Internal Wave Energy Research Articles

Models of the Sea Surface Height Expression of the Internal-Wave Continuum

Abstract Several models are presented for the sea surface height (SSH) signature of the interior-ocean internal-wave continuum. Most are based on the Garrett–Munk internal-wave model. One is derived from the frequency spectrum of dynamic height from mooring observations. The different models are all plausibly consistent with accepted dynamical and semiempirical spectral descriptions of the climatological interval-wave field in the interior ocean, but they result in different proportionalities between interior and SSH spectral energy levels. The differences arise in part from differences in the treatment of near-surface stratification, and a major source of uncertainty for all the models comes from inadequately constrained assumptions about the energy in the low-vertical-mode internal-wave field. Most of these models suggest that the SSH signature of the internal-wave continuum will be visible in SSH measurements from the Surface Water and Ocean Topography (SWOT) wide-swath satellite altimeter. Temporal variability of internal-wave energy levels and the internal-wave directional spectrum are less well characterized but will also be consequential for the observability of internal-wave signals in SWOT data.

Tidal Conversion into Vertical Normal Modes by Near-Critical Topography

Abstract The solution from linear theory for the barotropic-to-baroclinic tidal energy conversion into vertical modes is validated with numerical simulations and analytical results. The main result is the translation of the traditional critical slope condition into a modewise condition on the topographic height only. Our findings are then used for estimates of the global M2 tidal conversion into the first 10 vertical modes in the open ocean (excluding the continental shelves and slopes). We observe a rapid increase with mode number of the fraction of the World Ocean where linear theory is invalid. In terms of conversion, which is highly variable in space, this corresponds to an even more rapid increase with mode number of the fraction of the converted energy that is strongly affected by nonlinear effects. Out of the 373.6 GW of the globally integrated conversion into modes 1–10, only 241.7 GW occur in locations where linear theory is valid. While it represents 95% for mode 1, this fraction rapidly drops with mode number to reach 27% for mode 10. Moreover, for the conversion into a single mode, we show that capping the linear solution at supercritical topography is inappropriate. Hence, linear theory appears unfit to directly quantify the role played by high-mode internal tides in the internal wave energy budget.

Internal Waves Force Elevated Turbulent Mixing at Barkley Canyon

AbstractSubmarine canyons are hot spots for topography‐internal wave interactions, with elevated mixing contributing to regional water mass transport and productivity. Two velocity time series compare and contrast internal waves deep inside Barkley Canyon to a nearby site on the shelf‐break slope of the Vancouver Island Continental Shelf. Elevation of internal wave energy occurs near topography, up to a factor of 10 above the slope and 100 in the canyon. All frequency bands display strong seasonal variability but weak interannual variability. Diurnal (K1) energy is sub‐inertial, trapped along topography, and forced locally through barotropic motions. Both sites have high near‐inertial (NI) energy linked to wind events, though fewer events are observed deep inside the canyon. At the slope site, near‐inertial energy is attenuated with depth, while in the canyon it is amplified near the bottom. Freely propagating semidiurnal (M2) energy appears focused near critical shelf‐break and canyon floor topography, due to local and remote baroclinic forcing. The high‐frequency internal wave continuum has enhanced near‐bottom energy at both sites (up to 7 × the Garrett‐Munk spectrum), and inferred dissipation rates, ɛ, reaching 10−7 W kg−1 near topography. Dissipation is most strongly correlated with semidiurnal energy variability at both sites, with secondary contributors that are site dependent. Forcing power law fits are on the slope, and NI0.2 in the canyon. There is also a build‐up of “shoulder” energy (PSh) near the buoyancy frequency, with a power law fit to dissipation of PSh ∼ ɛ0.3 at both sites.

Parameterized Internal Wave Mixing in Three Ocean General Circulation Models

AbstractThe non‐local model of mixing based on internal wave breaking, IDEMIX, is implemented as an enhancement of a turbulent kinetic energy closure model in three non‐eddy resolving general circulation ocean models that differ in the discretization and choice of computational grids. In IDEMIX internal wave energy is generated by an energy flux resulting from near‐inertial waves induced by wind forcing at the surface, and at the bottom, by an energy flux that parameterizes the transfer of energy between baroclinic and barotropic tides. In all model simulations with IDEMIX, the mixing work is increased compared to the reference solutions without IDEMIX, reaching values in better agreement with finestructure observations. Furthermore, the horizontal structure of the mixing work is more realistic as a consequence of the heterogeneous forcing functions. All models with IDEMIX simulate deeper thermocline depths related to stronger shallow overturning cells in the Indo‐Pacific. In the North Atlantic, deeper mixed layers in simulations with IDEMIX are associated with an increased Atlantic overturning circulation and an increase of northward heat transports toward more realistic values. The response of the deep Indo‐Pacific overturning circulation and the weak bottom cell of the Atlantic to the inclusion of IDEMIX is incoherent between the models, suggesting that additional unidentified processes and numerical mixing may confound the analysis. Applying different tidal forcing functions leads to simulation differences that are small compared to differences between the different models or between simulations with IDEMIX and without IDEMIX.

Evolution of Internal Gravity Waves in a Mesoscale Eddy Simulated Using a Novel Model

Abstract We investigate the effect of wave–eddy interaction and dissipation of internal gravity waves propagating in a coherent mesoscale eddy simulated using a novel numerical model called the Internal Wave Energy Model based on the six-dimensional radiative transfer equation. We use an idealized mean flow structure and stratification, motivated by observations of a coherent eddy in the Canary Current System. In a spindown simulation using the Garret–Munk model spectrum as initial conditions, we find that wave energy decreases at the eddy rim. Lateral shear leads to wave energy gain due to a developing horizontal anisotropy outside the eddy and at the rim, while vertical shear leads to wave energy loss which is enhanced at the eddy rim. Wave energy loss by wave dissipation due to vertical shear dominates over horizontal shear. Our results show similar behavior of the internal gravity wave in a cyclonic as well as an anticyclonic eddy. Wave dissipation by vertical wave refraction occurs predominantly at the eddy rim near the surface, where related vertical diffusivities range from to . Significance Statement Using a novel model and observations from the Canary Current System of a coherent eddy of 100-km diameter, we explore the interaction between a realistic internal gravity wave field and this eddy. We study wave refraction and energy transfers between the waves and the eddy induced by the eddy’s lateral and vertical shear. Waves lose energy at the eddy rim by vertical shear and gain outside of the eddy rim by horizontal shear. We find large vertical wave refraction by vertical shear at the eddy rim, where waves break and mix density, which can have wide ranging effects on the ocean’s circulation. These results are important for understanding the ocean’s mixing and energy cycle and to develop eddy and wave parameterizations.

Turbulence Across the Antarctic Circumpolar Current in the Indian Southern Ocean: Micro‐Temperature Measurements and Finescale Parameterizations

AbstractTurbulence structures across the Antarctic circumpolar current (ACC) in the Indian Ocean at around 50°E were revealed using microstructure measurements. Depth‐averaged turbulent energy dissipation rates (ε) in 320 m segments estimated using a conductivity‐temperature‐depth (CTD)‐attached micro‐temperature fast‐response thermistor (FP07) were well reproduced using existing finescale parameterizations excluding near‐surface and near‐bottom 160 m. The spatial variations of ε are explained by density stratification N2, bottom topographic roughness, and depth‐averaged current speed U. Diapycnal diffusivity Kρ(=0.2εN−2) is found proportional to the squared internal wave energy () and increases toward the bottom, especially over rough bottom topography. The decay scale height is >1000m and the turbulence remains large even in the upper pycnocline. Existing shear‐based finescale parameterizations were generally consistent with the FP07 measurements but tended to overestimate in the areas with large shear‐strain ratio Rω and low ε in the Continental Zone (CZ) south of the ACC fronts (58–65°S). This overestimation is improved by using the strain‐based finescale parameterization with a constant Rω = 3.

The Vertical Structure of Internal Lee-Wave-Driven Benthic Mixing Hotspots

Abstract In global ocean circulation and climate models, bottom-enhanced turbulent mixing is often parameterized such that the vertical decay scale of the energy dissipation rate ζ is universally constant at 500 m. In this study, using a nonhydrostatic two-dimensional numerical model in the horizontal–vertical plane that incorporates a monochromatic sinusoidal seafloor topography and the Garrett–Munk (GM) background internal wave field, we find that ζ of the internal lee-wave-driven bottom-enhanced mixing is actually variable depending on the magnitude of the steady flow U0, the horizontal wavenumber kH, and the height hT of the seafloor topography. When the steepness parameter (Sp = NhT/U0 where N is the buoyancy frequency near the seafloor) is less than 0.3, internal lee waves propagate upward from the seafloor while interacting with the GM internal wave field to create a turbulent mixing region with ζ that extends farther upward from the seafloor as U0 increases, but is nearly independent of kH. In contrast, when Sp exceeds 0.3, inertial oscillations (IOs) not far above the seafloor are enhanced by the intermittent supply of internal lee-wave energy Doppler-shifted to the near-inertial frequency, which occurs depending on the sign and magnitude of the background IO shear. The composite flow, consisting of the superposition of U0 and the IOs, interacts with the seafloor topography to efficiently generate internal lee waves during the period centered on the time of the composite flow maximum, but their upward propagation is inhibited by the increased IO shear, creating a turbulent mixing region of small ζ.

Multi-Sensor Observations Reveal Large-Amplitude Nonlinear Internal Waves in the Kara Gates, Arctic Ocean

We present multi-sensor measurements from satellites, unmanned aerial vehicle, marine radar, thermal profilers, and repeated conductivity–temperature–depth casts made in the Kara Gates strait connecting the Barents and the Kara Seas during spring tide in August 2021. Analysis of the field data during an 18-h period from four stations provides evidence that a complex sill in the Kara Gates is the site of regular production of intense large-amplitude nonlinear internal waves. Satellite data show a presence of a relatively warm northeastward surface current from the Barents Sea toward the Kara Sea attaining 0.8–0.9 m/s. Triangle-shaped measurements using three thermal profilers revealed pronounced vertical thermocline oscillations up to 40 m associated with propagation of short-period nonlinear internal waves of depression generated by stratified flow passing a system of shallow sills in the strait. The most intense waves were recorded during the ebb tide slackening and reversal when the background flow was predominantly supercritical. Observed internal waves had wavelengths of ~100 m and traveled northeastward with phase speeds of 0.8–0.9 m/s. The total internal wave energy per unit crest length for the largest waves was estimated to be equal to 1.0–1.8 MJ/m.

The effect of Typhoon Kalmaegi on the modal energy and period of internal waves near the Dongsha Islands (South China Sea)

The effect of Typhoon Kalmaegi on the modal energy and period of internal waves near the Dongsha Islands (South China Sea)

Internal waves

Internal waves are ubiquitous oceanographic features that occur in various forms across the world’s oceans. They manifest themselves as interface waves across ocean density layers that represent the interplay between buoyancy and gravitational forces, and are typically classified as linear and nonlinear internal waves. Nonlinear internal waves are characterized by isopycnal displacements that can exceed 30 m, and current velocities that approach 1 m/s. Internal wave energy converters, if developed, could have the advantage of no surface expression and provide for the availability of renewable ocean energy in regions of scant surface wave energy resources.
 Here, internal wave energies were computed at two locations: the New Jersey continental shelf and the coast of Central California. The available energy resource calculated for internal waves was then compared against surface gravity wave resources at each of these locations. Results suggest that the internal wave energy flux is comparable to that of surface waves on the New Jersey continental shelf during the summer of 2006 but is two orders of magnitude lower than that of surface waves in Central California during the summer of 2017. When expressed in terms of forces on a cylindrical structure, internal wave forces are an order of magnitude lower than that of surface waves on identically sized cylinders. However, the forces of the two resources are comparable when the diameter of the cylinder is doubled for the internal wave calculations. This suggests that while a larger energy converter would be required to harness internal wave energy, the larger size could be a reasonable tradeoff for advantages such as the lack of surface expression and the availability of energy in regions of limited surface wave energy resources.
 These results could potentially pave the way for longer-time scale characterization of internal waves and the development of devices to harness this energy resource (thereby powering the Blue Economy), while augmenting the portfolio of marine renewable energy resources. Further, the dominance of internal wave energy resources during summer seasons when the water column is stratified can augment the surface wave energy resource that can be diminished during the summer season.

Turbulent wave-balance exchanges in the ocean

Oceanic flows are turbulent and multi-scale in nature, and are composed of fast internal waves and slowly evolving balanced eddies. Contrary to conventional wisdom in physical oceanography, the past two decades ofin situ, satellite altimeter and realistically forced global scale ocean model outputs have revealed that internal gravity waves can have comparable or higher energy levels than geostrophically balanced flows at 10–100 km scales in different parts of the world’s oceans. These relatively recent findings have fuelled a wide range of research activities aimed at understanding how fast internal gravity waves interact with slowly evolving balanced flows, particularly with the goal of deducing whether internal waves can form an energy sink for oceanic balanced flows. In this paper, we comprehensively review theoretical, numerical and observational investigations undertaken to study internal wave-balance flow exchanges. Theoretical calculations, inspired by different wave-balance regimes seen in observational and global ocean model outputs, are used to point out that internal waves can affect balanced flow dynamics. The theoretical results are followed up by a detailed discussion of numerical results on wave-balance interactions in a broad set of parameter regimes. The numerical results reveal how different kinds of waves exchange energy with balance flow, affect energy flux across scales of balanced flow and facilitate the generation of small-scale dissipative balanced flow structures. The numerical simulation results and global internal wave energy and balanced energy maps are used to conjecture that out of the 0.8 TW of power going to balanced flow kinetic energy in the ocean, at least 0.1 TW could be dissipated by internal gravity waves. We therefore hypothesize that internal waves can form a non-negligible energy sink for balanced flow in the world’s oceans.

A Model of Energy and Spectral Shape for the Internal Gravity Wave Field in the Deep Sea: The Parametric IDEMIX Model

Abstract The spectral description of the energy of oceanic internal gravity waves is generally represented by the Garrett–Munk (GM) model, a function with a power-law decrease of spectral energy in wavenumber–frequency space. Besides the slopes of these power laws, the spectrum is expressed as a function of energy and a bandwidth parameter that fixes the range of vertical modes excited in the respective state. Whereas concepts have been developed and agreed upon of what processes feed the wave spectrum and what dissipates energy, there is no explanation of what shapes the spectral distribution, i.e., how the power laws come about and what sets the bandwidth. The present study develops a parametric spectral model of energy and bandwidth from the basic underlying energy balance in terms of forcing, propagation, refraction, spectral transfer, and dissipation. The model is an extension of the IDEMIX (Internal Wave Dissipation, Energy and Mixing) models where bandwidth was taken as a constant parameter. The current version of the model is restricted to single-column mode and the slopes of the spectral power laws are fixed. A coupled system of predictive equations for energy and bandwidth (for up- and downward propagating waves) results. The equations imply that bandwidth relates to energy by a power law with an exponent given by the dynamical parameters. It agrees favorably with energy, bandwidth, and slope data from previously published fits of the GM model to Argo float observations. Numerical solutions of the coupled energy–bandwidth model in stand-alone modus are presented.

Acoustic travel-time variability observed on a 150-km radius tomographic array in the Canada Basin during 2016-2017.

The Arctic Ocean is undergoing dramatic changes in response to increasing atmospheric concentrations of greenhouse gases. The 2016-2017 Canada Basin Acoustic Propagation Experiment was conducted to assess the effects of the changes in the sea ice and ocean structure in the Beaufort Gyre on low-frequency underwater acoustic propagation and ambient sound. An ocean acoustic tomography array with a radius of 150 km that consisted of six acoustic transceivers and a long vertical receiving array measured the impulse responses of the ocean at a variety of ranges every four hours using broadband signals centered at about 250 Hz. The peak-to-peak low-frequency travel-time variability of the early, resolved ray arrivals that turn deep in the ocean was only a few tens of milliseconds, roughly an order of magnitude smaller than observed in previous tomographic experiments at similar ranges, reflecting the small spatial scale and relative sparseness of mesoscale eddies in the Canada Basin. The high-frequency travel-time fluctuations were approximately 2 ms root-mean-square, roughly comparable to the expected measurement uncertainty, reflecting the low internal-wave energy level. The travel-time spectra show increasing energy at lower frequencies and enhanced semidiurnal variability, presumably due to some combination of the semidiurnal tides and inertial variability.

Wind Power Input to Ocean Near‐Inertial Waves Diagnosed From a 5‐km Global Coupled Atmosphere‐Ocean General Circulation Model

AbstractUsing the 5 km coupled general circulation model ICON, the surface internal wave energy source, crucial for the oceanic circulation, is quantified as the wind‐induced wave energy flux that radiates from the mixed layer bottom (MLB) into the ocean interior. Our result lowers the previous estimates of the wind power input to surface near‐inertial motions from up to more than 1 TW down to about 0.23–0.27 TW, depending on season. We point out that the estimate of the wind input to ocean depends not only on the wind stress used—as suggested by previous studies—but also on the ocean model used. While the surface currents in a slab ocean model or a non‐eddying ocean circulation model are strongly determined by the wind forcing, the surface currents in the 5 km ICON model can be more strongly determined by internal instability process (eddy) than by wind stress forcing from less‐extreme weather disturbances. The resulting more or less random alignment of surface current and wind stress can presumably lead to a lower wind input to surface near‐inertial motions. Of the surface wave energy source, about 30% is fluxed down into the interior ocean. This percentage roughly doubles those from previous studies, due to the stronger wave energy flux related to stronger inertial waves generated by the tropical cyclones simulated by the 5 km ICON model. Overall, the low wind input at near‐inertial frequencies produces a wind‐induced wave energy source at the MLB that is well below 0.1 TW.

Importance of Background Vorticity Effect and Doppler Shift in Defining Near‐Inertial Internal Waves

AbstractNear‐inertial waves contain a significant fraction of the ocean's internal wave energy and can propagate long distances from their source before dissipating. However, a varying background flow velocity can alter the wave propagation in two ways. The background vorticity modifies the lower bound of the wave frequency bandwidth while Doppler shifts alter the wave intrinsic frequency. Both effects complicate the identification of the waves and the quantification of their energy content. This study analyses the output of a realistic simulation of the North Pacific using adaptive frequency filters to isolate the effects of vorticity and Doppler shift on the apparent wave energy. Spectral filters neglecting background vorticity effects results in apparent near‐inertial energy being underestimated by 40% in anticyclonic structures and overestimated by 100% in cyclonic structures. The asymmetry in energy bias is reinforced when both background vorticity and Doppler shift effects are omitted from the frequency filters.

Travel-time variability during the 2016–2017 deep-water Canada Basin Acoustic Propagation Experiment

The Arctic Ocean is undergoing dramatic changes in response to increasing atmospheric concentrations of greenhouse gases. The decreases in ice extent, the near disappearance of multiyear ice, and changes in the stratification of the ocean all have important implications for underwater acoustic propagation. During the 2016–2017 Canada Basin Acoustic Propagation Experiment (CANAPE), a long vertical receiving array was embedded within an ocean acoustic tomography array of six acoustic transceivers with a radius of 150 km. The impulse response of the ocean was measured every four hours using broadband signals centered at about 250 Hz. The observed travel-time variability was extraordinarily low, reflecting both the low internal-wave energy level and sparseness of mesoscale eddies in the Canada Basin. The peak-to-peak travel time variability of the early, resolved ray arrivals was only a few tens of milliseconds, and the standard deviations over the entire year were only a few milliseconds. The travel-time spectra show increasing energy at lower frequencies and enhanced semidiurnal variability, presumably due to some combination of the semidiurnal tides and inertial variability. The travel-time fluctuations are roughly an order of magnitude smaller than is typical in midlatitudes at similar ranges.

A new method to estimate the speed of internal solitary waves based on a single optical remote sensing image

ABSTRACT It is imperative to estimate the energy of internal solitary waves (ISWs) in the real ocean. The energy of ISW is related to speed and amplitude. It is a problem to obtain the propagation speed of ISW from a single optical remote sensing image. Generally, the nonlinear phase speed (NPS) of ISW can be regarded as the propagation speed of ISW. This paper proposes a new inversion approach for NPS of ISW based on an optical remote sensing image. The simulation platform of optical remote sensing was used to conduct the ISW experiment in the laboratory, and the data were obtained by a series of experiments. Three NPS inversion models of ISW are investigated by support vector regression (SVR), Random forest (RF) and Deep neural network (DNN) based on a single optical remote sensing image. The accuracy of the inversion models was verified by the in-situ data of GF-1 satellite images, GF-4 satellite images and Moderate-resolution Imaging Spectroradiometer (MODIS) images. In the verification results, the SVR inversion model has high accuracy in different sea areas and water depths. The RF and DNN inversion models both have high inversion accuracy in the water depth range of 93–299 m in the South China Sea. Compared with the other two traditional methods for calculating ISW NPS, the SVR inversion model still has the highest accuracy. The results showed that the NPS models of ISW are suitable and effective.

Decadal Observations of Internal Wave Energy, Shear, and Mixing in the Western Arctic Ocean

AbstractAs Arctic sea ice declines, wind energy has increasing access to the upper ocean, with potential consequences for ocean mixing, stratification, and turbulent heat fluxes. Here, we investigate the relationships between internal wave energy, turbulent dissipation, and ice concentration and draft using mooring data collected in the Beaufort Sea during 2003–2018. We focus on the 50–300 m depth range, using velocity and CTD records to estimate near‐inertial shear and energy, a finescale parameterization to infer turbulent dissipation rates, and ice draft observations to characterize the ice cover. All quantities varied widely on monthly and interannual timescales. Seasonally, near‐inertial energy increased when ice concentration and ice draft were low, but shear and dissipation did not. We show that this apparent contradiction occurred due to the vertical scales of internal wave energy, with open water associated with larger vertical scales. These larger vertical scale motions are associated with less shear, and tend to result in less dissipation. This relationship led to a seasonality in the correlation between shear and energy. This correlation was largest in the spring beneath full ice cover and smallest in the summer and fall when the ice had deteriorated. When considering interannually averaged properties, the year‐to‐year variability and the short ice‐free season currently obscure any potential trend. Implications for the future seasonal and interannual evolution of the Arctic Ocean and sea ice cover are discussed.

Modification of Internal Wave Generation and Energy Conversion in the Nearshore Due To Tide‐Tide and Tide‐Wind Interactions

AbstractInternal wave generation due to semi‐diurnal tides (M2) through the acceleration of barotropic tidal flow over sloped topography has received considerable attention over the past several decades. However, the contribution of other tidal constituents and their interactions with M2 have not been as extensively evaluated. Moreover, on the inner shelf, the cross‐shore wind, which is often neglected in the energy conversion studies, dominates the cross‐shore transport and can also affect the energy conversion process. This study addresses this gap by including a diurnal (K1) tidal component and a shoreward diurnal sea breeze in an idealized model of southern Monterey Bay as it represents a highly stratified system that experiences active surface and internal tides. Our simulations demonstrate the role of the K1 tide and its interaction with M2, which is constructive and insensitive to the initial phase lag. Wind‐induced perturbations grow with the wind speed and enhance M2 conversion. On the other hand, the wind interaction with the K1 and M2K1 tides highly depends on the timing with constructive (destructive) conversion occurring when the shoreward wind intensifies during the ebb (flood) tide. Interactions among tides and winds lead to highly variable conversion rates, changes in timing and location of peak conversion, and a range of internal wave frequencies. Such a dynamic alone can be responsible for the complex internal wave environments often observed in the nearshore.

Automated acoustic arrival matching using a convolutional neural network approach informed by statistics of acoustic scattering from internal waves

A machine learning model was developed to automatically align underwater acoustic measurements taken at various depths and ranges from a transmitting source in the Philippine Sea to a reference model of long range acoustic arrival structure, simultaneously determining source-receiver range and travel-time offsets associated with multipath arrivals. Ocean sound-speed variability complicates the task as the measured arrivals may exhibit scattering not present in range-independent predictions. Monte Carlo style broadband parabolic equation simulations through random internal wave fields consistent with the Garrett-Munk internal wave energy spectrum were used to generate a large data set of simulated acoustic receptions including scattered multipath arrivals with known source-receiver ranges and imposed travel time offsets. These simulated receptions were used to train and evaluate the machine learning model for arrival pattern matching to the reference model. The inclusion of various data dimensions, such as peak amplitude and width, and contextual information, such as range and depth, were also explored as input to the model. Ranging results for the machine learning model were compared to a programmatic solution engineered for the same task.