Internal Tide Generation Research Articles

The Vertical Mode Decomposition of Surface and Internal Tides in the Presence of a Free Surface and Arbitrary Topography

AbstractThe method of decomposing surface and internal tides determines the expression for internal tide energy, energy flux, and energy conversion. The de facto standard is to define surface tides as depth-averaged pressure and horizontal velocity and internal tides as the residuals. This decomposition, which is equivalent to projecting motion onto vertical modes that obey a rigid lid, is known to produce spurious energy conversion CS through movement of the free surface. Here, motion is instead projected onto modes that obey a linear, free-surface boundary condition. The free-surface modes are shown to obey a more complicated orthogonality condition than rigid-lid modes but are still straightforward to calculate numerically. The resulting decomposition (i) completely eliminates spurious energy conversion CS and (ii) leads to a more precise expression for topographic internal tide generation C, which now depends on horizontal gradients in the vertical structure of the surface tide. Numerical simulations and rough global estimates indicate that corrections to C are a maximum of a few percent. However, CS produces spurious energy flux divergences/convergences in the open ocean, which are the same order of magnitude [O(1–10) mW m−2] as open-ocean internal tide energy dissipation.

Modelling the tides and their impacts on the vertical stratification over the Sofala Bank, Mozambique

The Sofala Bank, a wide shelf located along the central coast of Mozambique, hosts tides with high amplitudes. The Regional Ocean Modelling System (ROMS) was used to analyse the tidal currents on the bank and to investigate their effects on the stratification and generation of tidal fronts. During spring tides, barotropic tidal currents with maximum values ranging from 40 cm s–1 to 70 cm s–1 are found on the central bank. The major axis of the tidal ellipses for M2 and S2 follow a cross-shelf direction with mainly anticlockwise rotation. Similar to observations, three distinct regimes occur: (i) a warm well-mixed region on the inner shelf where the depths are <30 m; (ii) a wellmixed colder region above the shelf edge; and (iii) a stratified region offshore. The model shows that the tides lead to cooling where two criteria are satisfied: the Simpson and Hunter parameter log10(h/U3) <3.2 and the depth h >30 m. The shelf edge of the bank is important for internal tide generation. Two frontal structures result, one offshore between cooler mixed waters and warmer stratified waters and the other in shallow inshore waters, between cooler mixed waters and solar heated mixed waters.

Long-range propagation and associated variability of internal tides in the South China Sea

The variability of internal tides during their generation and long-range propagation in the South China Sea (SCS) is investigated by driving a high-resolution numerical model. The present study clarifies the notably different processes of generation, propagation and dissipation between diurnal and semidiurnal internal tides. Internal tides in the SCS originate from multiple source sites, among which the Luzon Strait is dominant, and contributes approximately 90% and 74% of the baroclinic energy for M2 and K1, respectively. To the west of the Luzon Strait, local generation of K1 internal tides inside the SCS is more energetic than the M2 tides. Diurnal and semidiurnal internal tides from the Luzon Strait radiate into the SCS in a north-south asymmetry but with different patterns because of the complex two-ridge system. The tidal beams can travel across the deep basin and finally arrive at the Vietnam coast and Nansha Island more than 1000-1500 km away. During propagation, M2 internal tides maintain a southwestward direction, whereas K1 exhibit complicated wave fields because of the superposition of waves from local sources and island scattering effects. After significant dissipation within the Luzon Strait, the remaining energy travels into the SCS and reduces by more than 90% over a distance of ∼1000 km. Inside the SCS, the K1 internal tides with long crests and flat beam angles are more influenced by seafloor topographical features and thus undergo apparent dissipation along the entire path, whereas the prominent dissipation of M2 internal tides only occurs after their arrival at Zhongsha Island. This article is protected by copyright. All rights reserved.

Internal waves over the shelf in the western Bay of Bengal: a case study

Generation and propagation of internal waves (IWs) in the coastal waters of the extended shelf of the western Bay of Bengal are investigated for late winter by using the Massachusetts Institute of Technology General Circulation Model (MITgcm). The model is forced with astronomical tides and daily winds. Monthly climatological temperature and salinity fields are used as initial conditions. The simulations are compared with time series observations of temperature and currents from acoustic Doppler current profiler (ADCP) and conductivity-temperature-depth (CTD) moored at three locations south of Gopalpur: two at a local depth of 100 m and another at 400-m depth during 19–21 February 2012. The comparison of the spectral estimates for the time series of temperature from the model and observations are in reasonable agreement for the near-tidal frequency waves. The peak of temperature spectra is always found near the shelf break region which steadily lost its intensity over the continental shelf. The calculation of Richardson number reflected the presence of local mixing due to density overturning in the shelf region. To understand further the generation and propagation of internal tides in the region, energy flux and conversion of barotropic-to-baroclinic M2 tidal energy are examined. The model simulations suggest that the internal tide is generated all along the shelf slope. The energy flux analysis shows that the internal tides propagate to either side of the generation sites.

Tidal energy redistribution among vertical modes in a fluid with a mid-depth pycnocline

We modeled internal tide generation above a high sinusoidal ridge in a fluid with a mid-depth pycnocline and developed an original method to quantify internal tide vertical mode amplitude in two-dimensional-vertical simulations. Since lowest modes can propagate over considerable distances, while high modes are more likely to dissipate locally, estimating the tidal energy distribution among vertical modes is necessary to investigate the spatial redistribution of the tidal energy. Our numerical approach allows expansion and verification of previous analytical studies over a larger range of configurations. The tidal energy distribution among vertical modes is shown here to be dependent on the topographic resonance criterion and the topographic blocking parameter.

An extreme internal solitary wave event observed in the northern South China Sea.

With characteristics of large amplitude and strong current, internal solitary wave (ISW) is a major hazard to marine engineering and submarine navigation; it also has significant impacts on marine ecosystems and fishery activity. Among the world oceans, ISWs are particular active in the northern South China Sea (SCS). In this spirit, the SCS Internal Wave Experiment has been conducted since March 2010 using subsurface mooring array. Here, we report an extreme ISW captured on 4 December 2013 with a maximum amplitude of 240 m and a peak westward current velocity of 2.55 m/s. To the authors’ best knowledge, this is the strongest ISW of the world oceans on record. Full-depth measurements also revealed notable impacts of the extreme ISW on deep-ocean currents and thermal structures. Concurrent mooring measurements near Batan Island showed that the powerful semidiurnal internal tide generation in the Luzon Strait was likely responsible for the occurrence of the extreme ISW event. Based on the HYCOM data-assimilation product, we speculate that the strong stratification around Batan Island related to the strengthening Kuroshio may have contributed to the formation of the extreme ISW.

Using CryoSat‐2 altimeter data to evaluate M2 internal tides observed from multisatellite altimetry

AbstractThis paper evaluates M2 internal tides observed from multisatellite altimetry (MultiSat20yr) using CryoSat‐2 altimeter data. MultiSat20yr is constructed using 20 years of sea surface height measurements made by multiple satellite altimeters from 1992 to 2012. Here it is demonstrated that M2 internal tides can also be extracted using 4 years of CryoSat‐2 data from 2011 to 2014 (CryoSat4yr) by the same plane wave fit method. MultiSat20yr and CryoSat4yr are in good agreement in the central North Pacific, although they are from satellite data of different sampling patterns (1998 versus 10,688 tracks) and different observational periods (20 versus 4 years). Further comparisons are carried out for three isolated wave components. MultiSat20yr and CryoSat4yr agree very well for both Hawaiian components, suggesting that the Hawaiian Ridge is a relatively stable generation site. In contrast, the Aleutian Ridge is a relatively unstable source in that the M2 amplitudes in MultiSat20yr and CryoSat4yr are very different. With respect to MultiSat20yr, the M2 internal tide in 2011–2014 propagates slower (faster) to the south (north) of Hawaii, respectively, suggesting that the internal tide's propagation speed is subject to significant interannual variability. This feature is supported by M2 internal tides observed using multisatellite altimeter data in 2005 (MultiSat2005) and Argo measured upper ocean temperature profiles. MultiSat20yr is used to correct M2 internal tides in the CryoSat‐2 data. Significant and efficient variance reduction suggests that MultiSat20yr is a reliable internal tide model. A phase‐adjusted MultiSat20yr is built to account for the interannual variations, and it works better in internal tide correction.

Internal Tide Generation Using Green Function Analysis: To WKB or Not to WKB?

AbstractAn established analytical technique for modeling internal tide generation by barotropic flow over bottom topography in the ocean is the Green function–based approach. To date, however, for realistic ocean studies this method has relied on the WKB approximation. In this paper, the complete Green function method, without the WKB approximation, is developed and tested, and in the process, the accuracy of the WKB approximation for realistic ridge geometries and ocean stratifications is considered. For isolated Gaussian topography, the complete Green function approach is shown to be accurate via close agreement with the results of numerical simulations for a wide range of height ratios and criticality; in contrast, the WKB approach is found to be inaccurate for small height ratios in the subcritical regime and all tall topography that impinges on the pycnocline. Two ocean systems are studied, the Kaena and Wyville Thomson Ridges, for which there is again excellent agreement between the complete Green function approach and numerical simulations, and the WKB approximate solutions have substantial errors. This study concludes that the complete Green function approach, which is typically only modestly more computationally expensive than the WKB approach, should be the go-to analytical method to model internal tide generation for realistic ocean ridge scenarios.

Variability of nonlinear internal waves in the South China Sea affected by the Kuroshio and mesoscale eddies

AbstractLong‐term observations of nonlinear internal waves in the South China Sea reveal seasonal to interannual variability. During two selected segments of inverted echo sounder observations, tidal forcing in Luzon Strait is almost identical, but the observed amplitudes of nonlinear internal waves in the South China Sea are very different. The effects of the Kuroshio and mesoscale eddies, reproduced by HYbrid Cooridnate Ocean Model (HYCOM) reanalysis simulation, are then investigated. The Kuroshio can enhance the zonal tilt of the thermocline and induce intruding flow in Luzon Strait. During the two selected segments, different thermocline slopes did not significantly change the internal tide generation, but the intruding flow may result in a 11% difference in the amplitude of generated M2 internal tides. During the two selected segments, mesoscale eddies appeared on the path of internal wave propagation, a cold eddy in one case and a warm one in the other. The eddies changed local stratification and induced additional background currents, thus affecting the nonlinear evolution of internal tides. In addition, wave front steering due to the mesoscale eddies dramatically affected the observed amplitude changes of the nonlinear internal waves: the edge, rather than the center, of the nonlinear internal wave front passed through the observational stations, resulting in reduced amplitude in the observations.

Numerical study of the spatial distribution of the M internal tides in the Strait of Sicily

The present study investigates the spatial distribution of the M internal tide in the Strait of Sicily using a three-dimensional sigma coordinate model, the Regional Ocean Modeling System. Realistic topography and stratification from existing observational data were used. The numerical simulations show that there are three distinct sites of strong M internal tide generation, namely the western sill of the Adventure Bank, northwest of Sicily and north of Pantelleria isle. The conversion rate of energy from the M surface to internal tide integrated over the whole model domain amounts to 47.5 MW, 75% of which are found to be generated over the three prominent topographic features mentioned above. The depth- integrated baroclinic energy flux depicts the propagation away from these sites, particularly toward the north and southwest. The maximum flux amplitudes are found in the three main generation sites identified, with the largest value occurring at the narrowest passage through the western sill. A comparison between the model and current-meter measurements at two stations shows reasonable agreement for different depths. The similarities in the spatial distribution of the baroclinic energy flux divergence and the barotropic forcing suggest that the generation of the M internal tide in the Strait of Sicily results primarily from barotropic tidal flow over sloping topography.

Three-dimensional numerical simulation of M2 internal tides in the Luzon Strait

A three-dimensional isopycnic-coordinate internal tidal model is employed to investigate the generation, propagation, vertical structure and energy conversion of M2 internal tides in the Luzon Strait (LS) with mooring observations. Simulated results, especially the tidal current amplitudes, agree well with observations, demonstrating the reasonability and accuracy of the model. Results indicate that M2 internal tides mainly propagate into three directions horizontally, i.e., eastward towards the western Pacific Ocean, westward towards the Dongsha Island and southwestward towards the South China Sea Basin. In the horizontal direction, tidal current amplitudes decrease as distance increases away from the LS; in the vertical direction, they show an obvious decreasing tendency with depth. Between the double ridges of the LS, a clockwise gyre of M2 baroclinic energy flux appears, which is caused by reflections of M2 internal tides at supercritical topographies, and resonance of M2 internal tides happens along 19.5° and 21.5°N due to the heights and separation distance of the double ridges. The total energy conversion in the LS is about 14.20 GW.

Generation and propagation of internal tides and solitary waves at the shelf edge of the Bay of Biscay

AbstractHigh‐frequency mooring data were collected near the northern shelf edge of the Bay of Biscay to investigate the generation and propagation of internal tides and internal solitary waves (ISWs). During spring tide, strong nonlinear internal tides and large amplitude ISWs are observed every semidiurnal tidal period. While onshore propagation was expected since the mooring is located shoreward of the maximum internal tidal generation location, both onshore and seaward traveling internal tides are identified. Within a tidal period at spring tide, three ISW packets are observed. Like internal tides, different ISW packets have opposite (seaward and shoreward) propagating direction. Based on realistic hydrostatic HYCOM simulations, it is suggested that advection by the barotropic tide affects wave generation and propagation significantly and is essential for the seaward traveling internal tides to appear shoreward of their generation location. A two‐layer idealized nonhydrostatic model derived by Gerkema (1996) further confirms the effect of advection on the generation and propagation of internal tides. Moreover, the two‐layer model reproduces one seaward propagating ISW packet and one shoreward propagating ISW packet, indicating that the offshore and onshore traveling ISWs are excited by nonlinear steepening of the seaward and shoreward traveling internal tides, respectively.

An introduction to the physical oceanography of six seamounts in the southwest Indian Ocean

Exploratory surveys of six seamounts in the Southwest Indian Ocean provide a description of physical processes induced by seamounts along the Southwest Indian Ridge. Mean currents (15–25cms−1) in the vicinity of each seamount were dominated by mesoscale eddies. The dominant seamount-driven process was the generation of internal tides by the barotropic tide interacting with the seamount crests. This led to enhanced shear in the vicinity of the crests resulting in mixing where stratification was weak, for example in the core of an anticyclonic mesoscale eddy or where there had been a winter mixed layer. Tidally driven up- and downwelling was observed at the seabed with associated variability in bottom temperature of up to 3°C over a tidal cycle. Vertical displacement of isopycnals by internal tidal waves reached 200m peak to trough. Fluorescence in the surface (eutrophic) layer could thus extend down to the seamount crest on each tidal cycle. Apparently spatial variations in short conductivity/temperature/depth sections across each seamount were probably aliased temporal variations from the strong tidal signal. Evidence for Taylor caps or other potential trapped circulations at the seamount crest was weak, most likely because currents associated with mesoscale eddies were too strong to allow their formation.

Generation of internal tides: An interaction of tides with variable topography and coastal geometry

The paper describes tide-topography interaction with changeable width and angle of continental shelf. Experiments are designed with MITgcm over a study area representative of the western Bay of Bengal with an idealized bathymetry. As the actual coastline consists of an irregular configuration, the experiments are set with different coastline geometry. The tidal forcing is incorporated in the model to generate internal tides by adding tidal components in the momentum equations. The density stratification represents the region during May and is kept invariant for all the experiments. Spectral analysis suggests that semi-diurnal internal tides possess the maximum spectral estimate. The peak semi-diurnal estimate is computed to understand its variation over the shelfslope region. The analysis demonstrates that the estimate is smaller for wider shelves against narrow continental shelves. The peak estimate is observed close to 100m local depth over the shelf regardless of the angle and width. Experiments are further continued to distinguish the effect of rotation and geometry of the coast as the shelf width and shelf angle are kept constant. Comparison of spectral estimate is performed without and with rotation for three different coastline configurations: concave, convex and straight. The estimate is noticed maximum in the concave and minimum in the convex shape of the coast. Significant contribution of the rotational effect is seen as an increase in the semi-diurnal peak estimate towards the north of the domain. In order to confirm the effect of the rotation, a similar experiment is performed for the southern hemisphere revealing an enhancement of the estimate towards the south of the domain.

Structure and Variability of Internal Tides in Luzon Strait

AbstractThe Luzon Strait is the generation region for strong internal tides that radiate westward into the South China Sea and eastward into the western Pacific. Intrusions of the Kuroshio and strong mesoscale variability in the Luzon Strait can influence their generation and propagation. Here, the authors use eight moorings and two numerical models to investigate these relationships by quantifying the coherence of the diurnal and semidiurnal internal tides in the Luzon Strait. This study finds that the level of coherence of internal tide generation, energy, and energy flux is quite variable, depending on the specific location within the Luzon Strait. Large-scale spatial patterns in internal tide pressure and velocity exist across the region, shaped by the bathymetry, mean flow, and stratification. Internal tide coherence is lower (&lt;30%) near large gradients in this pattern (predominantly along the eastern ridge), which are shifted by the variable Kuroshio and mesoscale fields. At other locations within the Luzon Strait, the internal tide is largely coherent (&gt;80%), and simple calculations suggest that remote sources of internal tides could account for these small decreases in coherence. To the west of the Luzon Strait (away from the primary generation regions), the model suggests that diurnal internal tide energy is more coherent than semidiurnal.

Internal tides and associated vertical mixing in the Indonesian Archipelago

AbstractTidal mixing in the Indonesian Archipelago contributes to regulation of the tropical atmospheric circulation and water‐mass transformation in the Indonesian Throughflow. The present study quantifies the vertical diffusivity in the Indonesian Archipelago by driving a high‐resolution three‐dimensional numerical model and investigates the processes of internal tide generation, propagation, and dissipation. The numerical experiment shows that internal tides are effectively generated over prominent subsurface ridges. The conversion rate from barotropic to baroclinic energy over the whole analyzed model domain is estimated to be 85.5 GW. The generated internal tides dissipate 50–100% of their energy in close proximity to the generation sites (“near‐field”), and the remaining baroclinic energy propagates away causing relatively large energy dissipation far from the generation sites (“far‐field”). The local dissipation efficiency q, therefore, has an extremely nonuniform spatial distribution, although it has been assumed to be constant in the existing tidal mixing parameterization for the Indonesian Archipelago. Compared with the model‐predicted values, the existing parameterization yields the same order of vertical diffusivity averaged within the Indonesian Archipelago, but significantly overestimated (or underestimated) vertical diffusivity in the near‐field (or the far‐field). This discrepancy is attributable to the fact that the effects of internal wave propagation are completely omitted in the existing parameterization, suggesting the potential danger of using such parameterized vertical mixing in predicting the distribution of SST as well as water‐mass transformation in the Indonesian Seas.

Characteristics and seasonal variability of internal tides in the southern South China Sea

Two sets of current mooring records at the same location are used to investigate the generation and temporal variation of internal tides (ITs) near reefs in the southern South China Sea (SCS). The total records covered more than 900 days. ITs in this region are dominated by mode-1 diurnal motions, which are mainly composed of O1, P1 and K1 constituents. The major axes of both diurnal barotropic and baroclinic tidal ellipses are oriented in the northeast-southwest direction. The ITs over the entire observation period clearly show an approximately 14-day spring-neap cycle. Meanwhile, the diurnal ITs also displayed an evident seasonal change: their energy was higher in summer and winter than in spring and autumn. The modal decomposition of diurnal motion shows that their time-averaged kinetic energy in summer and winter was about 1.2kJ/m2, which was approximately 60% higher than the values in spring and autumn. The same seasonal variation also occurred at the diurnal barotropic tides with prominent O1, P1 and K1 constituents. Because stratification does not show a significant seasonal variation in the southern SCS, the enhanced diurnal ITs in winter and summer can be attributed to the barotropic forcing with the semi-annual cycle caused by the modulation of diurnal P1 and K1.

The Impact of Subtidal Circulation on Internal-Tide-Induced Mixing in the Philippine Sea

Abstract This study uses a primitive equation model to estimate the time-varying M2 internal tide dissipation in the Philippine Sea in the presence of the subtidal circulation. The time-mean diapycnal diffusivity due to the M2 internal tide is estimated to be 4.0–4.8 × 10−4 m2 s−1 at the Luzon Strait and 2–9 × 10−5 m2 s−1 in the Philippine Sea basin. The variability in internal tides and their interactions with the subtidal ocean circulation results in significant spatial and temporal variability in the energy available for mixing. The subtidal circulation influences internal-tide-induced mixing in two ways: by introducing variability in internal tide generation and by increased dissipation of baroclinic energy associated with greater velocity shear. Close to the generation site, mixing is dominated by high-mode internal tide dissipation, while in the far field the influence of the mesoscale energy on internal tide dissipation is significant, resulting in increased dissipation. This study presents model-based estimates of the important and relatively unknown effect of mesoscale circulation on internal-tide-induced mixing away from internal tide generation sites in a region of high eddy kinetic energy.

Density stratification influences on generation of different modes internal solitary waves

AbstractAn ideal tide‐topography interaction model is utilized for studying the influence of density stratification (pycnocline depth , thickness , and the density difference across the pycnocline) on nonlinear disintegration of the first (mode‐1) and second (mode‐2) baroclinic mode internal tides into internal solitary waves (ISWs). The solution methods include weakly nonlinear analysis and fully nonlinear simulation. It is found that as d increases, even though the energy flux into mode‐1 internal tides is always larger than that into mode‐2 ones at generation, mode‐2 ISWs emerge and mode‐1 ISWs are suppressed. As increases, the total energy conversion and the fluxes into both mode‐1 and mode‐2 tides all increase first and then decrease. During propagation, a thick pycnocline is actually not favorable for the emergence of mode‐2 ISWs, and the simulated well‐developed mode‐2 ISWs for a pycnocline of intermediate thickness are due to the tide generation process. As increases, the total conversion and the fluxes into both mode‐1 and mode‐2 tides all increase almost linearly. Even though the flux into mode‐1 tides is always larger than that into mode‐2 ones at generation, mode‐1 tides cannot disintegrate but mode‐2 ISWs develop very well. During propagation, has no influence on the generation of ISWs. The present work systematically investigates the influence of density stratification on formation of ISWs by considering both internal tide generation and propagation processes.

Theoretical study of the effect of topographic height and width on generation of internal tides

Internal tides generated upon two-dimensional Gaussian topographies of different sizes and steepness are investigated theoretically in a numerical methodology. Compared with previous theoretical works, this model is not restricted by weak topography, but provides an opportunity to examine the influence of topography. Ten typical cases are studied using different values of height and/or width of topography. By analyzing the baroclinic velocity fields, as well as their first eight baroclinic modes, it is found that the magnitude of baroclinic velocity increases and the vertical structure becomes increasingly complex as height increases or width decreases. However, when both height and width vary, while parameter s (the ratio of the topographic slope to the characteristic slope of the internal wave ray) remains invariant, the final pattern is influenced primarily by width. The conversion rate is studied and the results indicate that width determines where the conversion rate reaches a peak, and where it is positive or negative, whereas height affects only the magnitude. High and narrow topography is considerably more beneficial to converting energy from barotropic to baroclinic fields than low and wide topography. Furthermore, parameter s, which is an important non-dimensional parameter for internal tide generation, is not the sole parameter by which the baroclinic velocity fields and conversion rate are determined.