Interdependence of Internal Tide and Lee Wave Generation at Abyssal Hills: Global Calculations

2020 ◽  
Vol 50 (3) ◽  
pp. 655-677 ◽  
Author(s):  
Callum J. Shakespeare
Keyword(s):  
Energy Flux ◽  
Internal Tide ◽  
Mean Flow ◽  
Barotropic Tide ◽  
Geostrophic Flow ◽  
Midocean Ridges ◽  
Lee Waves ◽  
Wave Flux ◽  
Energy And Momentum ◽  
Abyssal Hills

AbstractThe generation of internal waves at abyssal hills has been proposed as an important source of bottom-intensified mixing and a sink of geostrophic momentum. Using the theory of Bell, previous authors have calculated either the generation of lee waves by geostrophic flow or the generation of the internal tide by the barotropic tide, but never both together. However, the Bell theory shows that the two are interdependent: that is, the presence of a barotropic tide modifies the generation of lee waves, and the presence of a geostrophic (time mean) flow modifies the generation of the internal tide. Here we extend the theory of Bell to incorporate multiple tidal constituents. Using this extended theory, we recalculate global wave fluxes of energy and momentum using the abyssal-hill spectra, model-derived abyssal ocean stratification and geostrophic flow estimates, and the TPX08 tidal velocities for the eight major constituents. The energy flux into lee waves is suppressed by 13%–19% as a result of the inclusion of tides. The generated wave flux is dominated by the principal lunar semidiurnal tide (M2), and its harmonics and combinations, with the strongest fluxes occurring along midocean ridges. The internal tide generation is strongly asymmetric because of Doppler shifting by the geostrophic abyssal flow, with 55%–63% of the wave energy flux (and stress) directed upstream, against the geostrophic flow. As a consequence, there is a net wave stress associated with generation of the internal tide that reaches magnitudes of 0.01–0.1 N m−2 in the vicinity of midocean ridges.

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 Baroclinic Energy Flux at the Hawaiian Ridge: Observations from the R/P FLIP

2006 ◽  
Vol 36 (6) ◽  
pp. 1104-1122 ◽  
Author(s):  
Luc Rainville ◽  
Robert Pinkel
Keyword(s):  
Internal Waves ◽  
Energy Flux ◽  
Neap Tide ◽  
Internal Tide ◽  
Field Site ◽  
Energy Fluxes ◽  
Barotropic Tide ◽  
Research Platform ◽  
Channel Beam ◽  
Made In

Abstract Estimates of baroclinic energy flux are made in the immediate “Nearfield” (September–October 2002) and 450 km offshore (“Farfield”; October–November 2001) of the Kaena Ridge, an active barotropic-to-baroclinic conversion site. The flux estimates are based on repeated profiles of velocity and density obtained from the Research Platform Floating Instrument Platform (FLIP) as an aspect of the Hawaii Ocean Mixing Experiment. Energetic beams associated with both semidiurnal and diurnal internal waves are observed in the Kauai Channel. Beam depths and orientations are consistent with generation along the upper flanks of the ridge. At the far-field site, the baroclinic energy flux is borne primarily by first-mode semidiurnal waves. The energy flux associated with the entire spectrum of internal waves is computed by cross-spectral analysis. Significant energy fluxes are found in the inertial, diurnal, semidiurnal, and twice-semidiurnal frequency bands. The semidiurnal energy flux strongly dominates the spectrum at both sites. The flux magnitude follows the spring–neap cycle of the semidiurnal barotropic tide. The averaged depth-integrated mode-1 semidiurnal energy flux (over the entire water column) in the Farfield is found to be 1.7 ± 0.3 kW m−1 away from the ridge, with peak values up to 4 kW m−1. Small fluxes toward the ridge are occasionally seen at neap tide. At both sites, energy fluxes in the diurnal frequency band represent 15%–20% of the semidiurnal energy flux. In the Farfield, the magnitude of the diurnal energy flux varies in accord with the fortnightly cycle of the barotropic semidiurnal tide, rather than with the diurnal forcing, suggesting that energy for those waves is supplied by a cross-frequency transfer from the low-vertical-mode M2 internal tide to higher-mode internal waves at frequencies ½M2. In the Nearfield, the diurnal flux varies with fluctuations in both diurnal and semidiurnal forcing.

scholarly journals Internal Tides and Mixing in a Submarine Canyon with Time-Varying Stratification

2012 ◽  
Vol 42 (12) ◽  
pp. 2121-2142 ◽  
Author(s):  
Zhongxiang Zhao ◽  
Matthew H. Alford ◽  
Ren-Chieh Lien ◽  
Michael C. Gregg ◽  
Glenn S. Carter
Keyword(s):  
Energy Flux ◽  
Spring Tide ◽  
Internal Tide ◽  
Submarine Canyon ◽  
Internal Tides ◽  
Time Variability ◽  
Thermocline Depth ◽  
Turbulent Dissipation ◽  
Submarine Ridge ◽  
Lee Waves

Abstract The time variability of the energetics and turbulent dissipation of internal tides in the upper Monterey Submarine Canyon (MSC) is examined with three moored profilers and five ADCP moorings spanning February–April 2009. Highly resolved time series of velocity, energy, and energy flux are all dominated by the semidiurnal internal tide and show pronounced spring-neap cycles. However, the onset of springtime upwelling winds significantly alters the stratification during the record, causing the thermocline depth to shoal from about 100 to 40 m. The time-variable stratification must be accounted for because it significantly affects the energy, energy flux, the vertical modal structures, and the energy distribution among the modes. The internal tide changes from a partly horizontally standing wave to a more freely propagating wave when the thermocline shoals, suggesting more reflection from up canyon early in the observational record. Turbulence, computed from Thorpe scales, is greatest in the bottom 50–150 m and shows a spring-neap cycle. Depth-integrated dissipation is 3 times greater toward the end of the record, reaching 60 mW m−2 during the last spring tide. Dissipation near a submarine ridge is strongly tidally modulated, reaching 10−5 W kg−1 (10–15-m overturns) during spring tide and appears to be due to breaking lee waves. However, the phasing of the breaking is also affected by the changing stratification, occurring when isopycnals are deflected downward early in the record and upward toward the end.

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.

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.

Analysis of Turbulence in the Tip Region of a Waterjet Pump Rotor

2010 ◽  
Author(s):  
Huixuan Wu ◽  
Rinaldo L. Miorini ◽  
Joseph Katz
Keyword(s):  
Energy Flux ◽  
Large Scale ◽  
Multiple Scales ◽  
Tip Clearance ◽  
Mean Flow ◽  
Production Characteristic ◽  
Pump Rotor ◽  
The Mean ◽  
Turbulence Production ◽  
Waterjet Pump

A series of high resolution planar particle image velocimetry measurements performed in a waterjet pump rotor reveal the inner structure of the tip leakage vortex (TLV) which dominates the entire flow field in the tip region. Turbulence generated by interactions among the TLV, the shear layer that develops as the backward leakage flow emerges from the tip clearance as a “wall jet”, the passage flow, and the endwall is highly inhomogeneous and anisotropic. We examine this turbulence in both RANS and LES modelling contexts. Spatially non-uniform distributions of Reynolds stress components are explained in terms of the local mean strain field and associated turbulence production. Characteristic length scales are also inferred from spectral analysis. Spatial filtering of instantaneous data enables the calculation of subgrid scale (SGS) stresses, along with the SGS energy flux (dissipation). The data show that the SGS energy flux differs from the turbulence production rate both in trends and magnitude. The latter is dominated by energy flux from the mean flow to the large scale turbulence, which is resolved in LES, whereas the former is dominated by energy flux from the mean flow to the SGS turbulence. The SGS dissipation rate is also used for calculating the static and dynamic Smagorinsky coefficients, the latter involving filtering at multiple scales; both vary substantially in the tip region, and neither is equal to values obtained in isotropic turbulence.

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.

scholarly journals Climate Process Team on Internal Wave–Driven Ocean Mixing

2017 ◽  
Vol 98 (11) ◽  
pp. 2429-2454 ◽  
Author(s):  
Jennifer A. MacKinnon ◽  
Zhongxiang Zhao ◽  
Caitlin B. Whalen ◽  
Amy F. Waterhouse ◽  
David S. Trossman ◽  
...  
Keyword(s):  
Internal Wave ◽  
Turbulent Mixing ◽  
Low Frequency ◽  
Internal Tide ◽  
Deep Ocean ◽  
Global Ocean ◽  
Primary Role ◽  
Inverse Models ◽  
Lee Waves ◽  
Mixing Rates

Abstract Diapycnal mixing plays a primary role in the thermodynamic balance of the ocean and, consequently, in oceanic heat and carbon uptake and storage. Though observed mixing rates are on average consistent with values required by inverse models, recent attention has focused on the dramatic spatial variability, spanning several orders of magnitude, of mixing rates in both the upper and deep ocean. Away from ocean boundaries, the spatiotemporal patterns of mixing are largely driven by the geography of generation, propagation, and dissipation of internal waves, which supply much of the power for turbulent mixing. Over the last 5 years and under the auspices of U.S. Climate Variability and Predictability Program (CLIVAR), a National Science Foundation (NSF)- and National Oceanic and Atmospheric Administration (NOAA)-supported Climate Process Team has been engaged in developing, implementing, and testing dynamics-based parameterizations for internal wave–driven turbulent mixing in global ocean models. The work has primarily focused on turbulence 1) near sites of internal tide generation, 2) in the upper ocean related to wind-generated near inertial motions, 3) due to internal lee waves generated by low-frequency mesoscale flows over topography, and 4) at ocean margins. Here, we review recent progress, describe the tools developed, and discuss future directions.

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