations, rather than reduced models, as a work around for flow decomposition, used in previous studies. We initialize the model with a balanced jet-like flow, and introduce a wave field with a typical Garett-Munk spectrum at the start of the simulation. This system is then evolved freely across a range of Rossby numbers. We use the method of higher order balance, with asymptotic expansion in Rossby number, to decompose the flow into its balanced and wave components, and analyze the associated energy transfers. Initial results show a clear increase in the internal wave energy over time at higher Rossby numbers.  The wave energy is enhanced at higher resolutions, especially for high Rossby numbers. However, the wave energy at low to moderate Rossby numbers remains non-negligible, as opposed to the case of spontaneous emission, bringing new insights to wave generation by stimulated emission at low Rossby number regimes.

The Weddell Sea is a key component of the Southern Ocean overturning circulation, as it is the most important location for overturning: surface currents are transformed to deep currents. The newly formed dense water is transported from its formation sites on the continental shelf to the deep sea by the Weddell Sea Bottom Water gravity current. The physical properties of Antarctic Bottom Water exported from the Weddell Sea are in part determined by the entrainment of upper, less dense water into the gravity current. Investigating the role and nature of the small-scale turbulent processes involved in the entrainment is therefore essential for advancing our understanding of Antarctic Bottom Water formation.

We investigate the role of wave-induced turbulence in the dynamics of the gravity current. Previous studies suggest that internal waves can play a crucial role in driving turbulence within gravity currents, yet their contribution has not been quantified. A key challenge thereby is distinguishing whether the observed turbulence arises from instabilities or waves, as their spatial and temporal scales often overlap. Our analysis is based on moored velocity records and vertical profiles of temperature and salinity along a transect across the continental slope. To quantify the contribution of internal waves to turbulence in this gravity current, we apply three independent methods to estimate dissipation rates:

1. the Thorpe-scale approach to compute total, process-independent dissipation rates.

2. the fine-structure parameterization to estimate wave-induced dissipation rates.

3. a wave-energy parameterization, where we estimate wave-induced dissipation rates from moored velocity time series. To our knowledge, this is one of the first applications of the underlying established theory.

Our results show that close to the interface to the ambient water, internal waves contribute considerably to turbulence and thus to the entrainment of warmer upper-layer water into the gravity current. Additionally, the wave-energy parameterization allows us to derive two-year-long time series of dissipation rates. This is an important result, given the lack of published dissipation rate time series longer than a few weeks in the Southern Ocean. We observe that internal tides control most of the general spatial variability but find temporal modulations in step with elevated wind stress, even in depths greater than 2500 m. If these correlations can really be attributed to wind-generated waves is as of now still uncertain. Furthermore, we look into decadal scales of variability in the turbulent processes of the Weddell Sea gravity current and discuss the potential impact of climate change.

Near-inertial wave (NIW) variability was examined in Barrow Strait within the Canadian Arctic Archipelago, a high latitude, seasonally ice-covered, shallow and complex bathymetric region. In-situ observations of ocean and ice velocities at four locations across Barrow Strait spanning a 13-year (1998 – 2011) record were utilized. A dominant portion of the variability in baroclinic currents was contained in the near-inertial (NI) band, suggesting that NIWs play an important role for localized turbulent mixing. NIWs were likely influenced by the bathymetry as NI current ellipses were elongated along channel and were more circular away from the channel boundaries. NI speed within the mixed layer exhibited a clear seasonal cycle, with increased strength from July to October, and decreased strength December to May. Below the mixed layer the seasonal cycle was not observed. A 1D ice-ocean slab model was used to explore the effects of various parameters on NIW generation within the mixed layer. Mixed layer depth was the primary driver of NI seasonality, with sea ice concentration and internal ice stress playing important secondary roles, particularly when mixed layer depth was shallower, while wind contributed to a lesser extent. Examining NIW variability leads to a better understanding of their influence on mixing in the region.

Internal gravity waves (IGWs) play a key role in ocean dynamics by interacting with mesoscale eddies, topography, and other waves, leading to wave breaking and mixing that influence small and large-scale circulations. Despite local variability, the IGW energy distribution exhibits a remarkably universal spectral shape—the Garrett-Munk (GM) spectrum— within which we study the scattering of IGWs via wave-wave interactions under the weak-interaction assumption.  

We use the kinetic equation derived from a non-hydrostatic Boussinesq system with constant rotation and stratification. The kinetic equation and coupling coefficients derived from Eulerian and Lagrangian equations are identical under the resonance condition. By developing Julia-native numerical codes, we evaluate the energy transfers for resonant and non-resonant interactions, including inertial and buoyancy oscillations. Our results confirm that resonant triads dominate energy transfers, while non-resonant interactions are negligible in isotropic spectra but can contribute under anisotropic conditions. We analyze local versus non-local energy transfers and show that parametric subharmonic instability drives a forward energy cascade in vertical wavenumber and an inverse cascade in frequency. Induced diffusion emerges as a primary energy sink to small scales, and elastic scattering plays a similar but weaker role. We assess the convergence of the scattering integral by introducing a cutoff in the IGW energy spectrum, which is primarily smoothed out by induced diffusion. Our findings provide convergent results at reduced computational costs, improving the efficiency and reliability of energy transfer evaluations in oceanic IGW spectra.

In recent years it has become evident that the spatiotemporal distribution of oceanic kinetic energy (KE) is strongly influenced by the interactions between oceanic mesoscale eddies, submesoscale currents, and near-inertial waves (NIWs). However, the proposed interaction mechanisms remain difficult to evaluate and quantify in complex oceanic numerical simulations. To address these difficulties we introduce an analysis framework that combines spectral KE flux computations across horizontal wavenumbers with temporal filtering and a Helmholtz decomposition, and apply it to idealized, high-resolution, baroclinic channel solutions consisting of eddies, fronts, and filaments in the O(1) Rossby parameter regime. By comparing solutions with and without NIW forcing we are able to demonstrate that externally forced NIWs lead to a reduction in the inverse KE cascade of the low-passed eddying flow, and to an enhancement in its forward cascade. These stimulated cascades are associated with the interactions between rotational and divergent eddy motions, characteristic of mesoscale eddies and submesoscale currents, respectively. Additionally, we demonstrate that at larger spatial scales the forward KE cascade of NIWs is accomplished through wave scattering and direct extraction by rotational eddy motions, whereas at smaller spatial scales it is also dominated by wave-wave interactions. The caveats of our framework, its suitability to investigate eddy-NIW interactions in realistic oceanic simulations and the disparities between the spectral KE flux and the coarse-graining methods are also discussed.

In this study, the effects of cross-front winds on a submesoscale dense filament are investigated using high-resolution turbulence and velocity observations, and idealized numerical simulations. Our study area is the Baltic Sea, which is characterized by strong frontal gradients and pronounced submesoscale dynamics. Embedded in a large-scale frontal region, our observations reveal the existence of a 3-4 km wide, dense filament with an asymmetric structure resulting from the interactions between cross-front winds and the two submesoscale fronts laterally bounding the filament. These two fronts are driven by either downgradient winds, directed from the lighter surrounding waters toward the dense center of the filament, or upgradient winds, directed in the opposite direction. While the effect of a wind stress that is aligned with the frontal jet has been investigated in numerous previous studies, especially field data focusing on the role of cross-front winds are largely lacking at the moment. We find that for downgradient winds, when the surface Ekman transport and the frontal jet are aligned, both the frontal jet and the cross-front secondary circulation are enhanced. The latter supports a tendency for frontal re-stratification, suppression of turbulence, and mixed-layer shoaling. For the front with upgradient wind forcing, the Ekman transport and the frontal jet nearly cancel, and also the cross-front secondary circulation is strongly suppressed. Restratification by the secondary circulation is weak in this case, and the well-mixed turbulent surface layer is approximately twice as deep compared to the other side of the filament with downgradient forcing. We show that these mechanisms are consistent with results from idealized numerical simulations of frontal regions with downgradient and upgradient wind forcing.

Internal tides (ITs) are inertia-gravity waves generated by oceanic barotropic tides (large-scale, vertically uniform tidal currents) flowing over topography, important to oceanographers due to their roles in problems such as deep/upper ocean mixing. Conventionally, for altimetric observations of Sea Surface Height (SSH) data, ITs have been extracted by harmonically fitting over observed time sequences. However, in presence of strong time-dependent phase shifts induced by interactions with mean flows or changes in stratifications, harmonic fits do not work well for data with coarse temporal sampling, as in the case for satellite observations. This problem is exacerbated at finer spatial scales resolved by the Surface Water Ocean Topography (SWOT) satellite mission.
Meanwhile, SWOT's wide swaths render SSH snapshots that are spatially two-dimensional, which allows the community to treat IT extraction as an operation on two-dimensional images. In 2022, as a proof of concept, we developed a deep neural network architecture, which, given a snapshot of raw SSH, generates a snapshot of the embedded tidal component. The algorithm is essentially an image transformation, and no temporal information is required. The performance is great in a set of idealized data. 

In this work, we revisit the problem, developing a simpler, cheaper architecture of deep neural network that performs equally well. This allows us to experiment with many different combinations of possible input fields conveniently. We report on the impacts of surface temperature, surface velocities and SSH on the performances of the IT extraction. The results are interesting from a theoretical perspective; for example, fields that don’t contain much IT imprints themselves (e.g., surface temperature) can still improve the performance. As the results inform which surface fields are more useful for the IT extraction, they can be used as a reference for designs of future observational campaigns; for example, we find surface velocities to deliver the best performances, which may inspire designs of satellite campaigns that measure surface velocities, such as the ODYSEA campaign currently being proposed. 

The cross-scale energy exchange between wave and non-wave motions is crucial in determining the ocean energy redistribution. The interaction of mesoscale and submesoscale eddies with internal tides is a key driver of this cross-scale energy exchange, but remains poorly understood. In this study, we characterize this process by analyzing high-resolution simulations using a regional model of the tropical western Atlantic. A Lagrangian filter is implemented to separate the dynamic fields into wave and non-wave motions and accounts for Doppler shifts. An Eulerian filter is then applied to extract the internal tide from the wave motion. The non-wave component is further separated into mesoscale and submesoscale motions. The interactions between the internal tides and the submesoscale are distinct from the interactions with the mesoscale. Horizontally, energy transfer predominantly occurs at regions of intense strain where eddies intersect. The interaction between the mesoscale and internal tides can vary in the direction of energy transfer in different regions, while the submesoscale and internal tide interactions tend to facilitate a forward energy transfer to the internal tides. Vertically, both the vertical wave stress term and the potential energy conversion term are significant and are primarily controlled by the vertical shear of the non-wave components. Internal tide interactions with the mixed-layer-instability-dominant submesoscales exhibit significant seasonal dependence, whereas those with frontogenesis-dominant submesoscales do not. The depth-averaged energy exchange is on the same order as the observed dissipation rate of internal tides, indicating this interaction can act as a significant source or sink of internal tide energy.