scholarly journals Internal wave generation by oscillation of a sphere, with application to internal tides

2010 ◽  
Vol 666 ◽  
pp. 308-357 ◽  
Author(s):  
B. VOISIN ◽  
E. V. ERMANYUK ◽  
J.-B. FLÓR
Keyword(s):  
Wave Amplitude ◽  
Near Field ◽  
Oscillation Amplitude ◽  
Tidal Flow ◽  
Three Dimensional ◽  
Tidal Energy ◽  
Internal Gravity Waves ◽  
Internal Tides ◽  
Correlation Technique ◽  
The Waves

A joint theoretical and experimental study is performed on the generation of internal gravity waves by an oscillating sphere, as a paradigm of the generation of internal tides by barotropic tidal flow over three-dimensional supercritical topography. The theory is linear and three-dimensional, applies both near and far from the sphere, and takes into account viscosity and the unsteadiness arising from the interference with transients generated at the start-up. The waves propagate in conical beams, evolving with distance from a bimodal to unimodal wave profile. In the near field, the profile is asymmetric with its major peak towards the axis of the cones. The experiments involve horizontal oscillations and develop a cross-correlation technique for the measurement of the deformation of fluorescent dye planes to sub-pixel accuracy. At an oscillation amplitude of one fifth of the radius of the sphere, the waves are linear and the agreement between experiment and theory is excellent. As the amplitude increases to half the radius, nonlinear effects cause the wave amplitude to saturate at a value that is 20% lower than its linear estimate. Application of the theory to the conversion rate of barotropic tidal energy into internal tides confirms the expected scaling for flat topography, and shows its transformation for hemispherical topography. In the ocean, viscous and unsteady effects have an essentially local role, in keeping the wave amplitude finite at the edges of the beams, and otherwise dissipate energy on such large distances that they hardly induce any decay.

scholarly journals Impact of Channel Geometry and Rotation on the Trapping of Internal Tides

2007 ◽  
Vol 37 (11) ◽  
pp. 2740-2763 ◽  
Author(s):  
Sybren Drijfhout ◽  
Leo R. M. Maas
Keyword(s):  
Continental Slope ◽  
Three Dimensional ◽  
Tidal Energy ◽  
Ocean Model ◽  
Internal Tides ◽  
Open Boundary ◽  
Kelvin Wave ◽  
Channel Geometry ◽  
Channel Slope ◽  
The Cross

Abstract The generation and propagation of internal tides has been studied with an isopycnic three-dimensional ocean model. The response of a uniformly stratified sea in a channel, which is forced by a barotropic tide on its open boundary, is considered. The tide progresses into the channel and forces internal tides over a continental slope at the other end. The channel has a length of 1200 km and a width of 191.25 km. The bottom profile has been varied. In a series of four experiments it is shown how the cross-channel geometry affects the propagation and trapping of internal tides, and the penetration scale of wave energy, away from the continental slope, is discussed. In particular it is found that a cross-channel bottom slope constrains the penetration of the internal tidal energy. Most internal waves refract toward a cross-channel plane where they are trapped. The exception is formed by edge waves that carry part of the energy away from the continental slope. In the case of rotation near the continental slope, the Poincaré waves that arise in the absence of a cross-channel slope no longer bear the characteristics of the wave attractor predicted by 2D theory, but are almost completely arrested, while the right-bound Kelvin wave preserves the 2D attractor in the cross-channel plane, which is present in the nonrotating case. The reflected, barotropic right-bound Kelvin wave acts as a secondary internal wave generator along the cross-channel slope.

scholarly journals Tidal Energy Flows between the Midriff Islands in the Gulf of California

Energies ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 621
Author(s):  
Federico Angel Velazquez-Muñoz ◽  
Anatoliy Filonov
Keyword(s):  
Kinetic Energy ◽  
Internal Wave ◽  
Gulf Of California ◽  
Current Flow ◽  
Tidal Flow ◽  
Three Dimensional ◽  
Tidal Energy ◽  
Ocean Model ◽  
Field Development ◽  
Wave Measurements

The Gulf of California has many regions of potential tidal-stream energy that have been identified and characterized using in-situ measurements and numerical ocean models. The Midriff Islands region has received particular attention due to its increased current speeds and high kinetic energy. This increase in energy can be seen in the formation of internal wave packets propagating for several hundred kilometers. Here we present a brief description of internal wave measurements travel towards the Northern Gulf and explore energy generation sites. In this paper we characterize the tidal inflow and outflow that passes throughout the Midriff Islands in the central part of the Gulf. We use a three-dimensional numerical ocean model that adequately reproduces the tidal flow and the increase in speed and kinetic energy between the islands. The current flow structure shows the highest velocity cores near the shore and far from the bottom. During the rising tide, the maximum current flow (~0.6 ms−1) was found between Turón Island and San Lorenzo Island, from the surface to 200 m depth. When the currents flowed out of the Gulf, during the falling tide, the maximum negative current (−0.8 ms−1) was found between Tiburon Island and Turón Island, from near the surface to 80 m depth. Although there are favorable conditions for power generation potential by tidal flows, the vertical variability of the current must be considered for field development and equipment installation sites.

scholarly journals An Energy Compartment Model for Propagation, Nonlinear Interaction, and Dissipation of Internal Gravity Waves

2014 ◽  
Vol 44 (8) ◽  
pp. 2093-2106 ◽  
Author(s):  
Carsten Eden ◽  
Dirk Olbers
Keyword(s):  
Gravity Waves ◽  
Bottom Topography ◽  
Compartment Model ◽  
Tidal Energy ◽  
Internal Gravity Waves ◽  
Internal Tides ◽  
Continental Margins ◽  
Wave Interactions ◽  
Dissipation Energy ◽  
Parametric Subharmonic Instability

Abstract The recently proposed Internal Wave Dissipation, Energy and Mixing (IDEMIX) model, describing the propagation and dissipation of internal gravity waves in the ocean, is extended. Compartments describing the energy contained in the internal tides and the near-inertial waves at low, vertical wavenumber are added to a compartment of the wave continuum at higher wavenumbers. Conservation equations for each compartment are derived based on integrated versions of the radiative transfer equation of weakly interacting waves. The compartments interact with each other by the scattering of tidal energy to the wave continuum by triad wave–wave interactions, which are strongly enhanced equatorward of 28° due to parametric subharmonic instability of the tide and by scattering to the continuum of both tidal and near-inertial wave energy over rough topography and at continental margins. Global numerical simulations of the resulting model using observed stratification, forcing functions, and bottom topography yield good agreement with available observations.

scholarly journals Percampuran Turbulen Di Laut Sulawesi Menggunakan Estimasi Thorpe Analisis

2021 ◽  
Vol 24 (2) ◽  
pp. 211-222
Author(s):  
Hadi Hermansyah ◽  
Agus Saleh Atmadipoera ◽  
Tri Prartono ◽  
Indra Jaya ◽  
Fadli Syamsudin
Keyword(s):  
Turbulent Mixing ◽  
Large Scale ◽  
Near Field ◽  
Tidal Energy ◽  
Eddy Diffusivity ◽  
Internal Tides ◽  
Strong Mixing ◽  
Ocean Energy ◽  
Average Value ◽  
Vertical Diffusivity

Dissipation of internal tides will cause mixing, The mixing process at sea plays a key role in controlling large-scale circulation and ocean energy distribution. The purpose of this research was to estimate the turbulent mixing values  (vertical eddy diffusivity) of water mass using Thorpe analysis. The results showed that the  location where strong mixing occurred in the “near-field” area around Sangihe Island with vertical diffusivity value . Even in areas far-field(far from the generating site) are found vertical diffusivity , the result of internal propagation tides dissipation. Based on the result of the observation, it shows that the level of kinetic energy of eddy turbulen dissipation (ε) in the Sulawesi Sea on all layers has an average value of . The value of ε in the thermocline layer is greatest  compared to the mixed surface layer and the almost homogeneous deep layer, the increase in mixing in the area near the ridge due to the closer water column to the base topography. The average turbulent rate of , the strongest fluctuation of value occurs in the thermocline layer, ranging from  to  with an average of about . The value of this turbulent mixing is higher than the previous measurements in some Indonesian ocean. This is allegedly due to the existence of a strong internal tidal energy and its interaction with topography in the Sulawesi Sea.Disipasi dari pasang surut internal akan menyebabkan terjadinya percampuran, proses percampuran di laut memainkan peran kunci dalam mengendalikan sirkulasi skala besar dan distribusi energi lautan. Tujuan dari penelitian ini adalah untuk mengestimasi nilai percampuran turbulen (difusivitas eddy vertikal) massa air dengan analisis Thorpe. Hasil penelitian ini menunjukkan bahwa percampuran yang kuat terjadi di area sekitar Pulau Sangihe-Talaud dengan nilai difusivitas vertikal . Bahkan pada area yang jauh dari pusat pembangkitan ditemukan difusivitas vertikal , hasil disipasi propagasi pasang surut internal. Berdasarkan hasil pengamatan menunjukan bahwa rata-rata tingkat energi kinetik disipasi turbulen eddy  Laut Sulawesi pada semua lapisan adalah . Nilai  di lapisan termoklin paling besar  dibandingkan dengan lapisan permukaan tercampur dan lapisan dalam yang hampir homogen, peningkatan percampuran di daerah dekat ridge disebabkan makin mendekatnya kolom air dengan topografi dasar. Rata-rata nilai percampuran turbulen sebesar , fluktuasi nilai yang paling kuat terjadi di lapisan termoklin, yang berkisar yaitu antara  sampai  dengan rerata sekitar . Nilai percampuran turbulen ini lebih tinggi dibandingkan dengan pengukuran sebelumnya di beberapa perairan Indonesia. Hal ini diduga karena adanya energi pasang surut internal yang kuat serta interaksinya dengan topografi yang ada di Laut Sulawesi.

Instability and focusing of internal tides in the deep ocean

2007 ◽  
Vol 588 ◽  
pp. 1-28 ◽  
Author(s):  
OLIVER BÜHLER ◽  
CAROLINE J. MULLER
Keyword(s):  
Ocean Circulation ◽  
Wave Breaking ◽  
Large Scale ◽  
Three Dimensional ◽  
Deep Ocean ◽  
Internal Gravity Waves ◽  
Internal Tides ◽  
Unstable Wave ◽  
Two Dimensional ◽  
Sea Floor

The interaction of tidal currents with sea-floor topography results in the radiation of internal gravity waves into the ocean interior. These waves are called internal tides and their dissipation due to nonlinear wave breaking and concomitant three-dimensional turbulence could play an important role in the mixing of the abyssal ocean, and hence in controlling the large-scale ocean circulation.As part of on-going work aimed at providing a theory for the vertical distribution of wave breaking over sea-floor topography, in this paper we investigate the instability of internal tides in a very simple linear model that helps us to relate the formation of unstable regions to simple features in the sea-floor topography. For two-dimensional tides over one-dimensional topography we find that the formation of overturning instabilities is closely linked to the singularities in the topography shape and that it is possible to have stable waves at the sea floor and unstable waves in the ocean interior above.For three-dimensional tides over two-dimensional topography there is in addition an effect of geometric focusing of wave energy into localized regions of high wave amplitude, and we investigate this focusing effect in simple examples. Overall, we find that the distribution of unstable wave breaking regions can be highly non-uniform even for very simple idealized topography shapes.

scholarly journals Tidal Conversion and Dissipation at Steep Topography in a Channel Poleward of the Critical Latitude

2019 ◽  
Vol 49 (5) ◽  
pp. 1269-1291 ◽  
Author(s):  
Kenneth G. Hughes ◽  
Jody M. Klymak
Keyword(s):  
Three Dimensional ◽  
Tidal Energy ◽  
Kelvin Waves ◽  
Internal Tides ◽  
The Arctic ◽  
Energy Budgets ◽  
Dimensional System ◽  
Deep Layers ◽  
The Stability ◽  
Critical Latitude

Abstract In high-latitude fjords and channels in the Canadian Arctic Archipelago, walls support radiating internal tides as Kelvin waves. Such waves allow for significant barotropic to baroclinic tidal energy conversion, which is otherwise small or negligible when poleward of the critical latitude. This fundamentally three-dimensional system of a subinertial channel is investigated with a suite of numerical simulations in rectangular channels of varying width featuring idealized, isolated ridges. Even in channels as wide as 5 times the internal Rossby radius, tidal conversion can remain as high as predicted by an equivalent two-dimensional, nonrotating system. Curves of tidal conversion as a function of channel width, however, do not vary monotonically. Instead, they display peaks and nulls owing to interference between the Kelvin waves along the wall and similar waves that propagate along the ridge flanks, the wavelengths of which can be estimated from linear theory to guide prediction. Because the wavelengths are comparable to width scales of Arctic channels and fjords, the interference will play a first-order role in tidal energy budgets and may consequently influence the stability of glaciers, the ventilation of deep layers, the locations of sediment deposition, and the fate of freshwater exiting the Arctic Ocean.

Tidal flow over topography: effect of excursion number on wave energetics and turbulence

2014 ◽  
Vol 750 ◽  
pp. 259-283 ◽  
Author(s):  
Masoud Jalali ◽  
Narsimha R. Rapaka ◽  
Sutanu Sarkar
Keyword(s):  
Near Field ◽  
Tidal Flow ◽  
Deep Ocean ◽  
Internal Gravity Waves ◽  
Form Analysis ◽  
Lee Waves ◽  
Flow Over Topography ◽  
Critical Slope ◽  
Wave Flux ◽  
Critical Regions

AbstractThe excursion number, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}Ex = U_0/\varOmega l$, is a parameter that characterizes the ratio of streamwise fluid advection during a tidal oscillation of amplitude $U_0$ and frequency $\varOmega $ to the streamwise topographic length scale $l$. Direct numerical simulations are performed to study how internal gravity waves and turbulence change when $Ex$ is varied from a low value (typical of a ridge in the deep ocean) to a value of unity (corresponding to energetic tides over a small topographic feature). An isolated obstacle having a smoothed triangular shape and 20 % of the streamwise length at critical slope is considered. With increasing values of $Ex$, the near field of the internal waves loses its beam-like character, the wave response becomes asymmetric with respect to the ridge centre, and transient lee waves form. Analysis of the baroclinic energy balance shows significant reduction in the radiated wave flux in the cases with higher $Ex$ owing to a substantial rise in advection and baroclinic dissipation as well as a decrease in conversion. Turbulence changes qualitatively with increasing $Ex$. In the situation with $Ex \sim 0.1$, turbulence is intensified at the near-critical regions of the slope, and is also significant in the internal wave beams above the ridge where there is intensified shear. At $Ex = O(1)$, the transient lee waves overturn adjacent to the ridge flanks and, owing to convective instability, buoyancy acts as a source for turbulent kinetic energy. The size of the turbulent overturns has a non-monotonic dependence on excursion number: the largest overturns, as tall as twice the obstacle height, occur in the $Ex = 0.4$ case, but there is a substantial decrease of overturn size at larger values of $Ex$ simulated here.

scholarly journals Nonlinear aspects of focusing internal waves

2019 ◽  
Vol 862 ◽  
Author(s):  
Natalia D. Shmakova ◽  
Jan-Bert Flór
Keyword(s):  
Wave Amplitude ◽  
Oscillation Amplitude ◽  
Three Dimensional ◽  
Nonlinear Effects ◽  
Focal Region ◽  
Mean Flow ◽  
Wave Focusing ◽  
Tidal Waves ◽  
Two Dimensional Flow ◽  
Major Radius

When a torus oscillates horizontally in a linearly stratified fluid, the wave rays form a double cone, one upward and one downward, with two focal points where the wave amplitude has a maximum due to wave focusing. Following a former study on linear aspects of wave focusing (Ermanyuk et al., J. Fluid Mech., vol. 813, 2017, pp. 695–715), we here consider experimental results on the nonlinear aspects that occur in the focal region below the torus for higher-amplitude forcing. A new non-dimensional number that is based on heuristic arguments for the wave amplitude in the focal area is presented. This focusing number is defined as $Fo=(A/a)\unicode[STIX]{x1D716}^{-1/2}f(\unicode[STIX]{x1D703})$, with oscillation amplitude $A$, $f(\unicode[STIX]{x1D703})$ a function for the variation of the wave amplitude with wave angle $\unicode[STIX]{x1D703}$, and $\unicode[STIX]{x1D716}^{1/2}=\sqrt{b/a}$ the increase in amplitude due to the focusing, with $a$ and $b$, respectively, the minor and major radius of the torus. Nonlinear effects occur for $Fo\geqslant 0.1$, with the shear stress giving rise to a mean flow which results in the focal region in a central upward motion partially surrounded by a downward motion. With increasing $Fo$, the Richardson number $Ri$ measured from the wave steepness monotonically decreases. Wave breaking occurs at $Fo\approx 0.23$, corresponding to $Ri=0.25$. In this regime, the focal region is unstable due to triadic wave resonance. For the different tori sizes under consideration, the triadic resonant instability in these three-dimensional flows resembles closely the resonance observed by Bourget et al. (J. Fluid Mech., vol. 723, 2013, pp. 1–20) for a two-dimensional flow, with only minor differences. Application to internal tidal waves in the ocean are discussed.

scholarly journals Tidal Energy Loss, Internal Tide Radiation, and Local Dissipation for Two-Layer Tidal Flow over a Sill

2017 ◽  
Vol 47 (7) ◽  
pp. 1521-1538 ◽  
Author(s):  
Lars Arneborg ◽  
Pär Jansson ◽  
André Staalstrøm ◽  
Göran Broström
Keyword(s):  
Energy Loss ◽  
Analytical Model ◽  
Tidal Flow ◽  
Internal Tide ◽  
Bottom Layer ◽  
Tidal Energy ◽  
Internal Tides ◽  
Nonlinear Flow ◽  
Wave Radiation ◽  
Hydraulic Control

AbstractA simple analytical model for tidal energy loss at fjord sills and its partitioning into local dissipation and radiated internal tides is presented. The analytical model builds on a two-layer assumption with quasi-steady nonlinear flow over the sill and wave radiation in the far field. When the interface is situated above sill level, upstream- and downstream-propagating internal waves are generated as the bottom-layer flow becomes partially blocked because of a hydraulic control over the sill. When this control sets in, energy is lost in the transition from supercritical flow over the sill to subcritical flow downstream of the sill. The analytical model is compared with observations at the Drøbak sill in the Oslo Fjord and with idealized numerical simulations with a nonhydrostatic primitive equation model. The overall good agreement between observations, analytical model, and numerical model results indicates that the hydraulic control over the sill is a key player for both the generation of internal tides and the local energy loss. The tidal energy loss decreases with increasing height of the interface above the sill. At the same time, the fraction of energy dissipated locally increases from about 20% for the interface situated at sill level to >50% when the upper-layer thickness is less than about 80% of the sill depth. These results correspond well with the observations in the Oslo Fjord where more energy is dissipated near the sill than is radiated away.

scholarly journals The Influence of Subinertial Internal Tides on Near-Topographic Turbulence at the Mendocino Ridge: Observations and Modeling

2017 ◽  
Vol 47 (8) ◽  
pp. 2139-2154 ◽  
Author(s):  
R. C. Musgrave ◽  
J. A. MacKinnon ◽  
R. Pinkel ◽  
A. F. Waterhouse ◽  
J. Nash ◽  
...  
Keyword(s):  
Tidal Flow ◽  
Internal Tide ◽  
Tidal Energy ◽  
Internal Tides ◽  
Trapped Waves ◽  
Tidal Constituent ◽  
Barotropic Tide ◽  
Small Channel ◽  
Lee Wave ◽  
Confined Flows

AbstractShipboard measurements of velocity and density were obtained in the vicinity of a small channel in the Mendocino Ridge, where flows were predominantly tidal. Measured daily inequalities in transport are much greater than those predicted by a barotropic tide model, with the strongest transport associated with full depth flows and the weakest with shallow, surface-confined flows. A regional numerical model of the area finds that the subinertial K1 (diurnal) tidal constituent generates topographically trapped waves that propagate anticyclonically around the ridge and are associated with enhanced near-topographic K1 transports. The interaction of the baroclinic trapped waves with the surface tide produces a tidal flow whose northward transports alternate between being surface confined and full depth. Full depth flows are associated with the generation of a large-amplitude tidal lee wave on the northward face of the ridge, while surface-confined flows are largely nonturbulent. The regional model demonstrates that, consistent with field observations, near-topographic dissipation over the entire ridge is diurnally modulated, despite the semidiurnal tidal constituent having larger barotropic velocities. It is concluded that at this location it is the bottom-trapped subinertial internal tide that governs near-topographic dissipation and mixing. The effect of the trapped wave on regional energetics is to increase the fraction of converted barotropic–baroclinic tidal energy that dissipates locally.

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