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 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 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 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).

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.

Dissipating and reflecting internal waves

2021 ◽  
Author(s):  
Callum J. Shakespeare ◽  
Brian K. Arbic ◽  
Andrew McC. Hogg
Keyword(s):  
Numerical Simulations ◽  
Linear Theory ◽  
Internal Waves ◽  
Energy Flux ◽  
Internal Tide ◽  
Internal Tides ◽  
Linear Wave ◽  
Lee Waves ◽  
Lee Wave ◽  
Upper Boundary

AbstractInternal waves generated at the seafloor propagate through the interior of the ocean, driving mixing where they break and dissipate. However, existing theories only describe these waves in two limiting cases. In one limit, the presence of an upper boundary permits bottom-generated waves to reflect from the ocean surface back to the seafloor, and all the energy flux is at discrete wavenumbers corresponding to resonant modes. In the other limit, waves are strongly dissipated such that they do not interact with the upper boundary and the energy flux is continuous over wavenumber. Here, a novel linear theory is developed for internal tides and lee waves that spans the parameter space in between these two limits. The linear theory is compared with a set of numerical simulations of internal tide and lee wave generation at realistic abyssal hill topography. The linear theory is able to replicate the spatially-averaged kinetic energy and dissipation of even highly non-linear wave fields in the numerical simulations via an appropriate choice of the linear dissipation operator, which represents turbulent wave breaking processes.

scholarly journals Global Observations of Open-Ocean Mode-1 M2 Internal Tides

2016 ◽  
Vol 46 (6) ◽  
pp. 1657-1684 ◽  
Author(s):  
Zhongxiang Zhao ◽  
Matthew H. Alford ◽  
James B. Girton ◽  
Luc Rainville ◽  
Harper L. Simmons
Keyword(s):  
Energy Loss ◽  
Internal Tide ◽  
Field Measurements ◽  
Open Ocean ◽  
Internal Tides ◽  
Global Integration ◽  
Tidal Waves ◽  
Topographic Features ◽  
Midocean Ridges ◽  
The Pacific

AbstractA global map of open-ocean mode-1 M2 internal tides is constructed using sea surface height (SSH) measurements from multiple satellite altimeters during 1992–2012, representing a 20-yr coherent internal tide field. A two-dimensional plane wave fit method is employed to 1) suppress mesoscale contamination by extracting internal tides with both spatial and temporal coherence and 2) separately resolve multiple internal tidal waves. Global maps of amplitude, phase, energy, and flux of mode-1 M2 internal tides are presented. The M2 internal tides are mainly generated over topographic features, including continental slopes, midocean ridges, and seamounts. Internal tidal beams of 100–300 km width are observed to propagate hundreds to thousands of kilometers. Multiwave interference of some degree is widespread because of the M2 internal tide’s numerous generation sites and long-range propagation. The M2 internal tide propagates across the critical latitudes for parametric subharmonic instability (28.8°S/N) with little energy loss, consistent with the 2006 Internal Waves across the Pacific (IWAP) field measurements. In the eastern Pacific Ocean, the M2 internal tide loses significant energy in propagating across the equator; in contrast, little energy loss is observed in the equatorial zones of the Atlantic, Indian, and western Pacific Oceans. Global integration of the satellite observations yields a total energy of 36 PJ (1 PJ = 1015 J) for all the coherent mode-1 M2 internal tides. Finally, satellite observed M2 internal tides compare favorably with field mooring measurements and a global eddy-resolving numerical model.

Internal tide generation due to topographically adjusted barotropic tide

2021 ◽  
Author(s):  
Christos Papoutsellis ◽  
Matthieu Mercier ◽  
Nicolas Grisouard
Keyword(s):  
Energy Flux ◽  
Internal Tide ◽  
Boussinesq Approximation ◽  
Internal Tides ◽  
Field Energy ◽  
Barotropic Tide ◽  
Good Convergence ◽  
Ambient Flow ◽  
Wide Range ◽  
Variable Topography

<p>We model internal tides generated by the interaction of a barotropic tide with variable topography. For the barotropic part, an asymptotic solution valid over the variable topography is considered. The resulting non-uniform ambient flow is used as a prescribed barotropic forcing for the baroclinic equations (linearized, non-hydrostatic, Euler equations within the Boussinesq approximation).</p><p>The internal-tide generation problem is reformulated by means of a Coupled-Mode System (CMS) based on the decomposition of the baroclinic stream function in terms of vertical basis functions that consistently satisfy the bottom boundary condition. The proposed CMS is solved numerically with a finite difference scheme and shows good convergence properties, providing efficient calculations of internal tides due to 2D topographies of arbitrary height and slope. We consider several seamounts and shelf profiles and perform calculations for a wide range of heights and slopes. Our results are compared against existing analytical estimates on the far-field energy flux in order to examine the limit of validity of common simplifications (Weak Topography Approximation, Knife edge). For subcritical cases, local extrema of the energy flux exist for different heights. Non-radiating topographies are also identified for some profiles of large enough heights. For supercritical cases, the energy flux is in general an increasing function with increasing height and criticality, and does not compare well against analytical results for very steep idealized topographies. The effect of the adjusted barotropic tide in the energy flux and the local properties of the baroclinic field is investigated through comparisons with other semi-analytical methods based on a uniform barotropic tide (Green’s function approach).  A method for estimating the sea-surface signature of internal tides is also provided.</p>

SPLASH Free-Surface Flow Code Methodology for Hydrodynamic Design and Analysis of IACC Yachts

1993 ◽  
Author(s):  
Bruce S. Rosen ◽  
Joseph P. Laiosa ◽  
Warren H. Davis ◽  
David Stavetski
Keyword(s):  
Free Surface ◽  
High Performance ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Surface Boundary ◽  
Induced Drag ◽  
Free Surface Boundary Condition ◽  
Surface Boundary Condition ◽  
America’S Cup ◽  
Areas Of Interest

A unique free-surface flow methodology and its application to design and analysis of IACC yachts are discussed. Numerical aspects of the inviscid panel code and details of the free-surface boundary condition are included, along with enhancements developed specifically for the '92 America's Cup defense. Extensive code validation using wind tunnel and towing tank experimental data address several areas of interest to the yacht designer. Lift and induced drag at zero Froude number are studied via a series of isolated fin/bulb/winglet appendages. An isolated surface piercing foil is used to evaluate simple lift/free­surface interactions. For complete IACC yacht models, upright wave resistance is investigated, as well as lift and induced drag at heel and yaw. The excellent correlation obtained for these cases demonstrates the value of this linear free-surface methodology for use in designing high performance sailing yachts.

scholarly journals Investigation of Free Surface Damping Models With Applications to Gap Resonance Problems

2017 ◽  
Author(s):  
Kevin Markeng ◽  
Torgeir Vada ◽  
Zhi Yuan Pan
Keyword(s):  
Free Surface ◽  
Energy Dissipation ◽  
Resonance Problem ◽  
Surface Boundary ◽  
Flow Solver ◽  
3 Dimensional ◽  
Energy Devices ◽  
Dissipation Term ◽  
Free Surface Boundary Condition ◽  
Damping Model

In this paper two methods for modelling the damping in a narrow gap are investigated. The first method is called the Pressure Damping Model. This method has been used in studies of wave energy devices. An attractive feature of this model is that the modified input is directly related to the energy dissipation in the gap, which means that if this dissipation is estimated the input to the model can be obtained directly. The idea of the method is to add a pressure input in the gap to suppress the resonant motion. A challenge with the method is that it contains a non-linear term. The second method is the Newtonian Cooling damping model. The method is based on introducing a dissipation term in the free surface boundary condition. This dissipation term contains a coefficient which is not directly related to the energy dissipation. Hence this method is not so easy to relate directly to the estimated energy dissipation. An advantage with this method is that it is linear and hence can be expected to be more robust. In the first part of the paper a 2-dimensional problem is investigated using both methods. In addition to the numerical performance and robustness, much focus is put on investigation of the energy balance in the solution, and we attempt to relate both models to the energy dissipation in the gap. In the second part the Newtonian cooling method is implemented in a 3-dimensional potential flow solver and it is shown that the method provides a robust way to handle the resonance problem. The method will give rise to a modified set of equations which are described. Two different problems are investigated with the 3D solver. First we look at a side-by-side problem, where the 3D results are also compared with 2D results. Finally, the moonpool problem is investigated by two different 3D solvers, a classical Green’s function based method and a Rankine solver. It is also shown how this damping model can be combined with a similar model on the internal waterplane to remove irregular frequencies.

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