scholarly journals Internal Wave Reflection on Shelf Slopes with Depth-Varying Stratification

2013 ◽  
Vol 43 (2) ◽  
pp. 248-258 ◽  
Author(s):  
Rob A. Hall ◽  
John M. Huthnance ◽  
Richard G. Williams
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Energy Flux ◽  
Internal Tide ◽  
Shelf Break ◽  
Maximum Slope ◽  
Near Surface ◽  
Shelf Slope ◽  
Linear Slope ◽  
Horizontal Wavelength

Abstract Reflection of internal waves from sloping topography is simple to predict for uniform stratification and linear slope gradients. However, depth-varying stratification presents the complication that regions of the slope may be subcritical and other regions supercritical. Here, a numerical model is used to simulate a mode-1, M2 internal tide approaching a shelf slope with both uniform and depth-varying stratifications. The fractions of incident internal wave energy reflected back offshore and transmitted onto the shelf are diagnosed by calculating the energy flux at the base of slope (with and without topography) and at the shelf break. For the stratifications/topographies considered in this study, the fraction of energy reflected for a given slope criticality is similar for both uniform and depth-varying stratifications. This suggests the fraction reflected is dependent only on maximum slope criticality and independent of the depth of the pycnocline. The majority of the reflected energy flux is in mode 1, with only minor contributions from higher modes due to topographic scattering. The fraction of energy transmitted is dependent on the depth-structure of the stratification and cannot be predicted from maximum slope criticality. If near-surface stratification is weak, transmitted internal waves may not reach the shelf break because of decreased horizontal wavelength and group velocity.

scholarly journals Internal tide energy flux over a ridge measured by a co-located ocean glider and moored acoustic Doppler current profiler

Ocean Science ◽  
2019 ◽  
Vol 15 (6) ◽  
pp. 1439-1453 ◽  
Author(s):  
Rob A. Hall ◽  
Barbara Berx ◽  
Gillian M. Damerell
Keyword(s):  
Energy Flux ◽  
Internal Tide ◽  
Acoustic Doppler Current Profiler ◽  
Small Scale ◽  
Negative Bias ◽  
Potential Density ◽  
Shelf Slope ◽  
Current Profiler ◽  
Circle Diameter ◽  
Horizontal Wavelength

Abstract. Internal tide energy flux is an important diagnostic for the study of energy pathways in the ocean, from large-scale input by the surface tide to small-scale dissipation by turbulent mixing. Accurate calculation of energy flux requires repeated full-depth measurements of both potential density (ρ) and horizontal current velocity (u) over at least a tidal cycle and over several weeks to resolve the internal spring–neap cycle. Typically, these observations are made using full-depth oceanographic moorings that are vulnerable to being “fished out” by commercial trawlers when deployed on continental shelves and slopes. Here we test an alternative approach to minimize these risks, with u measured by a low-frequency acoustic Doppler current profiler (ADCP) moored near the seabed and ρ measured by an autonomous ocean glider holding station by the ADCP. The method is used to measure the semidiurnal internal tide radiating from the Wyville Thomson Ridge in the North Atlantic. The observed energy flux (4.2±0.2 kW m−1) compares favourably with historic observations and a previous numerical model study. Error in the energy flux calculation due to imperfect co-location of the glider and ADCP is estimated by subsampling potential density in an idealized internal tide field along pseudorandomly distributed glider paths. The error is considered acceptable (<10 %) if all the glider data are contained within a “watch circle” with a diameter smaller than 1∕8 the mode-1 horizontal wavelength of the internal tide. Energy flux is biased low because the glider samples density with a broad range of phase shifts, resulting in underestimation of vertical isopycnal displacement and available potential energy. The negative bias increases with increasing watch circle diameter. If watch circle diameter is larger than 1∕8 the mode-1 horizontal wavelength, the negative bias is more than 3 % and all realizations within the 95 % confidence interval are underestimates. Over the Wyville Thomson Ridge, where the semidiurnal mode-1 horizontal wavelength is ≈100 km and all the glider dives are within a 5 km diameter watch circle, the observed energy flux is estimated to have a negative bias of only 0.4 % and an error of less than 3 % at the 95 % confidence limit. With typical glider performance, we expect energy flux error due to imperfect co-location to be <10 % in most mid-latitude shelf slope regions.

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

&lt;p&gt;The continental shelf/slope northeastern Taiwan is a &amp;#8216;hotspot&amp;#8217; 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.&lt;/p&gt;&lt;p&gt;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.&lt;/p&gt;

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 The Lifecycle of Nonlinear Internal Waves in the Northwestern South China Sea

2019 ◽  
Vol 49 (8) ◽  
pp. 2133-2145 ◽  
Author(s):  
Jianjun Liang ◽  
Xiao-Ming Li ◽  
Jin Sha ◽  
Tong Jia ◽  
Yongzheng Ren
Keyword(s):  
South China Sea ◽  
Internal Waves ◽  
South China ◽  
Internal Tide ◽  
In Situ Measurements ◽  
Shelf Break ◽  
Undular Bore ◽  
Nonlinear Internal Waves ◽  
Seasonal Thermocline

AbstractThe life cycle of nonlinear internal waves (NIWs) to the southeast of Hainan Island in the northwestern South China Sea is investigated using synergistic satellite observations, in situ measurements, and numerical simulations. A three-dimensional, fully nonlinear and nonhydrostatic model with ultrafine resolution shows that a diurnal internal tide emanates from a sill in the Xisha Islands at approximately 215 km away from the local shelf break. The internal tide transits the deep basin toward the shelf break and reflects at the sea bottom and seasonal thermocline in the form of a wave beam. Arriving at the shelf break, the internal tide undergoes nonlinear transformation and produces an undular bore. Analyses of in situ measurements reveal that the undular bore appears as sharp depressions of the strong near-surface seasonal thermocline. The undular bore gradually evolves into an internal solitary wave train on the midshelf, which was detected by the spaceborne synthetic aperture radar. This finding has great implications for investigating NIWs in other coastal oceans where waves are controlled by remotely generated internal tides.

Diapycnal diffusivity induced by the breaking of lee waves

2020 ◽  
Author(s):  
Thomas Eriksen ◽  
Carsten Eden ◽  
Dirk Olbers
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Energy Flux ◽  
Wave Energy ◽  
Diapycnal Mixing ◽  
Overturning Circulation ◽  
Lee Waves ◽  
Lee Wave ◽  
Wave Energy Flux ◽  
Diapycnal Diffusivity

&lt;p&gt;A key component in setting the large scale ocean circulation is the process of diapycnal mixing, since this can drive the meridional overturning circulation. Diapycnal mixing in the interior ocean is predominantly associated with the breaking of internal waves. Traditionally, diapycnal mixing has been represented in ocean models by a diapycnal diffusivity either constant or exponentially decreasing with depth. This approach, however, does not take into account the actual physics behind the breaking of internal waves. The energetically consistent internal wave model IDEMIX (Internal wave Dissipation, Energetics and MIXing), on the other hand, computes diffusivities directly on the basis of internal wave energetics. One such type of internal waves are lee waves. These are generated and subsequently dissipated when geostrophic currents interact with bottom topography and are therefore believed to be a source of energy for deep ocean mixing. In this study IDEMIX is coupled to a 1/12&lt;sup&gt;th&lt;/sup&gt;&amp;#160;degree regional model of the Atlantic. The lee wave energy flux is calculated and used as a bottom flux at each time step effectively allowing lee waves to propagate, interact with mean flow and waves, and subsequently dissipate. This setup enables not only an estimate of the lee wave energy flux but also a direct investigation of the influence of lee waves on dissipation, stratification and horizontal and overturning circulation.&lt;/p&gt;

scholarly journals Bispectral Analysis of Energy Transfer within the Two-Dimensional Oceanic Internal Wave Field

2005 ◽  
Vol 35 (11) ◽  
pp. 2104-2109 ◽  
Author(s):  
Naoki Furuichi ◽  
Toshiyuki Hibiya ◽  
Yoshihiro Niwa
Keyword(s):  
Internal Wave ◽  
Wave Field ◽  
Internal Waves ◽  
Internal Tide ◽  
Energy Cascade ◽  
Minor Role ◽  
Two Dimensional ◽  
Bispectral Analysis ◽  
Internal Wave Field ◽  
Oceanic Internal Wave

Abstract Bispectral analysis of the numerically reproduced spectral responses of the two-dimensional oceanic internal wave field to the incidence of the low-mode semidiurnal internal tide is performed. At latitudes just equatorward of 30°, the low-mode semidiurnal internal tide dominantly interacts with two high-vertical-wavenumber diurnal (near inertial) internal waves, forming resonant triads of parametric subharmonic instability (PSI) type. As the high-vertical-wavenumber near-inertial energy level is raised by this interaction, the energy cascade to small horizontal and vertical scales is enhanced. Bispectral analysis thus indicates that energy in the low-mode semidiurnal internal tide is not directly transferred to small scales but via the development of high-vertical-wavenumber near-inertial current shear. In contrast, no noticeable energy cascade to high vertical wavenumbers is recognized in the bispectra poleward of ∼30° as well as equatorward of ∼25°. A new finding is that, although PSI is possible equatorward of ∼30°, the efficiency drops sharply as the latitude falls below ∼25°. At all latitudes, another resonant interaction suggestive of induced diffusion is found to occur between the low-mode semidiurnal internal tide and two high-frequency internal waves, although bispectral analysis shows that this interaction plays only a minor role in cascading the low-mode semidiurnal internal tide energy.

scholarly journals Modeling and Analysis of Internal-Tide Generation and Beamlike Onshore Propagation in the Vicinity of Shelfbreak Canyons

2014 ◽  
Vol 44 (3) ◽  
pp. 834-849 ◽  
Author(s):  
Weifeng G. Zhang ◽  
Timothy F. Duda ◽  
Ilya A. Udovydchenkov
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Internal Tide ◽  
Propagation Model ◽  
Internal Tides ◽  
Wave Radiation ◽  
Beam Radiation ◽  
Control Simulation ◽  
Conversion Rates ◽  
The Cross

Abstract A hydrostatic numerical model with alongshore-uniform barotropic M2 tidal boundary forcing and idealized shelfbreak canyon bathymetries is used to study internal-tide generation and onshore propagation. A control simulation with Mid-Atlantic Bight representative bathymetry is supported by other simulations that serve to identify specific processes. The canyons and adjacent slopes are transcritical in steepness with respect to M2 internal wave characteristics. Although the various canyons are symmetrical in structure, barotropic-to-baroclinic energy conversion rates Cυ are typically asymmetrical within them. The resulting onshore-propagating internal waves are the strongest along beams in the horizontal plane, with the stronger beam in the control simulation lying on the side with higher Cυ. Analysis of the simulation results suggests that the cross-canyon asymmetrical Cυ distributions are caused by multiple-scattering effects on one canyon side slope, because the phase variation in the spatially distributed internal-tide sources, governed by variations in the orientation of the bathymetry gradient vector, allows resonant internal-tide generation. A less complex, semianalytical, modal internal wave propagation model with sources placed along the critical-slope locus (where the M2 internal wave characteristic is tangent to the seabed) and variable source phasing is used to diagnose the physics of the horizontal beams of onshore internal wave radiation. Model analysis explains how the cross-canyon phase and amplitude variations in the locally generated internal tides affect parameters of the internal-tide beams. Under the assumption that strong internal tides on continental shelves evolve to include nonlinear wave trains, the asymmetrical internal-tide generation and beam radiation effects may lead to nonlinear internal waves and enhanced mixing occurring preferentially on one side of shelfbreak canyons, in the absence of other influencing factors.

scholarly journals Strong Internal Waves Generated by the Interaction of the Kuroshio and Tides over a Shallow Ridge

2019 ◽  
Vol 49 (11) ◽  
pp. 2917-2934 ◽  
Author(s):  
Eiji Masunaga ◽  
Yusuke Uchiyama ◽  
Hidekatsu Yamazaki
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Energy Flux ◽  
Wave Energy ◽  
High Frequency ◽  
Deep Ocean ◽  
Internal Tides ◽  
Navier Stokes ◽  
Wave Energy Flux ◽  
The Kuroshio

AbstractThe Kuroshio and tides significantly influence the oceanic environment off the Japanese mainland and promote mass/heat transport. However, the interaction between the Kuroshio and tides/internal waves has not been examined in previous works. To investigate this phenomenon, the two-dimensional high-resolution nonhydrostatic oceanic Stanford Unstructured Nonhydrostatic Terrain-Following Adaptive Navier–Stokes Simulator (SUNTANS) model was employed. The results show that strong internal tides propagating upstream in the Kuroshio are generated at a near-critical internal Froude number (Fri = 0.91). The upstream internal wave energy flux reaches a magnitude of 12 kW m−1, which is approximately 3 times higher than that of internal waves without the Kuroshio. On the other hand, under supercritical conditions, the Kuroshio suppresses the internal wave energy flux. The interaction of internal tides and the Kuroshio also generates upstream propagating high-frequency internal waves and solitary wave packets. The high-frequency internal waves contribute to the increase in the total internal wave energy flux up to 40% at the near-critical Fri value. The results of this study suggest that the interaction of internal tides and the Kuroshio enhances the upstream propagating internal tides under the specified conditions (Fri ~ 1), which may lead to deep ocean mixing and transport at significant distances from the internal wave generation sites.

The temporal variability of near-inertial internal waves in an internal tide beam

2021 ◽  
Author(s):  
Jonas Löb ◽  
Monika Rhein
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Temporal Variability ◽  
Internal Tide ◽  
Internal Tides ◽  
Inertial Waves ◽  
Energy Fluxes ◽  
Wind Event ◽  
Mode 2 ◽  
Inertial Energy

&lt;p&gt;Low mode internal waves in the stratified ocean are generated by the interaction between barotropic tides and seafloor topography and by the wind field in the near-inertial range. They are crucial for interior mixing and for the oceanic energy pathways, since they carry a large portion of the energy of the entire internal wave field. Long-term observations of energy fluxes of internal waves are sparse. The aim of this work is to study the temporal variability of wind generated low mode near-inertial internal waves inside an internal tide beam emanating from seamounts south of the Azores. For this, 20 months of consecutive mooring observations are used to calculate the mode 1 and mode 2 near-inertial energy fluxes as well as kinetic and potential energies. The gathered time series of near-inertial internal wave energy flux is not steady due to its intermittent forcing and is neither dominated by either mode 1 or mode 2. It shows a peak induced by a distinct strong wind event which is directly linked to wind-power input into the mixed layer north-east of the mooring location, and allows a comparison between the wind event and a background state. Furthermore, indications of non-linear interactions of the near-inertial waves with the internal tides in the form of resonant triad interaction and non-linear self-interaction have been found. This study provides new insights on the relative importance of single wind events and reinforces the assumption of a global non-uniform distribution of near-inertial energy with emphasis in regions where these events occur often and regularly. It furthermore displays its importance to be adequately incorporated into ocean general circulation models and in generating ocean mixing estimates by near-inertial waves as a similarly important component next to the internal tides.&lt;/p&gt;

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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