Internal Tide Generation Research Articles

Impacts of Stratification Variation on the M2 Internal Tide Generation in Luzon Strait

ABSTRACT Topographic features, stratification, and barotropic tidal currents are three factors that determine internal tide (IT) generation. However, the mechanism of the impacts of stratification variation on IT generation in Luzon Strait (LS) has not been extensively explored. A three-dimensional high-resolution model is used to simulate the M2 ITs in the northern South China Sea (SCS) under different stratification conditions. The model is run with idealized topographies where the east or west ridge of LS is removed. Results indicate that both the M2 conversion rate and energy fluxes in the northern SCS show seasonal variations that are site dependent. By analyzing all the results from the simulations, we find that stratification variation changes IT generation in LS mainly through two mechanisms. First, the impact of stratification variation on the bottom pressure perturbation is caused by barotropic tidal currents flowing over topographic features, which directly affects the conversion. Second, stratification variation changes the wavelength of ITs and, hence, the interference of ITs within the double ridges, which finally changes the conversion in LS. The second mechanism is found to be the dominant one for seasonal variation of the M2 IT generation in LS.

Tidal Pressurization of the Ocean Cavity Near an Antarctic Ice Shelf Grounding Line

AbstractMass loss from the Antarctic ice sheet is sensitive to conditions in ice shelf grounding zones, the transition between grounded and floating ice. To observe tidal dynamics in the grounding zone, we moored an ocean pressure sensor to Ross Ice Shelf, recording data for 54 days. In this region the ice shelf is brought out of hydrostatic equilibrium by the flexural rigidity of ice, yet we found that tidal pressure variations at a constant geopotential surface were similar within and outside of the grounding zone. This implies that the grounding zone ocean cavity was overpressurized at high tide and underpressurized at low tide by up to 10 kPa with respect to glaciostatic pressure at the ice shelf base. Phase lags between ocean pressure and vertical ice shelf motion were tens of minutes for diurnal and semidiurnal tides, an effect that has not been incorporated into ocean models of tidal currents below ice shelves. These tidal pressure variations may affect the production and export of meltwater in the subglacial environment and may increase basal crevasse heights in the grounding zone by several meters, according to linear elastic fracture mechanics. We find anomalously high tidal energy loss at the K1 constituent in the grounding zone and hypothesize that this could be explained by seawater injection into the subglacial environment at high tide or internal tide generation through interactions with topography. These observations lay the foundation for improved representation of the grounding zone and its tidal dynamics in ocean circulation models of sub–ice shelf cavities.

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

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.

An inverse technique for reconstructing ocean’s density stratification from surface data

In this article, we propose an inverse technique that accurately reconstructs the ocean’s density stratification profile simply from free surface elevation data. Satellite observations suggest that ocean surface contains the signature of internal tides, which are internal gravity waves generated by the barotropic tides. Since internal tides contain the information of ocean’s density stratification, the latter can in principle be reconstructed from the free surface signature. We consider a simple theoretical model that approximates a continuously stratified ocean as discrete layers of constant buoyancy frequency; this facilitates the derivation of a closed-form dispersion relation. First, we numerically simulate internal tide generation for toy ocean scenarios and subsequently perform Space–Time Fourier Transform (STFT) of the free surface, which yields internal tide spectra with wavenumbers corresponding to the tidal frequency. The density profile is reconstructed by substituting these wavenumbers into the dispersion relation. Finally, we consider a more realistic situation with rotation, bottom topography, shear and density profiles representative of the Strait of Gibraltar. Density reconstruction in the presence and absence of shear is respectively found to be 90.2% and 94.2% accurate. The proposed method can be used to reconstruct climatological mean ocean density field of uniform spatial resolution using only surface elevation data obtained via satellite altimetry.

Modeling of Internal Tides in the Western Bay of Bengal: Characteristics and Energetics

AbstractGeneration and propagation of internal tides in the western Bay of Bengal (BoB) are investigated using observations from Acoustic Doppler Current Profilers and simulations from a very high resolution numerical ocean model. Observations show that semidiurnal internal tides in the southern and northern parts of the western BoB are more energetic during neap phase of the local barotropic tide than those during spring phase. Numerical simulations indicate that internal tides generated over the Andaman‐Nicobar Ridge propagate westward for about 1,000–1,450 km across the BoB and finally impinge on the continental slopes off the east coast of India after 5–7 days. Energetic internal tides observed during the neap phase of the barotropic tides in the western BoB are mainly due to the arrival of remotely generated internal tides. We show that the variation in the onshore transmission of these remotely generated internal tides due to the topographic slope in the western BoB controls the strength of internal tide activity along the shelf. Superposition of reflected internal tides from continental slope, which are very steep in some regions and onshore propagating‐waves generate partly standing waves. Numerical experiments suggest that internal tides coming from remote sources account for more than 80% of the total internal tide energy observed in the western BoB. Internal tide energy dissipation on the continental margins of the western BoB is about 3 to 4 times larger than the local generation, indicating that this region is a sink for remotely generated internal tide energy.

Coastally Generated Near-Inertial Waves

AbstractWind directly forces inertial oscillations in the mixed layer. Where these currents hit the coast, the no-normal-flow boundary condition leads to vertical velocities that pump both the base of the mixed layer and the free surface, producing offshore-propagating near-inertial internal and surface waves, respectively. The internal waves directly transport wind work downward into the ocean’s stratified interior, where it may provide mechanical mixing. The surface waves propagate offshore where they can scatter over rough topography in a process analogous to internal-tide generation. Here, we estimate mixed layer currents from observed winds using a damped slab model. Then, we estimate the pressure, velocity, and energy flux associated with coastally generated near-inertial waves at a vertical coastline. These results are extended to coasts with arbitrary across-shore topography and examined using numerical simulations. At the New Jersey shelfbreak, comparisons between the slab model, numerical simulations, and moored observations are ambiguous. Extrapolation of the theoretical results suggests that (10%) of global wind work (i.e., 0.03 of 0.31 TW) is transferred to coastally generated barotropic near-inertial waves.

Energetics of internal tides over the Sangihe-Talaud ridge - Sulawesi sea

An estimate of energetic barotropic and baroclinic tides over Sangihe-Talaud ridge (STR) - Sulawesi Sea is carried out by using a three-dimensional ROMS (Regional Ocean Modeling System) ocean model. The model is validated with satellite data. The estimate of tidal energy consists of generation, radiation, and dissipation. The model identified the generating internal tide area with strong barotropic-to-baroclinic conversion (above 10 kW/m) over S-T ridge. Away from this generating internal tides area that is in deep Sulawesi Sea basin, energy conversion is very weak (below 10−3Wm−2). Baroclinic energy is mostly dissipated in area near the coast. From the total of 9.45 GW (100%) of barotropic-to-baroclinic energy conversion, about 7.19 GW (76%) is converted into baroclinic energy through the generation of internal tide and about 4.13 GW (57%) of this baroclinic energy radiate to deep open sea. Distribution of tidal energy is highly dependent on topographic features. Estimate of strong vertical eddy diffusivity (KV) over the steep S-T ridge varies between 10−3 and 10−2 m2/s, in contrast to the weak KV in deep flat Sulawesi basin of about 10−4 m2/s.

Modal structure and propagation of internal tides in the northeastern South China Sea

The evolution of energy, energy flux and modal structure of the internal tides (ITs) in the northeastern South China Sea is examined using the measurements at two moorings along a cross-slope section from the deep continental slope to the shallow continental shelf. The energy of both diurnal and semidiurnal ITs clearly shows a ~14-day spring-neap cycle, but their phases lag that of barotropic tides, indicating that ITs are not generated on the continental slope. Observations of internal tidal energy flux suggest that they may be generated at the Luzon Strait and propagate west-northwest to the continental slope in the northwestern SCS. Because the continental slope is critical-supercritical with respect to diurnal ITs, about 4.6 kJ/m2 of the incident energy and 8.7 kW/m of energy flux of diurnal ITs are reduced from the continental slope to the continental shelf. In contrast, the semidiurnal internal tides enter the shelf because of the sub-critical topography with respect to semidiurnal ITs. From the continental slope to the shelf, the vertical structure of diurnal ITs shows significant variation, with dominant Mode 1 on the deep slope and dominant higher modes on the shelf. On the contrary, the vertical structure of the semidiurnal ITs is stable, with dominant Mode 1.

Internal Tide Generation and Dissipation by Small Periodic Topography in Deep Ocean

Internal tides generated by a rough sea floor are an important source of mixing in the abyssal ocean. Two linear models are employed to evaluate the conversion rate from barotropic tides to internal tides and the energy distribution in each mode. Considering the periodicity of internal tides, the topography is represented by periodically distributed knife edges and sinusoidal ridges within one wavelength of mode-1 internal tides. The knife edges generate greater internal tides than the sinusoidal ridges due to their sharp shape, which approximates an extremely supercritical condition. Energy flux concentrates in modes whose numbers are multiples of the knife edge or ridge number. Then, a fully nonlinear model that integrates viscosity and diffusion is implemented, and its results are compared with those of the linear model. Internal wave rays generated in the nonlinear model show a distribution similar to the linear models’ prediction. High dissipation rates coincide with the rays, suggesting that nonlinear wave-wave interaction is a dominant mechanism for internal tide dissipation in the abyssal ocean.

Coastal Semidiurnal Internal Tidal Incoherence in the Santa Maria Basin, California: Observations and Model Simulations

AbstractA series of five realistic, nested, hydrostatic numerical ocean model simulations are used to study semidiurnal internal tide generation and propagation from the continental slope, through the shelf break and to the midshelf adjacent to Point Sal, CA. The statistics of modeled temperature and horizontal velocity fluctuations are compared to midshelf observations (30‐ to 50‐m water depth). Time‐ and frequency‐domain methods are used to decompose internal tides into components that are coherent and incoherent with the barotropic tide, and the incoherence fraction is 0.5–0.7 at the midshelf locations in both the realistic model and observations. In contrast, the incoherence fraction is at the most 0.45 for a simulation with idealized stratification, and neither atmospheric forcing nor mesoscale currents. Negligible conversion from barotropic to baroclinic energy occurs at the local shelf break. Instead, the dominant internal tide energy sources are regions of small‐scale near‐critical to supercritical bathymetry on the Santa Lucia escarpment (1,000–3,000 m), 70–80 km from the continental shelf. Near the generation region, semidiurnal baroclinic energy is primarily coherent and rapidly decays adjacent to the shelf break. In the realistically forced model, incoherent energy is less than 10% in the generation region, with a steady increase in incoherence fraction from the continental slope to the midshelf. Backward ray tracing from the midshelf to the Santa Lucia escarpment identifies multiple energy pathways potentially leading to spatial interference. As internal tides shoal on the predominantly subcritical slope/shelf system, temporally variable stratification and Doppler shifting from mesoscale and submesoscale features appear equally important in leading to the loss of coherence.

Evolution of obliquely incident waves on the slope of the northern South China Sea

Internal solitary waves (ISWs) with distinct fronts were frequently captured by satellite images and were often obliquely incident to continental slopes in the region southwest of the Dongsha Islands in the northern South China Sea (NSCS), although few in situ observations and explanations were available. To study the generation and evolution of the wave front in this region, three moorings were deployed along the continental slope of NSCS from April to September 2009 and synthetic aperture radar (SAR) images were collected for ISWs analysis as well. It was found that ISWs normally came out in the form of two successive waves at an interval of approximately 3 h. Further research showed that, although the interval was short, the generation mechanisms of the two ISWs were completely different. The first arriving ISW had obviously different wave structure along the wave front and always appeared in advance of the internal tides (ITs) trough, which indicates that the first arriving ISW evolved from the interaction between the ITs and continental shelf topography. Furthermore, based on the Korteweg-de Vries (KdV) equation and Ostrovsky number, it was inferred that the appearance of the first ISW was determined by the relative importance of nonlinearity and rotation in the propagation of ITs. Comparatively, the second arriving ISW evolved solely from the ITs without interaction with topography in the deep basin between the Luzon Strait and continental shelf, and had the same wave structure along the wave front.

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

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.

Spatial and Temporal Variability of Semidiurnal Internal Tide Energetics in the Western Bay of Bengal

The three-dimensional Massachusetts Institute of Technology general circulation model (MITgcm) with time-dependent forcing is implemented to investigate the spatial and temporal variability of internal tides over the eastern coast of India. Numerical simulations are conducted for a number of different months of the year for which in situ observations are available at high temporal resolution. During the months of November–December and March–April, peak spectral estimates of density variability are evident in the semidiurnal frequency band in both observations and simulations, while during August, variability is dominantly in the near-inertial frequency band. Empirical orthogonal functions (EOF) analysis is applied to decompose the baroclinic tidal currents into vertical modes. The results show that about 70–80% of the total variance is in the first mode, while the first three modes represent 90–95% of the total variance in all seasons. Internal tide characteristics such as phase speed, group speed, and wavelength are largest in the postmonsoon season. The magnitude of the computed energy flux is greatest during November, while the direction of propagation of internal tides is almost unchanged through the year. The available potential energy peaks in November (20 kJ m−2) and is smallest in August (14 kJ m−2). Calculation of the energy budget shows that the energy conversion rate from barotropic forcing to internal tides is about 85% in November but only about 46% in August.

Deep-ocean mixing driven by small-scale internal tides

Turbulent mixing in the ocean is key to regulate the transport of heat, freshwater and biogeochemical tracers, with strong implications for Earth’s climate. In the deep ocean, tides supply much of the mechanical energy required to sustain mixing via the generation of internal waves, known as internal tides, whose fate—the relative importance of their local versus remote breaking into turbulence—remains uncertain. Here, we combine a semi-analytical model of internal tide generation with satellite and in situ measurements to show that from an energetic viewpoint, small-scale internal tides, hitherto overlooked, account for the bulk (>50%) of global internal tide generation, breaking and mixing. Furthermore, we unveil the pronounced geographical variations of their energy proportion, ignored by current parameterisations of mixing in climate-scale models. Based on these results, we propose a physically consistent, observationally supported approach to accurately represent the dissipation of small-scale internal tides and their induced mixing in climate-scale models.

Generation and Propagation of M2 Internal Tides Modulated by the Kuroshio Northeast of Taiwan

AbstractThe variability and energetics of M2 internal tides during their generation and propagation through the Kuroshio flows northeast of Taiwan are investigated using a high‐resolution numerical model. The corrugated continental slopes, particularly the I‐Lan Ridge and Mien‐Hua Canyon, are first identified as the energetic sources of M2 internal tides. The domain‐integrated M2 barotropic‐to‐baroclinic conversion rate under the Kuroshio influence is ~2.35 GW, ~0.9 GW of which is generated at the I‐Lan Ridge, ~0.93 GW at the Mien‐Hua Canyon, and ~0.52 GW at the north shelf. The M2 internal tide generation is influenced by the horizontally varying, zonally tilting stratification associated with the Kuroshio. In this situation, the conversion rate decreases by ~30% at the I‐Lan Ridge but increases to within ~10% at the Mien‐Hua Canyon and north shelf, in comparison to the simulation initiated with horizontal homogeneous stratification. Internal tides from multiple sources interfere to form a three‐dimensional baroclinic field. The interference by the internal tides from the Mien‐Hua Canyon and north shelf is refracted by the Kuroshio and exhibits a mesoscale gyre pattern, which can explain the frequent occurrence of internal solitary waves. An energetic along‐slope tidal beam (TBKC) from the I‐Lan Ridge radiates southward against the northward Kuroshio flows, causing strong vertical displacement, which favorably compares with recently reported field measurements. The M2 internal tide energy dissipates primarily near the source sites, and the remaining energy radiates outward over limited distances. Complex topographic features and background currents enhance the internal tide dissipation, which induces strong, inhomogeneous diapycnal mixing.

Toward global maps of internal tide energy sinks

Internal tides power much of the observed small-scale turbulence in the ocean interior. To represent mixing induced by this turbulence in ocean climate models, the cascade of internal tide energy to dissipation scales must be understood and mapped. Here, we present a framework for estimating the geography of internal tide energy sinks. The mapping relies on the following ingredients: (i) a global observational climatology of stratification; (ii) maps of the generation of M2, S2 and K1 internal tides decomposed into vertical normal modes; (iii) simplified representations of the dissipation of low-mode internal tides due to wave-wave interactions, scattering by small-scale topography, interaction with critical slopes and shoaling; (iv) Lagrangian tracking of low-mode energy beams through observed stratification, including refraction and reflection. We thus obtain a global map of the column-integrated energy dissipation for each of the four considered dissipative processes, each of the three tidal constituents and each of the first five modes. Modes ≥6 are inferred to dissipate within the local water column at the employed half-degree horizontal resolution. Combining all processes, modes and constituents, we construct a map of the total internal tide energy dissipation, which compares well with observational inferences of internal wave energy dissipation. This result suggests that tides largely shape observed spatial contrasts of dissipation, and that the framework has potential in improving understanding and modelling of ocean mixing. However, sensitivity to poorly constrained parameters and simplifying assumptions entering the parameterized energy sinks calls for additional investigation. The attenuation of low-mode internal tides by wave-wave interactions needs particular attention.

Resolving the horizontal direction of internal tide generation

The mixing induced by breaking internal gravity waves is an important contributor to the ocean’s energy budget, shaping, inter alia, nutrient supply, water mass transformation and the large-scale overturning circulation. Much of the energy input into the internal wave field is supplied by the conversion of barotropic tides at rough bottom topography, which hence needs to be described realistically in internal gravity wave models and mixing parametrisations based thereon. A new semi-analytical method to describe this internal wave forcing, calculating not only the total conversion but also the direction of this energy flux, is presented. It is based on linear theory for variable stratification and finite depth, that is, it computes the energy flux into the different vertical modes for two-dimensional, subcritical, small-amplitude topography and small tidal excursion. A practical advantage over earlier semi-analytical approaches is that the new one gives a positive definite conversion field. Sensitivity studies using both idealised and realistic topography allow the identification of suitable numerical parameter settings and corroborate the accuracy of the method. This motivates the application to the global ocean in order to better account for the geographical distribution of diapycnal mixing induced by low-mode internal gravity waves, which can propagate over large distances before breaking. The first results highlight the significant differences of energy flux magnitudes with direction, confirming the relevance of this more detailed approach for energetically consistent mixing parametrisations in ocean models. The method used here should be applicable to any physical system that is described by the standard wave equation with a very wide field of sources.

Seasonal and Spatial Variations of the M2 Internal Tide in the Yellow Sea

AbstractThe seasonality of internal tides is particularly conspicuous in shelf seas due to the dramatical variations in the marine environment. In this paper, the seasonal and spatial variabilities of M2 internal tides in the Yellow Sea (YS) are investigated using a high‐resolution numerical ocean model. The freshwater runoff of the Yangtze River is also considered. Because most nonlinear internal waves are of tidal origin, the simulated internal tides show good spatial consistency with the satellite‐detected nonlinear internal waves. During summer, the M2 internal tides are ubiquitous and originate from multiple generation sites (e.g., the west coast of the Korean Peninsula and the Yangtze River estuary). During other seasons, the spatial coverage of the internal tides becomes very limited. Multiple sources combined with seasonal onset and decay lead to complex seasonal interference patterns. The wavelengths vary both spatially and temporally, depending on the water depth and ocean stratification. Between spring and autumn, a seasonally reversed pattern of radiation of baroclinic energy flux is found in the southern YS, which may be induced by the seasonal variability of the YS Warm Current. Seasonal stratification controls the seasonality of the generation, propagation, and dissipation of internal tides and is maintained by the monsoon, seasonal circulation, and Yangtze River runoff. Our simulations suggest that, although internal tide dissipation is dispensable for the tidal energy budgets in the YS, internal tides seem to be the leading order contributor to the midcolumn diapycnal mixing, as they are more efficient mixers than barotropic tides.

Dissipation of mesoscale eddies and its contribution to mixing in the northern South China Sea

It is reported that turbulent mixing is enhanced in the South China Sea (SCS), and it is highly variable in both space and time. Generation and breaking of internal tides has been identified as the main process to drive turbulent mixing in the SCS, while the contributions from other processes are not clear enough. Here we investigate the potential contribution from mesoscale eddies to turbulent mixing in the SCS using a high resolution numerical simulation. Our results show that mesoscale eddies in the SCS effectively dissipate over complex rough topography and indicate that the generation of submesoscale motions and lee waves are two pathways for the transfer of mesoscale eddy energy down to small dissipation scales. The energy loss from mesoscale eddies near the Xisha Islands is estimated to be sufficient to sustain turbulent kinetic energy dissipation rate of O (10−8) W/kg. This study suggests an alternative and potentially efficient mechanism to internal tides for the local maintenance of turbulent mixing in the SCS.

Numerical Simulation of the Generation and Evolution of Internal Tides and Solitary Waves at Sofala Shelf Break

Numerical Simulation of the Generation and Evolution of Internal Tides and Solitary Waves at Sofala Shelf Break