Large-amplitude Internal Waves Research Articles

Large-amplitude internal waves benefit corals during thermal stress.

Tropical scleractinian corals are particularly vulnerable to global warming as elevated sea surface temperatures (SSTs) disrupt the delicate balance between the coral host and their algal endosymbionts, leading to symbiont expulsion, mass bleaching and mortality. While satellite sensing of SST has proved a reliable predictor of coral bleaching at the regional scale, there are large deviations in bleaching severity and mortality on the local scale that are poorly understood. Here, we show that internal waves play a major role in explaining local coral bleaching and mortality patterns in the Andaman Sea. Despite a severe region-wide SST anomaly in May 2010, frequent upslope intrusions of cold sub-pycnocline waters due to breaking large-amplitude internal waves (LAIW) mitigated coral bleaching and mortality in shallow waters. In LAIW-sheltered waters, by contrast, bleaching-susceptible species suffered severe bleaching and total mortality. These findings suggest that LAIW benefit coral reefs during thermal stress and provide local refugia for bleaching-susceptible corals. LAIW are ubiquitous in tropical stratified waters and their swash zones may thus be important conservation areas for the maintenance of coral diversity in a warming climate. Taking LAIW into account can significantly improve coral bleaching predictions and provide a valuable tool for coral reef conservation and management.

Experimental study on extracting internal solitary wave in a wind-wave tank of stratified fluid using line array CCD images at the free surface

According to the principles of wind-generating-wave and gravity fluid trapping-motion at the interface respectively, both the small-scale random surface wave and the large-amplitude internal solitary wave can be generated simultaneously in a large wind-wave tank of stratified fluid. The micro-structure variation of the small-scale wave on the surface of water is recoded continuously on a line array CCD image when an internal solitary wave is propagating under the water, and then its influence to the properties of those surface short gravitational waves and capillary waves is analyzed. So the underwater internal solitary wave can be retrieved by analyzing the weak variation of surface-wave field to establish the relation between the features of internal wave elements and CCD grey levels. The obtained results are shown to verity its effectiveness of this experimental method, and also provide a new avenue for the study on the remote sensing of ocean internal dynamics through the practical utilization of surface roughness and stratification properties.

On Stationary Solutions of the Reduced Gardner–Ostrovsky Equation

The detailed analysis of stationary solutions of the reduced Gardner–Ostrovsky (GO) equation is presented. The GO equation is the popular model for the description of large-amplitude internal oceanic waves affected by Earth’s rotation. Its reduced version in which the small-scale dispersion is neglected is used when very long internal waves are considered. The equation is also applicable to other types of nonlinear waves in various media (plasma, optical media, relaxing media, etc.) when the large-scale dispersion plays a dominant role in comparison with the small-scale dispersion. Balancing the nonlinear effect such dispersion gives rise to existence of stationary waves, both periodic and non-periodic. It is shown that only smooth periodic waves make physical sense. Systematic analysis of stationary solutions to the GO equation and their categorisation is presented.

Analysis of kinematic parameters of Internal Solitary Waves in the Northern South China Sea

The monthly climatology of observed temperature and salinity from the U.S. Navy Generalized Digital Environment Model (GDEM-Version 3.0) is used to derive the geographical and seasonal distribution of kinematic parameters of nonlinear internal waves in the Northern South China Sea (NSCS). Coefficients of the Generalized Extended Korteweg-de Vries Equation (GEKdV) with a background current are investigated (phase speed, dispersion, quadratic and cubic nonlinearity parameters, normalizing factor). These parameters are used to evaluate the possible polarities, shapes of internal solitary waves, their limiting amplitudes and propagation speed. We show that the long wave phase speed and dispersion parameters mainly depend on topography characteristics and have no obvious seasonal variation. The nonlinear parameters and normalizing factor are sensitive to variations in the density stratification and topography. Background current also exerts the distinct effects on the kinematic parameters; especially the nonlinear parameter can change by an order of magnitude. The nonlinear parameters take on larger values in the summer (July), and linear internal waves are prone to become steeper and develop into large-amplitude internal solitary waves under such circumstances. This explains why nonlinear internal solitary waves occur more frequently in summer. From the kinematic viewpoint, the dispersion parameter takes on larger values in the Pacific Ocean (PO) due to deeper water depth when compared with that in the NSCS. The stronger dispersion effect in the PO hinders the formation of large amplitude internal solitary waves, explaining why nonlinear internal solitary waves are rarely found to the east of the Luzon Strait. Large near-bottom velocities dominate the shallow area and tend to increase in the warm season. The largest values are induced by internal solitary waves, indicating that internal waves are the major drivers of sediment re-suspension and erosion processes.

Three‐dimensional seismic analysis of sediment waves and related geomorphological features on a carbonate shelf exposed to large amplitude internal waves, Browse Basin region, Australia

AbstractThis study analyses the three‐dimensional geometry of sedimentary features recorded on the modern sea floor and in the shallow subsurface of a shelf to upper slope region offshore Australia that is characterized by a pronounced internal wave regime. The data interpreted comprise an extensive, >12 500 km2 industrial three‐dimensional seismic‐reflection survey that images the northern part of the Browse Basin, Australian North West Shelf. The most prominent seismic–morphological features on the modern sea floor are submarine terrace escarpments, fault‐scarps and incised channels, as well as restricted areas of seismic distortion interpreted as mass wasting deposits. Besides these kilometre‐scale sea floor irregularities, smaller bedforms were discovered also, including a multitude of sediment waves with a lateral extent of several kilometres and heights up to 10 m. These sedimentological features generally occur in extensive fields in water depths below 250 m mostly at the foot of submerged terraces, along the scarps of modern faults and along the shelf break between the outer shelf and the upper continental rise. Additional bedforms that characterize the more planar regions of the outer shelf are elongate, north‐west/south‐east oriented furrows and ridges. The formation of both sediment waves and furrow‐ridge systems requires flow velocities between 0·3 m sec−1 and 1·5 m sec−1, which could be generated by oceanic currents, gravity currents or internal waves. In the studied setting, these velocities can be best explained as being generated by bottom currents induced by internal waves, an interpretation that is discussed against oceanographic background data and modelling results. In addition to the documentation of three‐dimensional seismic–geomorphological features of the modern sea floor, it was also possible to map kilometre‐scale buried sediment wave fields in the seismic volume down to ca 500 ms two‐way‐time below the present sea floor, indicating the general potential for the preservation of such bedforms in the sedimentary record.

Transcritical generation of nonlinear internal waves in the presence of background shear flow

While the occurrence of large amplitude internal waves in the Earth's natural bodies of water is widely documented, the generation of these waves remains an active area of exploration. We discuss numerical simulations of transcritical flows of a density stratified fluid with a dual focus on the role of a background shear current and transitions of the background current from super to subcritical. We demonstrate that the presence of a background shear can lead to the formation of large quasi-trapped regions of high vorticity over the downstream slope of the topography, but that this vorticity leads to only moderate perturbations of the underlying pycnocline, and hence that a wave and instability can co-exist for long times. Subsequently, we demonstrate the existence of hysteresis in the wave amplitude when the current is accelerated to supercritical then decelerated to subcritical, as opposed to accelerated to the subcritical value from rest. Finally, we explore situations in which the background shear is strong enough to preclude the formation of solitary-like waves, and discuss possible implications for the coastal ocean.

Direct breaking of large-amplitude internal waves in the Urup Strait

Observations and model data have been analyzed for the Urup Strait, one of the Kuril Straits, focusing on processes driving the extremely strong vertical mixing. Observations over 1day on the Pacific side of the sill of the Urup Strait show the generation of a large-amplitude internal wave (LAIW), characterized by the depression of potential density surfaces caused by a strong off-sill flow. When the LAIW developed, the potential density surface of 26.7 σθ was depressed downward by more than 300m, and vertical mixing was markedly elevated within the 400-m-thick layer 26.6–26.7 σθ, with a layer-mean (maximum) energy dissipation rate and vertical diffusivity of 1.2×10−6 (7.9×10−6Wkg−1) and 4.0×10−1 (2.8m2s−1), respectively. A three-dimensional model simulation of the Kuril Straits driven by the diurnal barotropic tide reproduces well the observed features relevant to the generation of LAIWs in and around the Urup Strait. The structure and generation pattern of LAIWs in the Urup Strait are consistent with those of the arrested lee waves observed in the Hawaiian ridge and Luzon Strait, although the depth at the top of the sill is far shallower in the Urup Strait. It is suggested that barotropic tidal energy with diurnal frequency is converted into LAIWs through the excitation of topographically trapped waves with hydraulically supercritical velocity near the sill top, and it is these waves that are responsible for the extremely strong mixing on the sill-flanks of the shallow Kuril Straits.

Large-Amplitude Internal Solitary Waves Observed in the Northern South China Sea: Properties and Energetics

Abstract Five large-amplitude internal solitary waves (ISWs) propagating westward on the upper continental slope in the northern South China Sea were observed in May–June 2011 with nearly full-depth measurements of velocity, temperature, salinity, and density. As they shoaled, at least three waves reached the convective breaking limit: along-wave current velocity exceeded the wave propagation speed C. Vertical overturns of ~100 m were observed within the wave cores; estimated turbulent kinetic energy was up to 1.5 × 10−4 W kg−1. In the cores and at the pycnocline, the gradient Richardson number was mostly <0.25. The maximum ISW vertical displacement was 173 m, 38% of the water depth. The normalized maximum vertical displacement was ~0.4 for three convective breaking ISWs, in agreement with laboratory results for shoaling ISWs. Observed ISWs had greater available potential energy (APE) than kinetic energy (KE). For one of the largest observed ISWs, the total wave energy per unit meter along the wave crest E was 553 MJ m−1, more than three orders of magnitude greater than that observed on the Oregon Shelf. Pressure work contributed 77% and advection contributed 23% of the energy flux. The energy flux nearly equaled CE. The Dubriel–Jacotin–Long model with and without a background shear predicts neither the observed APE > KE nor the subsurface maximum of the along-wave velocity for shoaling ISWs, but does simulate the total energy and the wave shape. Including the background shear in the model results in the formation of a surface trapped core.

Experimental investigation of the generation of large-amplitude internal solitary wave and its interaction with a submerged slender body

A principle of generating the nonlinear large-amplitude internal wave in a stratified fluid tank with large cross-section is proposed according to the ‘jalousie’ control mode. A new wave-maker based on the principle was manufactured and the experiments on the generation and evolution of internal solitary wave were conducted. Both the validity of the new device and applicability range of the KdV-type internal soliton theory were tested. Furthermore, a measurement technique of hydrodynamic load of internal waves was developed. By means of accurately measuring slight variations of internal wave forces exerted on a slender body in the tank, their interaction characteristics were determined. It is shown that through establishing the similarity between the model scale in the stratified fluid tank and the full scale in the numerical simulation the obtained measurement results of internal wave forces are confirmed to be correct.

Coral Growth and Bioerosion of Porites lutea in Response to Large Amplitude Internal Waves

The Similan Islands (Thailand) in the Andaman Sea are exposed to large amplitude internal waves (LAIW), as evidenced by i.a. abrupt fluctuations in temperature of up to 10°C at supertidal frequencies. Although LAIW have been shown to affect coral composition and framework development in shallow waters, the role of LAIW on coral growth is so far unknown. We carried out a long-term transplant experiment with live nubbins and skeleton slabs of the dominating coral Porites lutea to assess the net growth and bioerosion in LAIW-exposed and LAIW-protected waters. Depth-related, seasonal and interannual differences in LAIW-intensities on the exposed western sides of the islands allowed us to separate the effect of LAIW from other possible factors (e.g. monsoon) affecting the corals. Coral growth and bioerosion were inversely related to LAIW intensity, and positively related to coral framework development. Accretion rates of calcareous fouling organisms on the slabs were negligible compared to bioerosion, reflecting the lack of a true carbonate framework on the exposed W faces of the Similan Islands. Our findings show that LAIW may play an important, yet so far overlooked, role in controlling coral growth in tropical waters.

Benthic reef primary production in response to large amplitude internal waves at the Similan Islands (Andaman Sea, Thailand).

Coral reefs are facing rapidly changing environments, but implications for reef ecosystem functioning and important services, such as productivity, are difficult to predict. Comparative investigations on coral reefs that are naturally exposed to differing environmental settings can provide essential information in this context. One prevalent phenomenon regularly introducing alterations in water chemistry into coral reefs are internal waves. This study therefore investigates the effect of large amplitude internal waves (LAIW) on primary productivity in coral reefs at the Similan Islands (Andaman Sea, Thailand). The LAIW-exposed west sides of the islands are subjected to sudden drops in water temperature accompanied by enhanced inorganic nutrient concentrations compared to the sheltered east. At the central island, Ko Miang, east and west reefs are only few hundred meters apart, but feature pronounced differences. On the west lower live coral cover (-38 %) coincides with higher turf algae cover (+64 %) and growth (+54 %) compared to the east side. Turf algae and the reef sand-associated microphytobenthos displayed similar chlorophyll a contents on both island sides, but under LAIW exposure, turf algae exhibited higher net photosynthesis (+23 %), whereas the microphytobenthos displayed reduced net and gross photosynthesis (-19 % and -26 %, respectively) accompanied by lower respiration (-42 %). In contrast, the predominant coral Porites lutea showed higher chlorophyll a tissues contents (+42 %) on the LAIW-exposed west in response to lower light availability and higher inorganic nutrient concentrations, but net photosynthesis was comparable for both sides. Turf algae were the major primary producers on the west side, whereas microphytobenthos dominated on the east. The overall primary production rate (comprising all main benthic primary producers) was similar on both island sides, which indicates high primary production variability under different environmental conditions.

On regularizing the strongly nonlinear model for two-dimensional internal waves

To study the evolution of two-dimensional large amplitude internal waves in a two-layer system with variable bottom topography, a new asymptotic model is derived. The model can be obtained from the original Euler equations for weakly rotational flows under the long-wave approximation, without making any smallness assumption on the wave amplitude, and it is asymptotically equivalent to the strongly nonlinear model proposed by Choi and Camassa (1999) [3]. This new set of equations extends the regularized model for one-dimensional waves proposed by Choi et al. (2009) [30], known to be free from shear instability for a wide range of physical parameters. The two-dimensional generalization exhibits new terms in the equations, related to rotational effects of the flow, and possesses a conservation law for the vertical vorticity. Furthermore, it is proved that if this vorticity is initially zero everywhere in space, then it will remain so for all time. This property–in clear contrast with the original strongly nonlinear model formulated in terms of depth-averaged velocity fields–allows us to simplify the model by focusing on the case when the velocity fields involved by large amplitude waves are irrotational. Weakly two-dimensional and weakly nonlinear limits are then discussed. Finally, after investigating the shear stability of the regularized model for flat bottom, the effect of slowly-varying bottom topography is included in the model.

Effect of internal waves on near-surface chlorophyll concentration and primary production in the Nazaré Canyon (west of the Iberian Peninsula)

Internal tidal wave propagation introduces vertical motions within the water column, especially near the pycnocline, forcing water particles to undergo upward and downward motions. Since neutrally buoyant phytoplankton cells are usually passive, these cells can be significantly displaced in the vertical (tens of metres). In this paper we investigate the effects of large-amplitude internal tidal waves on chlorophyll vertical distribution in the region of the Nazaré Canyon west of Portugal, using in-situ and multi-sensor satellite data. The results confirm the occurrence of enhanced levels of chlorophyll detected by a satellite ocean colour sensor that are spatially correlated with internal tides. It is shown that internal tidal waves expose phytoplankton to larger light intensities. Maximum exposure is localised where the internal tide crests occur at noon, but an average increase occurs along the wavelength of a progressive semi-diurnal internal tide during a full day, due to the exponential attenuation of light in the water column. Hence, internal waves can increase the amount of carbon uptake in comparison with an unperturbed water column. The results suggest that internal tidal waves can make a significant impact on biological processes such as primary production, with the generation of local-scale (35km×10km) patchiness of enhanced production on 3–4 day timescales.

Surface Imprints of Water-Column Turbulence: A Case Study of Tidal Flow over an Estuarine Sill

Turbulent mixing in the ocean can, in some cases, be so intense as to leave surface imprints, or “boils”, that are detectable from space. Examples include turbulent flow over a submerged obstacle and instability of large-amplitude internal waves. In this paper we examine the particular case of tidal flow over a ~60-m-deep sill, which forms a barrier for the flow of dense water from the Pacific Ocean into the Strait of Georgia. The flow response during flood tide is illustrated using visible and thermal-band satellite and airborne imagery, the latter having high-resolution multi-looks that capture the formative stage of the boils. The image examples capture aspects of the expected flow response based on in situ measurements reported in the literature, but they also suggest differences, and they reveal the level of complexity of the surface structure. A new result is that, after the front is pushed well off the sill, boils emerge several hundred meters downstream from the sill crest, grow at a rate of ~60 m2/s, and attain a size of 3,800 m2 (an equivalent diameter of 70 m) after one minute. These boils appear to arise from vorticity generated by vertical shear at the sill crest, and provide an additional source of vertical mixing and (through wave breaking) air-sea gas exchange.

The importance of sub-mesoscale processes for the exchange of properties through the Strait of Gibraltar

This article presents a detailed analysis of the sub-mesoscale transport processes in the Strait of Gibraltar. The interest is focussed on the Camarinal Sill region, and special attention is paid to the across-strait transport processes, the divergences and convergences in the central zone, and the small-scale circulation patterns along the northern coastal margin. The analysis is based on high-resolution (7m) SST images acquired by an air-borne hyper-spectral scanner, and has been complemented with a rhodamine-release experiment, continuous thermo-salinograph records, acoustic Doppler current (ADCP) profiles from both moorings and vessel-mounted experiments, and numerical modelling. It is deduced from the analysis that the coupling between the upwelling processes, induced by the internal tide and the generation of large-amplitude internal waves, and the cyclonic eddies formed on the coastal margin, seems to be the mechanism that explains the chlorophyll maxima frequently found on the coastal margin of the studied area. Further, as a consequence of the small-scale patterns of circulation induced by the internal waves, the suspended substances are displaced from the coastal margins toward the central zones and later are carried by the westward current toward the convergence zones created by the internal waves, where they may be retained and accumulate. Then, in the eastward phase of the tidal current over the Camarinal Sill, these nuclei of concentrated substances (nutrients, chlorophyll, and plankton) are transported toward the Alboran Sea, where they must contribute, in part, to the primary productivity there.

Trapped internal waves over topography: Non-Boussinesq effects, symmetry breaking and downstream recovery jumps

It is well-known that in certain parameter regimes, the steady flow of a density stratified fluid over topography can yield large amplitude internal waves. We discuss an embedded boundary method to solve the Dubreil-Jacotin-Long (DJL) equation for steady-state, supercritical flows over topography in an inviscid, stratified fluid. The DJL equation is equivalent to the full set of stratified steady Euler equations and thus the waves we compute are exact nonlinear solutions. The numerical method presented yields far better scaling with increase in grid size than other iterative methods that have been used to solve this equation, and this in turn allows for a more thorough exploration of parameter space. For waves under the Boussinesq approximation, we contrast the properties of trapped waves over hill-like and valley-like topography, finding that the symmetry of freely propagating solitary waves when the stratification is reflected across the middepth is not present for trapped waves. We extend the derivation of the DJL equation to the non-Boussinesq case and discuss the effect of the new, non-Boussinesq terms on the structure of the trapped waves, finding that the sharp transition between large and small amplitude waves observed under the Boussinesq approximation is much more gradual when the Boussinesq approximation is relaxed. Finally, we demonstrate the existence of asymmetric steady states over hill-like topography where the flow is subcritical upstream of the topography but transitions to supercritical somewhere over the hill. Waves in this new class of exact solutions are related to so-called downstream recovery jumps predicted on the basis of hydrostatic (shallow water) theories, but when breaking does not occur the recovery jump does not stop propagating downstream and an asymmetric state across the topography maximum is reached for long times.

Internal waves in the Strait of Gibraltar and their role in the vertical mixing processes within the Bay of Algeciras

This article presents some of the results of an oceanographic survey carried out in the Bay of Algeciras (Strait of Gibraltar) as part of a research project intended to assess the environmental quality of the Bay. One of the most interesting findings was the step-like patterns presented by density profiles within the Bay, which were indicative of notable vertical mixing activity there. The analysis of the observations indicates that those mixing processes may be explained by the interaction between the local internal tide dynamics and the large amplitude internal waves entering the Bay, which seem to originate from the Camarinal Sill region.

The interface mixing layer and the tidal dynamics at the eastern part of the Strait of Gibraltar

A non-hydrostatic numerical model forced by tides has been adapted to the Strait of Gibraltar area to investigate the dynamics of the interface layer in the eastern part of the strait, namely the area that extends from the main sill of Camarinal to the eastern exit of the strait. The model reproduces the tidal oscillations of the interface thickness and the mean depth, showing that the westward barotropic tide raises the interface and reduces its thickness, thus being the physical mechanism that re-stratifies the water column. Several processes are involved in the thickening and sinking tidal phase of the interface: (1) the eastward horizontal advection from Tangier basin, located west of Camarinal sill, where the huge dissipation associated with hydraulic transitions generates a remarkable mixing layer, (2) entrainment as the interface waters progress towards the Mediterranean Sea and (3) internal friction associated with the large amplitude internal waves radiated into the Mediterranean. Some biologically-related implications of the interface dynamics are also examined.

Internal solitary wave transformation over a bottom step: Loss of energy

In this paper, we extend the numerical study of Maderich et al. [“Interaction of a large amplitude interfacial solitary wave of depression with a bottom step,” Phys. Fluids 22, 076602 (2010)10.1063/1.3455984] on the interaction of an interfacial solitary wave with a bottom step, considering (i) the energy loss of solitary waves of both polarities interacting with a bottom step and (ii) features of the transformation of a large-amplitude internal solitary waves at the step. We show that the dependence of energy loss on the step height is not monotonic, but has different maximum positions for different incident wave polarities. The energy loss does not exceed 50% of the energy of an incident wave. The results of our numerical modeling are compared with some recent results from laboratory tank modeling.

Auto- and heterotrophic responses of the coralPorites luteato large amplitude internal waves

Large amplitude internal waves (LAIW) cause frequent and severe changes in the physico-chemical environment of Andaman Sea coral reefs and are a potentially important source of disturbance for corals. To explore the coral response to LAIW, prey capture disposition and photosynthesis were investigated in relation to changes in seawater temperature, pH, flow speed and food availability in LAIW simulation studies under controlled laboratory conditions, using Porites lutea as a model organism. Although food presence stimulated polyp expansion, we found an overriding effect of low temperature (19°C) causing retraction of the coral polyps into their calices, particularly when pH was altered concomitantly. Decreases in pH alone, however, caused the expansion of the polyps. The exposure history of the colonies played a crucial role in coral responses: prior field exposure to LAIW yielded lower retraction levels than in LAIW-inexperienced corals, suggesting acclimatization. Low temperature (19°C) exposure did not seem to influence the photosynthetic performance, but LAIW-experienced corals showed higher values of maximum dark-adapted quantum yield (Fv/Fm) of photosystem II than LAIW-inexperienced controls. Collectively, these data suggest that P. lutea, the dominant hermatypic coral in the Andaman Sea, can acclimatize to extreme changes in its abiotic environment by modulating its mixotrophic nutrition, through polyp expansion and potential feeding, as well as its photosynthetic efficiency.