scholarly journals On the Body-Force Term in Internal-Tide Generation

2007 ◽  
Vol 37 (8) ◽  
pp. 2172-2175 ◽  
Author(s):  
Chris Garrett ◽  
Theo Gerkema
Keyword(s):  
Governing Equation ◽  
Body Force ◽  
Internal Tide ◽  
The Body ◽  
Internal Tides ◽  
Force Term ◽  
Barotropic Tide ◽  
Topographic Features ◽  
Barotropic Flow ◽  
Baroclinic Tide

Abstract The generation of internal tides can be ascribed to the action of a buoyancy force caused by the flow of the barotropic tide over topographic features. It is commonly assumed that the barotropic flow can be taken as hydrostatic, but it is shown here that this leads to a linearized governing equation for the baroclinic tide that is only valid if the baroclinic tide is also hydrostatic. A governing equation for the baroclinic tide, valid for any situation, is derived here and is shown to be exactly equivalent to a simple transformation of the governing equation for the combined barotropic and baroclinic tides.

scholarly journals The Drag on the Barotropic Tide due to the Generation of Baroclinic Motion

2020 ◽  
Vol 50 (12) ◽  
pp. 3467-3481 ◽  
Author(s):  
Callum J. Shakespeare ◽  
Brian K. Arbic ◽  
Andrew McC. Hogg
Keyword(s):  
Wave Motion ◽  
Body Force ◽  
Wave Drag ◽  
Internal Tides ◽  
Mean Flow ◽  
Barotropic Tide ◽  
Barotropic Flow ◽  
Spring Force ◽  
Mechanical Spring ◽  
The Impact

AbstractThe interaction of a barotropic flow with topography generates baroclinic motion that exerts a stress on the barotropic flow. Here, explicit solutions are calculated for the spatial-mean flow (i.e., the barotropic tide) resulting from a spatially uniform but time-varying body force (i.e., astronomical forcing) acting over rough topography. This approach of prescribing the force contrasts with that of previous authors who have prescribed the barotropic flow. It is found that the topographic stress, and thus the impact on the spatial-mean flow, depend on the nature of the baroclinic motion that is generated. Two types of stress are identified: (i) a “wave drag” force associated with propagating wave motion, which extracts energy from the spatial-mean flow, and (ii) a topographic “spring” force associated with standing motion at the seafloor, including bottom-trapped internal tides and propagating low-mode internal tides, which significantly damps the time-mean kinetic energy of the spatial-mean flow but extracts no energy in the time-mean. The topographic spring force is shown to be analogous to the force exerted by a mechanical spring in a forced-dissipative harmonic oscillator. Expressions for the topographic stresses appropriate for implementation as baroclinic drag parameterizations in global models are presented.

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

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.

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>

scholarly journals Altimeter and Current Meter Observations of Internal Tides: Do They Agree?

2006 ◽  
Vol 36 (9) ◽  
pp. 1860-1872 ◽  
Author(s):  
Stephen M. Chiswell
Keyword(s):  
Internal Tide ◽  
Internal Tides ◽  
Energy Estimates ◽  
Negligible Probability ◽  
High Vertical Resolution ◽  
Baroclinic Tide ◽  
Ocean Topography ◽  
Low Amplitude ◽  
A Current

Abstract Baroclinic tides can be observed both remotely from the Ocean Topography Experiment (TOPEX)/Poseidon (T/P) altimeter and in situ using current meters. However, it is rare that current meter moorings have high vertical resolution and are located under T/P ground tracks so that a direct comparison can be made between the two methods of observations. Here, data from a current meter mooring directly under a T/P ground track off the Bounty Plateau, New Zealand, are used to obtain energy estimates of the first baroclinic mode. These estimates are compared with those calculated from the T/P surface elevation. The two methods return estimates of the internal tide that are in agreement in phase and direction but have about a factor-of-2 difference in amplitude (and a factor-of-4 difference in energy); the flux estimates are 787 and 170 W m−1, respectively. Uncertainties in these estimates are relatively large, and there is a low but not negligible probability that the differences are entirely due to measurement error. However, there are other reasons that might explain the differences in the estimates. It may be that the baroclinic tide is highly modulated in time and the current meters were deployed during a period of relatively low amplitude.

scholarly journals The Unpredictable Nature of Internal Tides on Continental Shelves

2012 ◽  
Vol 42 (11) ◽  
pp. 1981-2000 ◽  
Author(s):  
Jonathan D. Nash ◽  
Samuel M. Kelly ◽  
Emily L. Shroyer ◽  
James N. Moum ◽  
Timothy F. Duda
Keyword(s):  
Neap Tide ◽  
Spring Tide ◽  
Internal Tide ◽  
Open Ocean ◽  
Shelf Break ◽  
Internal Tides ◽  
Barotropic Tide ◽  
Continental Shelves ◽  
The Waves ◽  
Counterintuitive Result

Abstract Packets of nonlinear internal waves (NLIWs) in a small area of the Mid-Atlantic Bight were 10 times more energetic during a local neap tide than during the preceding spring tide. This counterintuitive result cannot be explained if the waves are generated near the shelf break by the local barotropic tide since changes in shelfbreak stratification explain only a small fraction of the variability in barotropic to baroclinic conversion. Instead, this study suggests that the occurrence of strong NLIWs was caused by the shoaling of distantly generated internal tides with amplitudes that are uncorrelated with the local spring-neap cycle. An extensive set of moored observations show that NLIWs are correlated with the internal tide but uncorrelated with barotropic tide. Using harmonic analysis of a 40-day record, this study associates steady-phase motions at the shelf break with waves generated by the local barotropic tide and variable-phase motions with the shoaling of distantly generated internal tides. The dual sources of internal tide energy (local or remote) mean that shelf internal tides and NLIWs will be predictable with a local model only if the locally generated internal tides are significantly stronger than shoaling internal tides. Since the depth-integrated internal tide energy in the open ocean can greatly exceed that on the shelf, it is likely that shoaling internal tides control the energetics on shelves that are directly exposed to the open ocean.

scholarly journals The Effects of Remote Internal Tides on Continental Slope Internal Tide Generation

2019 ◽  
Vol 49 (6) ◽  
pp. 1651-1668 ◽  
Author(s):  
Yankun Gong ◽  
Matthew D. Rayson ◽  
Nicole L. Jones ◽  
Gregory N. Ivey
Keyword(s):  
Energy Conversion ◽  
Phase Difference ◽  
Principal Direction ◽  
Internal Tide ◽  
Internal Tides ◽  
Global Ocean ◽  
Nonlinear Dependence ◽  
Linear Wave ◽  
Barotropic Tide ◽  
Conversion Rates

AbstractInternal tide generation at sloping topography is nominally determined by the local slope geometry, density stratification, and tidal forcing. Recent global ocean models have revealed that remotely generated internal tides (RITs) can also influence locally generated internal tides (LITs). Field measurements with through-the-water column moorings on the southern portion of the Australian North West Shelf (NWS) suggested that RITs led to local regions with either positive or negative barotropic to baroclinic energy conversion. Three-dimensional numerical simulations were used to examine the role of RITs on local internal tide climatology on the inner slope and shelf portion of the NWS. The model demonstrated the principle remote generation site was the western portion of the offshore Exmouth Plateau. Extending the model domain to include this offshore plateau region increased the local net energy conversion on the inner shelf by 13.5% and on the slope by 8%. Simulations using an idealized 2D model configuration aligned along the principal direction of RIT propagation demonstrated that the sign and magnitude of the local energy conversion was dependent on the distance between the remote and local generation sites, the phase difference between the local barotropic tide and the RIT, and the amplitude of both the local barotropic tide and the RIT. For RITs with a low-wave Froude number (Fr < 0.05), where Fr is the ratio of the internal wave baroclinic velocity to the linear wave speed, the conversion rates were consistent with kinematic predictions based on the phase difference only. For stronger flows with Fr > 0.05, the conversion rates showed a nonlinear dependence on Fr.

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.

scholarly journals Homogenization in elastodynamics with force term depending on time

2000 ◽  
Vol 23 (10) ◽  
pp. 723-728
Author(s):  
Ping Wang
Keyword(s):  
Elastic Material ◽  
Body Force ◽  
Gas Bubbles ◽  
The Body ◽  
Force Term ◽  
Homogenization Problem ◽  
Approximating Sequence ◽  
Distributed Array

We extend the study on the homogenization problem for an elastic material containing a distributed array of gas bubbles to the case when the body force depends on time. By technically constructing an approximating sequence, we are able to show the convergence of semigroups and therefore prove the main result that such spongy material can be approximated by an elastic material without holes in the elastodynamics with the force term depending on time.

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.

Sign in / Sign up

Export Citation Format

Share Document