scholarly journals A Coupled Model for Laplace's Tidal Equations in a Fluid with One Horizontal Dimension and Variable Depth

2013 ◽  
Vol 43 (8) ◽  
pp. 1780-1797 ◽  
Author(s):  
Samuel M. Kelly ◽  
Nicole L. Jones ◽  
Jonathan D. Nash
Keyword(s):  
Energy Flux ◽  
Internal Tide ◽  
Surface Displacement ◽  
Tidal Energy ◽  
Internal Tides ◽  
Energy Fluxes ◽  
Flux Divergence ◽  
Flat Bottom ◽  
Horizontal Dimension ◽  
Continental Slopes

Abstract Tide–topography interactions dominate the transfer of tidal energy from large to small scales. At present, it is poorly understood how low-mode internal tides reflect and scatter along the continental margins. Here, the coupling equations for linear tides model (CELT) are derived to determine the independent modal solutions to Laplace's Tidal Equations (LTE) over stepwise topography in one horizontal dimension. CELT is (i) applicable to arbitrary one-dimensional topography and realistic stratification without requiring numerically expensive simulations and (ii) formulated to quantify scattering because it implicitly separates incident and reflected waves. Energy fluxes and horizontal velocities obtained using CELT are shown to converge to analytical solutions, indicating that “flat bottom” modes, which evolve according to LTE, are also relevant in describing tides over sloping topography. The theoretical framework presented can then be used to quantify simultaneous incident and reflected energy fluxes in numerical simulations and observations of tidal flows that vary in one horizontal dimension. Thus, CELT can be used to diagnose internal-tide scattering on continental slopes. Here, semidiurnal mode-1 scattering is simulated on the Australian northwest, Brazil, and Oregon continental slopes. Energy-flux divergence and directional energy fluxes computed using CELT are shown to agree with results from a finite-volume model that is significantly more numerically expensive. Last, CELT is used to examine the dynamics of two-way surface–internal-tide coupling. Semidiurnal mode-1 internal tides are found to transmit about 5% of their incident energy flux to the surface tide where they impact the continental slope. It is hypothesized that this feedback may decrease the coherence of sea surface displacement on continental shelves.

scholarly journals Energy Fluxes due to the Surface and Internal Tides in Knight Inlet, British Columbia

2005 ◽  
Vol 35 (11) ◽  
pp. 2219-2227 ◽  
Author(s):  
Michael W. Stacey ◽  
S. Pond
Keyword(s):  
Energy Flux ◽  
Linear Models ◽  
Internal Tide ◽  
Acoustic Doppler Current Profiler ◽  
Tidal Energy ◽  
Tidal Height ◽  
Internal Tides ◽  
Energy Fluxes ◽  
Net Flux ◽  
Adcp Observations

Abstract A laterally integrated (two dimensional) nonlinear numerical model is used to examine the flux of M2 tidal energy in Knight Inlet. The simulated flux of tidal energy into the inlet is somewhat smaller than that estimated using the change in phase of the M2 tidal height along the inlet, a method that does not account for the effect of the internal tide on the surface elevation. The simulated energy flux into the inlet is close to the energy flux of the internal tide away from the sill determined from observations using an acoustic Doppler current profiler (ADCP). The net flux due to the internal tide is significantly less than (<1/2 of) the rate at which energy is removed from the surface tide. Earlier linear models of the internal tide produced energy fluxes that agreed with those estimated from the phase change of the tidal height but were larger than the fluxes that could be found in the observations. The reason for this discrepancy is not that these simple models neglected nonlinear effects, but rather that they did not take reflections of the internal tide into account. Also, the simulated flux of energy into the inlet less the net flux of internal tidal energy away from the sill is about equal to the simulated dissipation within 2 km on either side of the sill. The simulated net flux of internal tidal energy away from the sill is in agreement with the flux determined from the ADCP observations on the downinlet side of the sill, but not on the upinlet side of the sill. A possible explanation is that only the first internal mode (which is surface intensified) was important on the downinlet side but the first three internal modes were important on the upinlet side. The flux calculation using the ADCP observations took variations in the inlet width into account but did not take depth variations into account; thus, the reflection coefficients of the second and third modes may have been underestimated.

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.

scholarly journals Internal tides and energy fluxes over Great Meteor Seamount

Ocean Science ◽  
2007 ◽  
Vol 3 (3) ◽  
pp. 441-449 ◽  
Author(s):  
T. Gerkema ◽  
H. van Haren
Keyword(s):  
Water Column ◽  
Energy Flux ◽  
Internal Tide ◽  
Internal Tides ◽  
Generation Model ◽  
Southern Slope ◽  
Energy Fluxes ◽  
Using Data ◽  
Great Meteor Seamount ◽  
Whole Water

Abstract. Internal-tide energy fluxes are determined halfway over the southern slope of Great Meteor Seamount (Canary Basin), using data from combined CTD/LADCP yoyoing, covering the whole water column. The strongest signal is semi-diurnal and is concentrated in the upper few hundred meters of the water column. An indeterminacy in energy flux profiles is discussed; it is argued that a commonly applied condition used to determine these profiles is in fact invalid over sloping bottoms. However, the vertically integrated flux can be established unambiguously; the observed results are compared with the outcome of a numerical internal-tide generation model. For the semi-diurnal internal tide, the vertically integrated flux found in the model corresponds well to the observed one. The observed diurnal signal appears to be largely of non-tidal origin.

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.

Observations of Internal Tides on the Oregon Continental Slope

2011 ◽  
Vol 41 (9) ◽  
pp. 1772-1794 ◽  
Author(s):  
Kim I. Martini ◽  
Matthew H. Alford ◽  
Eric Kunze ◽  
Samuel M. Kelly ◽  
Jonathan D. Nash
Keyword(s):  
Continental Slope ◽  
Energy Flux ◽  
Large Scale ◽  
Spring Tide ◽  
Internal Tide ◽  
Internal Tides ◽  
Energy Fluxes ◽  
Multiple Sources ◽  
Spatial And Temporal Patterns ◽  
Three Dimensional Model

Abstract A complex superposition of locally forced and shoaling remotely generated semidiurnal internal tides occurs on the Oregon continental slope. Presented here are observations from a zonal line of five profiling moorings deployed across the continental slope from 500 to 3000 m, a 24-h expendable current profiler (XCP) survey, and five 15–48-h lowered ADCP (LADCP)/CTD stations. The 40-day moored deployment spans three spring and two neap tides, during which the proportions of the locally and remotely forced internal tides vary. Baroclinic signals are strong throughout spring and neap tides, with 4–5-day-long bursts of strong cross-slope baroclinic semidiurnal velocity and vertical displacement . Energy fluxes exhibit complex spatial and temporal patterns throughout both tidal periods. During spring tides, local barotropic forcing is strongest and energy flux over the slope is predominantly offshore (westward). During neap tides, shoaling remotely generated internal tides dominate and energy flux is predominantly onshore (eastward). Shoaling internal tides do not exhibit a strong spring–neap cycle and are also observed during the first spring tide, indicating that they originate from multiple sources. The bulk of the remotely generated internal tide is hypothesized to be generated from south of the array (e.g., Mendocino Escarpment), because energy fluxes at the deep mooring 100 km offshore are always directed northward. However, fluxes on the slope suggest that the northbound internal tide is turned onshore, most likely by reflection from large-scale bathymetry. This is verified with a simple three-dimensional model of mode-1 internal tides propagating obliquely onto a near-critical slope, whose output conforms fairly well to observations, in spite of its simplicity.

scholarly journals Internal tides and energy fluxes over Great Meteor Seamount

2007 ◽  
Vol 4 (2) ◽  
pp. 371-398 ◽  
Author(s):  
T. Gerkema ◽  
H. van Haren
Keyword(s):  
Water Column ◽  
Energy Flux ◽  
Internal Tide ◽  
Internal Tides ◽  
Generation Model ◽  
Southern Slope ◽  
Energy Fluxes ◽  
Using Data ◽  
Great Meteor Seamount ◽  
Whole Water

Abstract. Internal-tide energy fluxes are determined halfway over the southern slope of Great Meteor Seamount (Canary Basin), using data from combined CTD/LADCP yoyoing, covering the whole water column. The strongest signal is semi-diurnal and is concentrated in the upper few hundred meters of the water column. An indeterminacy in energy flux profiles is discussed; it is argued that a commonly applied condition used to uniquely determine these profiles does in fact not apply over sloping bottoms. However, the vertically integrated flux can be established unambiguously. The observed results are compared to the outcome of a numerical internal-tide generation model. For the semi-diurnal internal tide, the vertically integrated flux found in the model corresponds well to the observed one. For the diurnal tide, however, the former is much smaller; this points to non-tidal origins of the diurnal signal, which is indeed to be expected at this latitude (30°), where near-inertial and diurnal periods coincide.

Observations of the Tasman Sea Internal Tide Beam

2018 ◽  
Vol 48 (6) ◽  
pp. 1283-1297 ◽  
Author(s):  
Amy F. Waterhouse ◽  
Samuel M. Kelly ◽  
Zhongxiang Zhao ◽  
Jennifer A. MacKinnon ◽  
Jonathan D. Nash ◽  
...  
Keyword(s):  
Plane Wave ◽  
Energy Flux ◽  
Internal Tide ◽  
Surface Displacement ◽  
Internal Tides ◽  
Near Surface ◽  
Tasman Sea ◽  
Stationary Energy ◽  
In Situ Observations

AbstractLow-mode internal tides, a dominant part of the internal wave spectrum, carry energy over large distances, yet the ultimate fate of this energy is unknown. Internal tides in the Tasman Sea are generated at Macquarie Ridge, south of New Zealand, and propagate northwest as a focused beam before impinging on the Tasmanian continental slope. In situ observations from the Tasman Sea capture synoptic measurements of the incident semidiurnal mode-1 internal-tide, which has an observed wavelength of 183 km and surface displacement of approximately 1 cm. Plane-wave fits to in situ and altimetric estimates of surface displacement agree to within a measurement uncertainty of 0.3 cm, which is the same order of magnitude as the nonstationary (not phase locked) mode-1 tide observed over a 40-day mooring deployment. Stationary energy flux, estimated from a plane-wave fit to the in situ observations, is directed toward Tasmania with a magnitude of 3.4 ± 1.4 kW m−1, consistent with a satellite estimate of 3.9 ± 2.2 kW m−1. Approximately 90% of the time-mean energy flux is due to the stationary tide. However, nonstationary velocity and pressure, which are typically 1/4 the amplitude of the stationary components, sometimes lead to instantaneous energy fluxes that are double or half of the stationary energy flux, overwhelming any spring–neap variability. Despite strong winds and intermittent near-inertial currents, the parameterized turbulent-kinetic-energy dissipation rate is small (i.e., 10−10 W kg−1) below the near surface and observations of mode-1 internal tide energy-flux convergence are indistinguishable from zero (i.e., the confidence intervals include zero), indicating little decay of the mode-1 internal tide within the Tasman Sea.

Energy Flux and Dissipation in Luzon Strait: Two Tales of Two Ridges

2011 ◽  
Vol 41 (11) ◽  
pp. 2211-2222 ◽  
Author(s):  
Matthew H. Alford ◽  
Jennifer A. MacKinnon ◽  
Jonathan D. Nash ◽  
Harper Simmons ◽  
Andy Pickering ◽  
...  
Keyword(s):  
Energy Flux ◽  
Spring Tide ◽  
Internal Tide ◽  
Wave Pattern ◽  
The Philippines ◽  
Luzon Strait ◽  
Net Energy ◽  
Energy Fluxes ◽  
Flux Divergence ◽  
Turbulent Dissipation

Abstract Internal tide generation, propagation, and dissipation are investigated in Luzon Strait, a system of two quasi-parallel ridges situated between Taiwan and the Philippines. Two profiling moorings deployed for about 20 days and a set of nineteen 36-h lowered ADCP–CTD time series stations allowed separate measurement of diurnal and semidiurnal internal tide signals. Measurements were concentrated on a northern line, where the ridge spacing was approximately equal to the mode-1 wavelength for semidiurnal motions, and a southern line, where the spacing was approximately two-thirds that. The authors contrast the two sites to emphasize the potential importance of resonance between generation sites. Throughout Luzon Strait, baroclinic energy, energy fluxes, and turbulent dissipation were some of the strongest ever measured. Peak-to-peak baroclinic velocity and vertical displacements often exceeded 2 m s−1 and 300 m, respectively. Energy fluxes exceeding 60 kW m−1 were measured at spring tide at the western end of the southern line. On the northern line, where the western ridge generates appreciable eastward-moving signals, net energy flux between the ridges was much smaller, exhibiting a nearly standing wave pattern. Overturns tens to hundreds of meters high were observed at almost all stations. Associated dissipation was elevated in the bottom 500–1000 m but was strongest by far atop the western ridge on the northern line, where >500-m overturns resulted in dissipation exceeding 2 × 10−6 W kg−1 (implying diapycnal diffusivity Kρ > 0.2 m2 s−1). Integrated dissipation at this location is comparable to conversion and flux divergence terms in the energy budget. The authors speculate that resonance between the two ridges may partly explain the energetic motions and heightened dissipation.

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>

The Cascade of Tidal Energy from Low to High Modes on a Continental Slope

2012 ◽  
Vol 42 (7) ◽  
pp. 1217-1232 ◽  
Author(s):  
Samuel M. Kelly ◽  
Jonathan D. Nash ◽  
Kim I. Martini ◽  
Matthew H. Alford ◽  
Eric Kunze
Keyword(s):  
Continental Slope ◽  
Internal Tide ◽  
Tidal Energy ◽  
Internal Tides ◽  
Local Surface ◽  
Tidal Dynamics ◽  
Flat Bottom ◽  
Tidally Driven ◽  
Energy Balances

Abstract The linear transfer of tidal energy from large to small scales is quantified for small tidal excursion over a near-critical continental slope. A theoretical framework for low-wavenumber energy transfer is derived from “flat bottom” vertical modes and evaluated with observations from the Oregon continental slope. To better understand the observations, local tidal dynamics are modeled with a superposition of two idealized numerical simulations, one forced by local surface-tide velocities and the other by an obliquely incident internal tide generated at the Mendocino Escarpment 315 km southwest of the study site. The simulations reproduce many aspects of the observed internal tide and verify the modal-energy balances. Observed transfer of tidal energy into high-mode internal tides is quantitatively consistent with observed turbulent kinetic energy (TKE) dissipation. Locally generated and incident simulated internal tides are superposed with varying phase shifts to mimic the effects of the temporally varying mesoscale. Altering the phase of the incident internal tide alters (i) internal-tide energy flux, (ii) internal-tide generation, and (iii) energy conversion to high modes, suggesting that tidally driven TKE dissipation may vary between 0 and 500 watts per meter of coastline on 3–5-day time scales. Comparison of observed in situ internal-tide generation and satellite-derived estimates of surface-tide energy loss is inconclusive.

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