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 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 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 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.

Energetics of Barotropic and Baroclinic Tides in the Monterey Bay Area

2012 ◽  
Vol 42 (2) ◽  
pp. 272-290 ◽  
Author(s):  
Dujuan Kang ◽  
Oliver Fringer
Keyword(s):  
Energy Flux ◽  
Three Dimensional ◽  
Internal Tide ◽  
Submarine Canyon ◽  
Tidal Energy ◽  
Energy Partitioning ◽  
Navier Stokes ◽  
Monterey Bay ◽  
Topographic Features ◽  
Bay Area

Abstract A detailed energy analysis of the barotropic and baroclinic M2 tides in the Monterey Bay area is performed. The authors first derive a theoretical framework for analyzing internal tide energetics based on the complete form of the barotropic and baroclinic energy equations, which include the full nonlinear and nonhydrostatic energy flux contributions as well as an improved evaluation of the available potential energy. This approach is implemented in the Stanford Unstructured Nonhydrostatic Terrain-Following Adaptive Navier–Stokes Simulator (SUNTANS). Results from three-dimensional, high-resolution SUNTANS simulations are analyzed to estimate the tidal energy partitioning among generation, radiation, and dissipation. A 200 km × 230 km domain including all typical topographic features in this region is used to represent the Monterey Bay area. Of the 152-MW energy lost from the barotropic tide, approximately 133 MW (88%) is converted into baroclinic energy through internal tide generation, and 42% (56 MW) of this baroclinic energy radiates away into the open ocean. The tidal energy partitioning depends greatly on the topographic features. The Davidson Seamount is most efficient at baroclinic energy generation and radiation, whereas the Monterey Submarine Canyon acts as an energy sink. Energy flux contributions from nonlinear and nonhydrostatic effects are also examined. In the Monterey Bay area, the nonlinear and nonhydrostatic contributions are quite small. Moreover, the authors investigate the character of internal tide generation and find that in the Monterey Bay area the generated baroclinic tides are mainly linear and in the form of internal tidal beams. Comparison of the modeled tidal conversion to previous theoretical estimates shows that they are consistent with one another.

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.

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 Model Estimates of M2 Internal Tide Generation over Mid-Atlantic Ridge Topography

2009 ◽  
Vol 39 (10) ◽  
pp. 2635-2651 ◽  
Author(s):  
N. V. Zilberman ◽  
J. M. Becker ◽  
M. A. Merrifield ◽  
G. S. Carter
Keyword(s):  
Internal Tide ◽  
Tidal Energy ◽  
Ocean Model ◽  
Equation Model ◽  
Internal Tides ◽  
Analytical Models ◽  
Topographic Slope ◽  
Conversion Rates ◽  
Mid Atlantic Ridge ◽  
Model Conversion

Abstract The conversion of barotropic to baroclinic M2 tidal energy is examined for a section of the Mid-Atlantic Ridge in the Brazil Basin using a primitive equation model. Model runs are made with different horizontal smoothing (1.5, 6, and 15 km) applied to a 192 km × 183 km section of multibeam bathymetry to characterize the influence of topographic resolution on the model conversion rates. In all model simulations, barotropic to baroclinic conversion is highest over near- and supercritical slopes on the flanks of abyssal hills and discordant zones. From these generation sites, internal tides propagate upward and downward as tidal beams. The most energetic internal tide mode generated is mode 2, consistent with the dominant length scales of the topographic slope spectrum (50 km). The topographic smoothing significantly affects the model conversion amplitudes, with the domain-averaged conversion rate from the 1.5-km run (15.1 mW m−2) 4% and 19% higher than for the 6-km (14.5 mW m−2) and 15-km runs (12.2 mW m−2), respectively. Analytical models for internal tide generation by subcritical topography predict conversion rates with modal dependence and spatial patterns qualitatively similar to the Princeton Ocean Model (POM) and also show a decrease in conversion with smoother topography. The POM conversion rates are approximately 20% higher than the analytical estimates for all model grids, which is attributed to spatial variations in the barotropic flow and near-bottom stratification over generation sites, which are incorporated in the model but not in the analytical estimates.

scholarly journals Interference Pattern and Propagation of the M2 Internal Tide South of the Hawaiian Ridge

2010 ◽  
Vol 40 (2) ◽  
pp. 311-325 ◽  
Author(s):  
Luc Rainville ◽  
T. M. Shaun Johnston ◽  
Glenn S. Carter ◽  
Mark A. Merrifield ◽  
Robert Pinkel ◽  
...  
Keyword(s):  
Interference Pattern ◽  
Satellite Altimetry ◽  
Internal Tide ◽  
Equation Model ◽  
Internal Tides ◽  
Multiple Sources ◽  
Propagating Waves ◽  
Generation Region ◽  
Hawaiian Ridge ◽  
Energy Flux Density

Abstract Most of the M2 internal tide energy generated at the Hawaiian Ridge radiates away in modes 1 and 2, but direct observation of these propagating waves is complicated by the complexity of the bathymetry at the generation region and by the presence of interference patterns. Observations from satellite altimetry, a tomographic array, and the R/P FLIP taken during the Farfield Program of the Hawaiian Ocean Mixing Experiment (HOME) are found to be in good agreement with the output of a high-resolution primitive equation model, simulating the generation and propagation of internal tides. The model shows that different modes are generated with different amplitudes along complex topography. Multiple sources produce internal tides that sum constructively and destructively as they propagate. The major generation sites can be identified using a simplified 2D idealized knife-edge ridge model. Four line sources located on the Hawaiian Ridge reproduce the interference pattern of sea surface height and energy flux density fields from the numerical model for modes 1 and 2. Waves from multiple sources and their interference pattern have to be taken into account to correctly interpret in situ observations and satellite altimetry.

Scattering of internal tide energy to super-tidal frequencies in global HYCOM 

2021 ◽  
Author(s):  
Miguel Solano ◽  
Maarten Buijsman
Keyword(s):  
Internal Tide ◽  
Tidal Energy ◽  
Horizontal Resolution ◽  
Internal Tides ◽  
Numerical Dispersion ◽  
Global Ocean ◽  
Wave Interactions ◽  
Continental Shelves ◽  
Lee Wave ◽  
Ocean Models

<p>Energy decay in realistically forced global ocean models has been mostly studied in the diurnal and semi-diurnal tidal bands and it is unclear how much of the tidal energy in these bands is scattered to higher frequencies. Global ocean models and satellite altimetry have shown that low-mode internal tides can propagate thousands of kilometers from their generation sites before being dissipated in the ocean interior but their pathway to dissipation is obscured due to lee-wave breaking at generation, wave-wave interactions, topographic scattering, shearing instabilities and shoaling on continental shelves. Internal tides from some generation sites, such as the Amazon shelf and the Nicobar and Andaman island chain, have large amounts of energy resulting in a steepening of the internal waves into solitary wave trains due to non-hydrostatic dispersion. In HYCOM, a hydrostatic model, this process is partially simulated by numerical dispersion. However, it is yet unknown how the dissipation of internal tides is affected by the numerical dispersion in hydrostatic models. In this study we use the method of vertical modes and rotary spectra to quantify the scattering of internal tides to higher-frequencies and analyze the dissipation processes in global HYCOM simulations with 4-km horizontal resolution.</p>

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.

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