Global Calculation of Tidal Energy Conversion into Vertical Normal Modes

Abstract A direct calculation of the tidal generation of internal waves over the global ocean is presented. The calculation is based on a semianalytical model, assuming that the internal tide characteristic slope exceeds the bathymetric slope (subcritical slope) and the bathymetric height is small relative to the vertical scale of the wave, as well as that the horizontal tidal excursion is smaller than the horizontal topographic scale. The calculation is performed for the M2 tidal constituent. In contrast to previous similar computations, the internal tide is projected onto vertical eigenmodes, which gives two advantages. First, the vertical density profile and the finite ocean depth are taken into account in a fully consistent way, in contrast to earlier work based on the WKB approximation. Nevertheless, the WKB-based total global conversion follows closely that obtained using the eigenmode decomposition in each of the latitudinal and vertical distributions. Second, the information about the distribution of the conversion energy over different vertical modes is valuable, since the lowest modes can propagate over long distances, while high modes are more likely to dissipate locally, near the generation site. It is found that the difference between the vertical distributions of the tidal conversion into the vertical modes is smaller for the case of very deep ocean than the shallow-ocean depth. The results of the present work pave the way for future work on the vertical and horizontal distribution of the mixing caused by internal tides.

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Scattering of internal tide energy to super-tidal frequencies in global HYCOM

10.5194/egusphere-egu21-13990 ◽

2021 ◽

Author(s):

Miguel Solano ◽

Maarten Buijsman

Keyword(s):

Internal Tide ◽

Tidal Energy ◽

Horizontal Resolution ◽

Internal Tides ◽

Numerical Dispersion ◽

Global Ocean ◽

Wave Interactions ◽

Continental Shelves ◽

Lee Wave ◽

Ocean Models

Energy decay in realistically forced global ocean models has been mostly studied in the diurnal and semi-diurnal tidal bands and it is unclear how much of the tidal energy in these bands is scattered to higher frequencies. Global ocean models and satellite altimetry have shown that low-mode internal tides can propagate thousands of kilometers from their generation sites before being dissipated in the ocean interior but their pathway to dissipation is obscured due to lee-wave breaking at generation, wave-wave interactions, topographic scattering, shearing instabilities and shoaling on continental shelves. Internal tides from some generation sites, such as the Amazon shelf and the Nicobar and Andaman island chain, have large amounts of energy resulting in a steepening of the internal waves into solitary wave trains due to non-hydrostatic dispersion. In HYCOM, a hydrostatic model, this process is partially simulated by numerical dispersion. However, it is yet unknown how the dissipation of internal tides is affected by the numerical dispersion in hydrostatic models. In this study we use the method of vertical modes and rotary spectra to quantify the scattering of internal tides to higher-frequencies and analyze the dissipation processes in global HYCOM simulations with 4-km horizontal resolution.

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Satellite Investigation of Semidiurnal Internal Tides in the Sulu-Sulawesi Seas

Remote Sensing ◽

10.3390/rs13132530 ◽

2021 ◽

Vol 13 (13) ◽

pp. 2530

Author(s):

Xiaoyu Zhao ◽

Zhenhua Xu ◽

Ming Feng ◽

Qun Li ◽

Peiwen Zhang ◽

...

Keyword(s):

Interference Pattern ◽

Energy Flux ◽

Internal Tide ◽

Tidal Energy ◽

Internal Tides ◽

Altimeter Data ◽

Band Pass Filter ◽

Pass Filter ◽

Sulu Sea ◽

Tidal Energy Flux

The mode-1 semidiurnal internal tides that emanate from multiple sources in the Sulu-Sulawesi Seas are investigated using multi-satellite altimeter data from 1993–2020. A practical plane-wave analysis method is used to separately extract multiple coherent internal tides, with the nontidal noise in the internal tide field further removed by a two-dimensional (2-D) spatial band-pass filter. The complex radiation pathways and interference patterns of the internal tides are revealed, showing a spatial contrast between the Sulu Sea and the Sulawesi Sea. The mode-1 semidiurnal internal tides in the Sulawesi Sea are effectively generated from both the Sulu and Sangihe Island chains, forming a spatially inhomogeneous interference pattern in the deep basin. A cylindrical internal tidal wave pattern from the Sibutu passage is confirmed for the first time, which modulates the interference pattern. The interference field can be reproduced by a line source model. A weak reflected internal tidal beam off the Sulawesi slope is revealed. In contrast, the Sulu Island chain is the sole energetic internal tide source in the Sulu Sea, thus featuring a relatively consistent wave and energy flux field in the basin. These energetic semidiurnal internal tidal beams contribute to the frequent occurrence of internal solitary waves (ISWs) in the study area. On the basis of the 28-year consistent satellite measurements, the northward semidiurnal tidal energy flux from the Sulu Island chain is 0.46 GW, about 25% of the southward energy flux. For M2, the altimetric estimated energy fluxes from the Sulu Island chain are about 80% of those from numerical simulations. The total semidiurnal tidal energy flux from the Sulu and Sangihe Island chains into the Sulawesi Sea is about 2.7 GW.

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M2 tidal dynamics in the Ross Sea

Antarctic Science ◽

10.1017/s0954102003001044 ◽

2003 ◽

Vol 15 (1) ◽

pp. 41-46 ◽

Cited By ~ 13

Author(s):

ROBIN ROBERTSON ◽

AIKE BECKMANN ◽

HARTMUT HELLMER

Keyword(s):

Continental Shelf ◽

Ross Sea ◽

Tidal Energy ◽

Ocean Model ◽

Internal Tides ◽

Global Ocean ◽

Tidal Dynamics ◽

Tidal Elevation ◽

Shelf Slope ◽

Continental Shelf Slope

In certain regions of the Southern Ocean, tidal energy is believed to foster the mixing of different water masses, which eventually contribute to the formation of deep and bottom waters. The Ross Sea is one of the major ventilation sites of the global ocean abyss and a region of sparse tidal observations. We investigated M2 tidal dynamics in the Ross Sea using a three-dimensional sigma coordinate model, the Regional Ocean Model System (ROMS). Realistic topography and hydrography from existing observational data were used with a single tidal constituent, the semi-diurnal M2. The model fields faithfully reproduced the major features of the tidal circulation and had reasonable agreement with ten existing tidal elevation observations and forty-two existing tidal current measurements. The differences were attributed primarily to topographic errors. Internal tides were generated at the continental shelf/slope break and other areas of steep topography. Strong vertical shears in the horizontal velocities occurred under and at the edges of the Ross Ice Shelf and along the continental shelf/slope break. Estimates of lead formation based on divergence of baroclinic velocities were significantly higher than those based on barotrophic velocities, reaching over 10% at the continental shelf/slope break.

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Investigation of the Internal Tides in the Northwest Pacific Ocean Considering the Background Circulation and Stratification

Journal of Physical Oceanography ◽

10.1175/jpo-d-19-0177.1 ◽

2020 ◽

Vol 50 (11) ◽

pp. 3165-3188

Author(s):

Pengyang Song ◽

Xueen Chen

Keyword(s):

Pacific Ocean ◽

Ocean Circulation ◽

Conversion Rate ◽

Internal Tide ◽

Internal Tides ◽

Global Ocean ◽

Northwest Pacific ◽

Northwest Pacific Ocean ◽

Baroclinic Tide ◽

The Northwest Pacific Ocean

AbstractA global ocean circulation and tide model with nonuniform resolution is used in this work to resolve the ocean circulation globally as well as mesoscale eddies and internal tides regionally. Focusing on the northwest Pacific Ocean (NWP, 0°–35°N, 105°–150°E), a realistic experiment is conducted to simulate internal tides considering the background circulation and stratification. To investigate the influence of a background field on the generation and propagation of internal tides, idealized cases with horizontally homogeneous stratification and zero surface fluxes are also implemented for comparison. By comparing the realistic cases with idealized ones, the astronomical tidal forcing is found to be the dominant factor influencing the internal tide conversion rate magnitude, whereas the stratification acts as a secondary factor. However, stratification deviations in different areas can lead to an error exceeding 30% in the local internal tide energy conversion rate, indicating the necessity of a realistic stratification setting for simulating the entire NWP. The background shear is found to refract propagating diurnal internal tides by changing the effective Coriolis frequencies and phase speeds, while the Doppler-shifting effect is remarkable for introducing biases to semidiurnal results. In addition, nonlinear baroclinic tide energy equations considering the background circulation and stratification are derived and diagnosed in this work. The mean flow–baroclinic tide interaction and nonlinear energy flux are the most significant nonlinear terms in the derived equations, and nonlinearity is estimated to contribute approximately 5% of the total internal tide energy in the greater Luzon Strait area.

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A parameterization of local and remote tidal mixing

10.5194/egusphere-egu2020-3390 ◽

2020 ◽

Author(s):

Casimir de Lavergne ◽

Clément Vic ◽

Gurvan Madec ◽

Fabien Roquet ◽

Amy Waterhouse ◽

...

Keyword(s):

Vertical Mixing ◽

Three Dimensional ◽

Internal Tide ◽

Ocean Model ◽

Internal Tides ◽

Tidal Mixing ◽

Global Ocean ◽

Energy Conserving ◽

Energy Constrained ◽

Lagrangian Tracking

Vertical mixing is often regarded as the Achilles&#8217; heel of ocean models. In particular, few models include a comprehensive and energy-constrained parameterization of mixing by internal ocean tides. Here, we present an energy-conserving mixing scheme which accounts for the local breaking of high-mode internal tides and the distant dissipation of low-mode internal tides. The scheme relies on four static two-dimensional maps of internal tide dissipation, constructed using mode-by-mode Lagrangian tracking of energy beams from sources to sinks. Each map is associated with a distinct dissipative process and a corresponding vertical structure. Applied to an observational climatology of stratification, the scheme produces a global three-dimensional map of dissipation which compares well with available microstructure observations and with upper-ocean finestructure mixing estimates. Implemented in the NEMO global ocean model, the scheme improves the representation of deep water-mass transformation and obviates the need for a constant background diffusivity.

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Climate Process Team on Internal Wave–Driven Ocean Mixing

Bulletin of the American Meteorological Society ◽

10.1175/bams-d-16-0030.1 ◽

2017 ◽

Vol 98 (11) ◽

pp. 2429-2454 ◽

Cited By ~ 81

Author(s):

Jennifer A. MacKinnon ◽

Zhongxiang Zhao ◽

Caitlin B. Whalen ◽

Amy F. Waterhouse ◽

David S. Trossman ◽

...

Keyword(s):

Internal Wave ◽

Turbulent Mixing ◽

Low Frequency ◽

Internal Tide ◽

Deep Ocean ◽

Global Ocean ◽

Primary Role ◽

Inverse Models ◽

Lee Waves ◽

Mixing Rates

Abstract Diapycnal mixing plays a primary role in the thermodynamic balance of the ocean and, consequently, in oceanic heat and carbon uptake and storage. Though observed mixing rates are on average consistent with values required by inverse models, recent attention has focused on the dramatic spatial variability, spanning several orders of magnitude, of mixing rates in both the upper and deep ocean. Away from ocean boundaries, the spatiotemporal patterns of mixing are largely driven by the geography of generation, propagation, and dissipation of internal waves, which supply much of the power for turbulent mixing. Over the last 5 years and under the auspices of U.S. Climate Variability and Predictability Program (CLIVAR), a National Science Foundation (NSF)- and National Oceanic and Atmospheric Administration (NOAA)-supported Climate Process Team has been engaged in developing, implementing, and testing dynamics-based parameterizations for internal wave–driven turbulent mixing in global ocean models. The work has primarily focused on turbulence 1) near sites of internal tide generation, 2) in the upper ocean related to wind-generated near inertial motions, 3) due to internal lee waves generated by low-frequency mesoscale flows over topography, and 4) at ocean margins. Here, we review recent progress, describe the tools developed, and discuss future directions.

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Decay Rates of Internal Tides Estimated by an Improved Wave–Wave Interaction Analysis

Journal of Physical Oceanography ◽

10.1175/jpo-d-17-0278.1 ◽

2018 ◽

Vol 48 (11) ◽

pp. 2689-2701 ◽

Cited By ~ 8

Author(s):

Yohei Onuki ◽

Toshiyuki Hibiya

Keyword(s):

Kinetic Equation ◽

Energy Loss ◽

Interaction Analysis ◽

Wave Interaction ◽

Deep Ocean ◽

Energy Decay ◽

Decay Rates ◽

Internal Tides ◽

Global Ocean ◽

Resonant Wave

AbstractRecent numerical and observational studies have reported that resonant wave–wave interaction may be a crucial process for the energy loss of internal tides and the associated vertical water mixing in the midlatitude deep ocean. Special attention has been directed to the remarkable latitudinal dependence of the resonant interaction intensity; semidiurnal internal tides promptly lose their energy to near-inertial motions through parametric subharmonic instability equatorward of the critical latitudes 29°N/S, where half the tidal frequency coincides with the local inertial frequency. This feature contradicts the classical theoretical prediction that resonant wave–wave interaction does not play a major role in the tidal energy loss in the open ocean. By reformulating the kinetic equation for long internal waves and developing its calculation method, we estimate the energy decay rates of the low-vertical-mode semidiurnal internal tides interacting with the “ubiquitous” oceanic internal wave field. The result shows rapid energy decay of the internal tides, typically within O(10) days for the lowest-mode component, near their critical latitudes. This decay time is severalfold shorter than those in the classical studies and, additionally, varies by a factor of 2 depending on the local depth and density structure. We suggest from this study that the numerical integration of the kinetic equation is a more effective approach than recognized to determine the decay parameter of wave energy, which is indispensable for the global ocean models.

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Model Estimates of M2 Internal Tide Generation over Mid-Atlantic Ridge Topography

Journal of Physical Oceanography ◽

10.1175/2008jpo4136.1 ◽

2009 ◽

Vol 39 (10) ◽

pp. 2635-2651 ◽

Cited By ~ 65

Author(s):

N. V. Zilberman ◽

J. M. Becker ◽

M. A. Merrifield ◽

G. S. Carter

Keyword(s):

Internal Tide ◽

Tidal Energy ◽

Ocean Model ◽

Equation Model ◽

Internal Tides ◽

Analytical Models ◽

Topographic Slope ◽

Conversion Rates ◽

Mid Atlantic Ridge ◽

Model Conversion

Abstract The conversion of barotropic to baroclinic M2 tidal energy is examined for a section of the Mid-Atlantic Ridge in the Brazil Basin using a primitive equation model. Model runs are made with different horizontal smoothing (1.5, 6, and 15 km) applied to a 192 km × 183 km section of multibeam bathymetry to characterize the influence of topographic resolution on the model conversion rates. In all model simulations, barotropic to baroclinic conversion is highest over near- and supercritical slopes on the flanks of abyssal hills and discordant zones. From these generation sites, internal tides propagate upward and downward as tidal beams. The most energetic internal tide mode generated is mode 2, consistent with the dominant length scales of the topographic slope spectrum (50 km). The topographic smoothing significantly affects the model conversion amplitudes, with the domain-averaged conversion rate from the 1.5-km run (15.1 mW m−2) 4% and 19% higher than for the 6-km (14.5 mW m−2) and 15-km runs (12.2 mW m−2), respectively. Analytical models for internal tide generation by subcritical topography predict conversion rates with modal dependence and spatial patterns qualitatively similar to the Princeton Ocean Model (POM) and also show a decrease in conversion with smoother topography. The POM conversion rates are approximately 20% higher than the analytical estimates for all model grids, which is attributed to spatial variations in the barotropic flow and near-bottom stratification over generation sites, which are incorporated in the model but not in the analytical estimates.

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Near-inertial waves modulated by background flow in realistic global ocean simulations

10.5194/egusphere-egu21-14207 ◽

2021 ◽

Author(s):

Keshav Raja ◽

Maarten Buijsman ◽

Oladeji Siyanbola ◽

Miguel Solano ◽

Jay Shriver ◽

...

Keyword(s):

Kinetic Energy ◽

Normal Modes ◽

Deep Ocean ◽

Ocean Model ◽

Global Ocean ◽

Inertial Waves ◽

Flux Divergence ◽

Large Wave ◽

Wind Input ◽

Anticyclonic Eddies

Wind generated near-inertial waves (NIWs) are a major source of energy for deep-ocean mixing by transmitting wind energy from the ocean surface into the interior. Recently, it has been established that the NIW energy transmission to ocean depths is significantly modulated by background mesoscale vorticity. Thus, understanding NIW energetics in the presence of mesoscale eddies on a global scale is crucial.We study the generation, propagation and dissipation of NIWs in global 1/25o Hybrid Coordinate Ocean Model (HYCOM) simulations with realistic tidal forcing. The model has 41 layers with uniform vertical coordinates in the mixed layer and isopycnal coordinates in the ocean interior. The model is forced by 1/3hr wind from the NAVGEM atmospheric model. We analyze one month of model data for May-June 2019. The 3D HYCOM fields are projected on vertical normal modes to compute the wind input, wave kinetic energy (KE), flux divergence and dissipation per mode.We find that the globally integrated wind input in surface near-inertial motions is 0.21 TW for the 30-day period and is consistent with previous studies. The sum of the wind input to the first 5 modes accounts to only 31% of the total wind input while the sum of the NIW kinetic energy in the first 5 modes adds up to 60% of the total NIW KE. The difference in the fraction of the total between the wind input and NIW KE (31% and 60%) suggests that a significant portion of wind-induced near-inertial motions is dissipated close to the surface without being projected onto modes. We also find that NIW horizontal fluxes diverge from areas with cyclonic vorticity and converge in areas with anticyclonic vorticity, i.e., anticyclonic eddies are a sink for NIW energy in the global ocean.The residual NIW KE that does not project onto modes is found to be largely trapped in anticyclonic eddies. In a next step, we will study the fate of this energy, which most likely propagate downward as beam-like features with large wave numbers. We will compute the near-inertial wave energy balance for fixed subsurface layers and consider the energy exchange between these layers to understand the vertical structure of NIW energy dissipation. We find that the downward NIW radiation to the ocean interior at 500 m depth is 19% of the surface near-inertial wind input for the 30-day period.

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Calculating Global Dissipation of Internal Tides in Submarine Canyons

10.5194/egusphere-egu21-512 ◽

2021 ◽

Author(s):

Robert Nazarian ◽

Christian Burns ◽

Sonya Legg ◽

Maarten Buijsman ◽

Brian Arbic

Keyword(s):

Internal Tide ◽

Submarine Canyon ◽

Internal Gravity Waves ◽

Internal Tides ◽

Global Ocean ◽

Submarine Canyons ◽

Incoming Wave ◽

Geometrical Properties ◽

Length Width ◽

Global Estimates

The breaking of tidally-generated internal gravity waves (hereafter internal tides) is a significant driver of ocean mixing, and observations and model simulations show that a non-negligible amount of this internal tide-driven mixing occurs in submarine canyons. While previous studies have used single observations of canyon mixing to estimate the global magnitude of internal tide-driven mixing within canyons, there is still significant uncertainty in these estimates.To address this question, we have constructed an algorithm based on the modelled energy loss in idealized simulations (Nazarian & Legg 2017b) to calculate the magnitude of mixing in each submarine canyon and to determine the percentage of the global internal tide energy budget that is dissipated in canyons. The algorithm utilizes the Harris et al. 2014 analysis of the SRTM30_PLUS global bathymetry map to provide the geometrical properties of each canyon (i.e. height, length, width) and a high-resolution, tidally-forced HYCOM simulation to determine the internal tide field (sea surface height, angle of propagation, stratification, etc.). Preliminary calculations show that the canyon&#8217;s geometrical properties as well as local hydrographic properties have significant effects on the magnitude of mixing. Specifically, canyons that are tall relative to the depth of the water column and long relative to the incoming internal tide&#8217;s wavelength dissipate approximately 100% of the incoming wave&#8217;s energy. Consistent with previous studies, we find that regardless of bathymetry, submarine canyons can dissipate a significant fraction of the incident internal tide energy. Our estimate of the globally-integrated energy dissipation in canyons, taking into account geometric properties of each canyon, is two to three times larger than prior global estimates extrapolated from observations of individual canyons. Furthermore, our research highlights canyon hotspots of internal tide-driven mixing in the global ocean, for which observations do not presently exist. Taken together, these results raise larger questions about the location of internal tide dissipation and the inclusion of such dissipation in global ocean models.

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