scholarly journals Global Patterns of Low-Mode Internal-Wave Propagation. Part I: Energy and Energy Flux

2007 ◽  
Vol 37 (7) ◽  
pp. 1829-1848 ◽  
Author(s):  
Matthew H. Alford ◽  
Zhongxiang Zhao
Keyword(s):  
Internal Wave ◽  
Time Scales ◽  
Energy Flux ◽  
Internal Tide ◽  
Companion Paper ◽  
Internal Tides ◽  
Frequency Bands ◽  
Order Of Magnitude ◽  
Hawaiian Ridge ◽  
Mesoscale Currents

Abstract Extending an earlier attempt to understand long-range propagation of the global internal-wave field, the energy E and horizontal energy flux F are computed for the two gravest baroclinic modes at 80 historical moorings around the globe. With bandpass filtering, the calculation is performed for the semidiurnal band (emphasizing M2 internal tides, generated by flow over sloping topography) and for the near-inertial band (emphasizing wind-generated waves near the Coriolis frequency). The time dependence of semidiurnal E and F is first examined at six locations north of the Hawaiian Ridge; E and F typically rise and fall together and can vary by over an order of magnitude at each site. This variability typically has a strong spring–neap component, in addition to longer time scales. The observed spring tides at sites northwest of the Hawaiian Ridge are coherent with barotropic forcing at the ridge, but lagged by times consistent with travel at the theoretical mode-1 group speed from the ridge. Phase computed from 14-day windows varies by approximately ±45° on monthly time scales, implying refraction by mesoscale currents and stratification. This refraction also causes the bulk of internal-tide energy flux to be undetectable by altimetry and other long-term harmonic-analysis techniques. As found previously, the mean flux in both frequency bands is O(1 kW m−1), sufficient to radiate a substantial fraction of energy far from each source. Tidal flux is generally away from regions of strong topography. Near-inertial flux is overwhelmingly equatorward, as required for waves generated at the inertial frequency on a β plane, and is winter-enhanced, consistent with storm generation. In a companion paper, the group velocity, ĉg ≡ FE−1, is examined for both frequency bands.

scholarly journals On the Equilibration of Numerical Simulation of Internal Tide: A Case Study around the Hawaiian Ridge

2017 ◽  
Vol 34 (7) ◽  
pp. 1545-1563 ◽  
Author(s):  
Guang-Zhen Jin ◽  
An-Zhou Cao ◽  
Xian-Qing Lv
Keyword(s):  
Numerical Simulation ◽  
Energy Flux ◽  
Eddy Viscosity ◽  
Internal Tide ◽  
Tidal Energy ◽  
Temporal Variations ◽  
Internal Tides ◽  
Damping Coefficient ◽  
Tidal Period ◽  
Hawaiian Ridge

AbstractTo investigate the equilibration of numerical simulation (ENS) of internal tide, a three-dimensional isopycnic coordinate internal tide model is applied to simulate the M2 internal tide on idealized topography and around the Hawaiian Ridge. An idealized experiment is carried out on a Gaussian topography, and the temporal variations of the baroclinic velocity and the baroclinic energy flux are analyzed, then ENS is studied, and two criteria are presented. Moreover, the impacts of four parameters [horizontal and vertical eddy viscosity coefficients, bottom friction coefficient, and damping coefficient (to parameterize the nonhydrostatic processes in the model)] on ENS during numerical simulations, the baroclinic velocity, the baroclinic tidal energy, and the baroclinic energy flux are investigated. It appears that ENS for the M2 internal tide is more sensitive to the horizontal eddy viscosity coefficient and the damping coefficient. To further examine the criteria of ENS, a numerical experiment is carried out to simulate the M2 internal tidal constituent near the Hawaiian Ridge. The simulated surface tide shows good agreement with results from the Oregon State University tidal model and TOPEX/Poseidon (T/P) observations. The simulation results indicate that a 50 M2 tidal period (25.88 days) run is capable of ensuring ENS for the M2 internal tide in this case. In short, this paper presents a method and two criteria for examining ENS for internal tides for modelers.

scholarly journals Propagation and dissipation of internal tides in the Oslofjord

2012 ◽  
Vol 9 (1) ◽  
pp. 315-357
Author(s):  
A. Staalstrøm ◽  
E. Aas ◽  
B. Liljebladh
Keyword(s):  
Energy Dissipation ◽  
Energy Density ◽  
Internal Wave ◽  
Energy Flux ◽  
Internal Tides ◽  
Mixing Efficiency ◽  
New Information ◽  
Order Of Magnitude ◽  
Perturbation Pressure ◽  
Velocity Pressure

Abstract. Observations of velocity, pressure, temperature and salinity in the inner Oslofjord have been analysed. The data is used to provide new information about energy dissipation and mixing efficiency of internal tides generated by tidal current across the Drøbak Sill. The ratio between the observed amplitude of the internal wave in the pycnocline and the amplitude of the surface elevation is in the range 38 ± 6 at a distance of 1 km inside the sill and 11 ± 2 at 10 km. The energy flux of the internal wave propagating from the Drøbak Sill into the inner fjord is estimated to vary in the range 155–480 kW. This is the same order of magnitude as the estimated baroclinic energy loss (250 kW). Approximately 40–70% of this energy flux is dissipated within a distance of 7 km from the sill. The mixing efficiency is estimated to 0.09–0.11 based on energy density and group velocity, and 0.22–0.26 based on perturbation pressure and baroclinic velocity. These numbers are larger than earlier estimates. Only a fraction in the range 0.01–0.03 is transferred to work against buoyancy in the first basin within a distance of 7 km from the sill.

scholarly journals Inferences and Observations of Turbulent Dissipation and Mixing in the Upper Ocean at the Hawaiian Ridge

2007 ◽  
Vol 37 (3) ◽  
pp. 476-494 ◽  
Author(s):  
Joseph P. Martin ◽  
Daniel L. Rudnick
Keyword(s):  
Energy Density ◽  
Internal Wave ◽  
Dissipation Rate ◽  
Internal Tide ◽  
Eddy Diffusivity ◽  
Internal Tides ◽  
Upper Ocean ◽  
Turbulent Dissipation ◽  
Hawaiian Ridge ◽  
Wave Induced

Abstract The Hawaiian Ridge is one of the most energetic generators of internal tides in the pelagic ocean. The density and current structure of the upper ocean at the Hawaiian Ridge were observed using SeaSoar and Doppler sonar during a survey extending from Oahu to Brooks Banks and up to 200 km from the ridge peak. Survey observations are used to quantify spatial changes in internal-wave-induced turbulent dissipation and mixing. The turbulent dissipation rate of kinetic energy ɛ and diapycnal eddy diffusivity Kρ are inferred from an established parameterization using internal wave shear as input. At the Kauai Channel (KC) and French Frigate Shoals/Brooks Banks sites, ɛ and Kρ decay away from the ridge with maxima exceeding minima by 5 times. At both sites, average Kρ is everywhere greater than the canonical open-ocean value of 10−5 m2 s−1. Along the ridge, ɛ and Kρ vary by up to 100 times and are largest at sites of largest numerical model internal tide energy density. In the eastern KC, Kρ > 10−3 m2 s−1 is typical in a patch more than 200 m thick located above the path of an M2 internal tide ray. An upper limit on the dissipation rate from M2 internal tides to turbulence within 50 km of the Hawaiian Ridge is roughly estimated to be in the range of 4–9 GW. At KC, the depth-integrated internal wave energy density and dissipation rate are positively correlated. Potential density inversions occur near the main ridge axis at significant topographic features. Average Kρ is larger inside inversions.

The Surface Expression of Semidiurnal Internal Tides near a Strong Source at Hawaii. Part II: Interactions with Mesoscale Currents*

2010 ◽  
Vol 40 (6) ◽  
pp. 1180-1200 ◽  
Author(s):  
C. Chavanne ◽  
P. Flament ◽  
D. Luther ◽  
K-W. Gurgel
Keyword(s):  
Internal Wave ◽  
Ray Tracing ◽  
Internal Tide ◽  
Wave Dispersion ◽  
Internal Tides ◽  
Vertical Shear ◽  
Buoyancy Frequency ◽  
Phase Lag ◽  
Vertical Wavelength ◽  
Mesoscale Currents

Abstract Observations of semidiurnal surface currents in the Kauai Channel, Hawaii, are interpreted in the light of the interaction of internal tides with energetic surface-intensified mesoscale currents. The impacts on internal tide propagation of a cyclone of 55-km diameter and ∼100-m vertical decay scale, as well as of vorticity waves of ∼100-km wavelength and 100–200-m vertical decay scales, are investigated using 3D ray tracing. The Doppler-shifted intrinsic frequency is assumed to satisfy the classic hydrostatic internal wave dispersion relation, using the local buoyancy frequency associated with the background currents through thermal-wind or gradient-wind balance. The M2 internal tide rays with initial horizontal wavelength of 50 km and vertical wavelength of O(1000 m) are propagated from possible generation locations at critical topographic slopes through idealized mesoscale currents approximating the observed currents. Despite the lack of scale separation between the internal waves and background state, which is required by the ray-tracing approximation, the results are qualitatively consistent with observations: the cyclone causes the energy of internal tide rays propagating through its core to increase near the surface (up to a factor of 15), with surfacing time delayed by up to 5 h (∼150° phase lag), and the vorticity waves enhance or reduce the energy near the surface, depending on their phase. These examples illustrate the fact that, even close to their generation location, semidiurnal internal tides can become incoherent with astronomical forcing because of the presence of mesoscale variability. Internal tide energy is mainly affected by refraction through the inhomogeneous buoyancy frequency field, with Doppler shifting playing a secondary but not negligible role, inducing energy transfers between the internal tides and background currents. Furthermore, the vertical wavelength can be reduced by a factor of 6 near the surface in the presence of the cyclone, which, combined with the energy amplification, leads to increased vertical shear within the internal tide rays, with implications for internal wave-induced mixing in the ocean.

scholarly journals Observations of Tidal Internal Wave Beams at Kauai Channel, Hawaii

2009 ◽  
Vol 39 (2) ◽  
pp. 421-436 ◽  
Author(s):  
S. T. Cole ◽  
D. L. Rudnick ◽  
B. A. Hodges ◽  
J. P. Martin
Keyword(s):  
Internal Wave ◽  
Energy Flux ◽  
Momentum Flux ◽  
Internal Tides ◽  
Turbulent Dissipation ◽  
Ridge Structure ◽  
Almost Everywhere ◽  
Hawaiian Ridge ◽  
Internal Wave Generation ◽  
Almost All

Abstract To observe the across-ridge structure of internal tides, density and velocity were measured using SeaSoar and a Doppler sonar over the upper 400–600 m of the ocean extending 152 km on each side of the Hawaiian Ridge at Kauai Channel. Eighteen sections were completed in about 18 days with sampling intentionally detuned from the lunar semidiurnal (M2) tide so that averaging over all sections was equivalent to phase averaging the M2 tide. Velocity and displacement variance and several covariances involving velocity and displacement showed one M2 internal wave beam on each side of the ridge and reflection of the beams off of the surface. Theoretical ray slopes aligned with the observed beams and originated from the sides of the ridge. Energy flux was in agreement with internal wave generation at the ridge. Inferred turbulent dissipation was elevated relative to open ocean values near tidal beams. Energy flux was larger than total dissipation almost everywhere across the ridge. Internal wave energy flux and dissipation at Kauai Channel were 1.5–2.5 times greater than at the average location along the Hawaiian Ridge. The upper 400–600 m was about 1/3 to 1/2 as energetic as the full-depth ocean. Tidal beams interact with each other over the entire length of the beams causing gradients along beams in almost all covariances, momentum flux divergences, and mean flows. At Kauai Channel, momentum flux divergences corresponded to mean flows of 1–4 cm s−1.

scholarly journals Internal Tides in Monterey Submarine Canyon

2011 ◽  
Vol 41 (1) ◽  
pp. 186-204 ◽  
Author(s):  
Rob A. Hall ◽  
Glenn S. Carter
Keyword(s):  
Energy Conversion ◽  
Energy Flux ◽  
Internal Tide ◽  
Submarine Canyon ◽  
Ocean Model ◽  
Internal Tides ◽  
Remote Areas ◽  
Order Of Magnitude ◽  
Baroclinic Energy Conversion

Abstract The M2 internal tide in Monterey Submarine Canyon is simulated using a modified version of the Princeton Ocean Model. Most of the internal tide energy entering the canyon is generated to the south, on Sur Slope and at the head of Carmel Canyon. The internal tide is topographically steered around the large canyon meanders. Depth-integrated baroclinic energy fluxes are up canyon and largest near the canyon axis, up to 1.5 kW m−1 at the mouth of the upper canyon and increasing to over 4 kW m−1 around Monterey and San Gregorio Meanders. The up-canyon energy flux is bottom intensified, suggesting that topographic focusing occurs. Net along-canyon energy flux decreases almost monotonically from 9 MW at the canyon mouth to 1 MW at Gooseneck Meander, implying that high levels of internal tide dissipation occur. The depth-integrated energy flux across the 200-m isobath is order 10 W m−1 along the majority of the canyon rim but increases by over an order of magnitude near the canyon head, where internal tide energy escapes onto the shelf. Reducing the size of the model domain to exclude remote areas of high barotropic-to-baroclinic energy conversion decreases the depth-integrated energy flux in the upper canyon by 20%. However, quantifying the role of remote internal tide generation sites is complicated by a pressure perturbation feedback between baroclinic energy flux and barotropic-to-baroclinic energy conversion.

scholarly journals Propagation and dissipation of internal tides in the Oslofjord

Ocean Science ◽  
2012 ◽  
Vol 8 (4) ◽  
pp. 525-543 ◽  
Author(s):  
A. Staalstrøm ◽  
E. Aas ◽  
B. Liljebladh
Keyword(s):  
Energy Flux ◽  
Mean Diffusivity ◽  
Internal Tide ◽  
Maximum Amplitude ◽  
Vertical Displacement ◽  
Internal Tides ◽  
New Information ◽  
Vertical Displacements ◽  
Order Of Magnitude ◽  
Sill Depth

Abstract. Observations of velocity, pressure, temperature and salinity in the inner Oslofjord have been analysed to provide new information about the relationships between internal tides generated by tidal currents across the Drøbak Sill and dissipation and diffusivity in the fjord. The most energetic vertical displacement of density surfaces inside the sill is associated with the first internal mode that has maximum amplitude around sill depth. The amplitude of the vertical displacement around sill depth correlates with the amplitude of the surface elevation, and, at a distance of 1 km inside the sill, the ratio between the amplitudes is 38, decreasing to 11 at a distance of 10 km. The greatest vertical displacements inside the sill, however, are found at 40 m depth. These latter internal waves are not associated with a first-mode internal tide, but are rather associated with higher internal modes controlled by stratification. The energy flux of the internal wave propagating from the Drøbak Sill into the inner fjord on the east side of the Håøya Island is estimated to vary in the range 155–430 kW. This is the same order of magnitude as the estimated barotropic energy loss over the Drøbak Sill (250 kW), but only 4–10% of the total barotropic flux. Approximately 40–70% of the internal energy flux is lost within a distance of 10 km from the sill. The mean diffusivity below 90 m depth in this area (~20 cm2 s−1) is more than four times higher than in the rest of the fjord (~5 cm2 s−1 or less).

Dynamics and energetics of nonlinear internal wave around a double-canyon system

2020 ◽  
Author(s):  
Qun Li
Keyword(s):  
Continental Shelf ◽  
Internal Wave ◽  
Energy Flux ◽  
Internal Tide ◽  
Internal Tides ◽  
Flux Divergence ◽  
Wave Regime ◽  
Nonlinear Internal Wave ◽  
The North ◽  
Shelf Slope

<p>The continental shelf/slope northeastern Taiwan is a ‘hotspot’ of nonlinear internal wave (NLIW). The complex spatial pattern of NLIW indicates the complexity of the source and the background conditions. In this talk, we investigated the dynamic and energetics of the internal tide (IT) and NLIW around this region based on a 3D high resolution nonhydrostatic numerical model. Special attention is paid on the role of two main topographic features-the Mien-Hua Canyon and the North Mien-Hua Canyon, which are the energetic sources for ITs and NLIW.</p><p>The complex IT field is excited by the double-Canyon system and the rotary tidal current. ITs from different sources and formation time interference with each other further strengthen the complexity. The area-integrated energy flux divergence (the area-integrated dissipation rate) is ~0.45GW (~0.28GW) and ~0.26 GW (~0.17 GW) over the Mien-Hua Canyon and the North Mien-Hua Canyon, respectively. Along with the energetic internal tides, large-amplitude NLIW and trains are also generated over the continental shelf and slope region. The amplitude of the NLIW can reach to about 30 m on the continental slope with a water depth of 130 m and shows similar spatial complexity, which is consistent with in situ and satellite observations. Further analysis shows that the dominant generation mechanism of the NLIW belongs to the mixed tidal-lee wave regime. In addition, the dynamic processes can be significantly modulated by the Kuroshio. With the present of Kuroshio, the energy flux of the M2 internal tide shows a distinct gyre pattern and strengthens over the double canyon system, which is more close to the mooring observations and previous study.</p>

scholarly journals The Vertical Mode Decomposition of Surface and Internal Tides in the Presence of a Free Surface and Arbitrary Topography

2016 ◽  
Vol 46 (12) ◽  
pp. 3777-3788 ◽  
Author(s):  
Samuel M. Kelly
Keyword(s):  
Free Surface ◽  
Energy Conversion ◽  
Energy Flux ◽  
Internal Tide ◽  
Open Ocean ◽  
Internal Tides ◽  
Surface Boundary ◽  
Free Surface Boundary Condition ◽  
Mode Decomposition ◽  
Order Of Magnitude

AbstractThe method of decomposing surface and internal tides determines the expression for internal tide energy, energy flux, and energy conversion. The de facto standard is to define surface tides as depth-averaged pressure and horizontal velocity and internal tides as the residuals. This decomposition, which is equivalent to projecting motion onto vertical modes that obey a rigid lid, is known to produce spurious energy conversion CS through movement of the free surface. Here, motion is instead projected onto modes that obey a linear, free-surface boundary condition. The free-surface modes are shown to obey a more complicated orthogonality condition than rigid-lid modes but are still straightforward to calculate numerically. The resulting decomposition (i) completely eliminates spurious energy conversion CS and (ii) leads to a more precise expression for topographic internal tide generation C, which now depends on horizontal gradients in the vertical structure of the surface tide. Numerical simulations and rough global estimates indicate that corrections to C are a maximum of a few percent. However, CS produces spurious energy flux divergences/convergences in the open ocean, which are the same order of magnitude [O(1–10) mW m−2] as open-ocean internal tide energy dissipation.

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

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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