Train Of Internal Solitary Waves Research Articles

On the transition from single- to multi-humped internal solitary waves

We provide numerical evidence of the transition from rank-ordered trains of internal solitary waves (ISWs) to multi-humped packets. We ascribe such peculiar and unexplored dynamics to the emergence of a long-range influence among waves, mediated by the hydrodynamic conditions developing in the wake of each ISW and promoting acceleration of the trailing waves. Both the train during the transition and its final multi-humped configuration share hydrodynamic features which are consistent with the recently proposed theory of ISWs propagating through moving stratified environments.

Fiber‐Optic Observations of Internal Waves and Tides

AbstractAlthough typically used to measure dynamic strain from seismic and acoustic waves, Rayleigh‐based distributed acoustic sensing (DAS) is also sensitive to temperature, offering longer range and higher sensitivity to small temperature perturbations than conventional Raman‐based distributed temperature sensing. Here, we demonstrate that ocean‐bottom DAS can be employed to study internal wave and tide dynamics in the bottom boundary layer, a region of enhanced ocean mixing but scarce observations. First, we show temperature transients up to about 4 K from a power cable in the Strait of Gibraltar south of Spain, associated with passing trains of internal solitary waves in water depth <200 m. Second, we show the propagation of thermal fronts associated with the nonlinear internal tide on the near‐critical slope of the island of Gran Canaria, off the coast of West Africa, with perturbations up to about 2 K at 1‐km depth and 0.2 K at 2.5‐km depth. With spatial averaging, we also recover a signal proportional to the barotropic tidal pressure, including the lunar fortnightly variation. In addition to applications in observational physical oceanography, our results suggest that contemporary chirped‐pulse DAS possesses sufficient long‐period sensitivity for seafloor geodesy and tsunami monitoring if ocean temperature variations can be separated.

Time series prediction of shallow water sound speed profile in the presence of internal solitary wave trains

The internal waves, especially the internal solitary wave (ISW) trains, cause violent perturbations of sound speed. Sound speed profile (SSPs) facilitates the pre-understanding of the sound field distribution in the experimental sea, therefore, the real-time prediction of SSPs in the presence of ISW trains are of great significance. In this paper, an orthogonal representation of SSPs that considers the background field (background SSP) variation is proposed. Based on the statistical characteristics of time-series SSPs, high-precision SSP prediction is realized by the long short-term memory recurrent neural network (LSTM). The prediction accuracy is demonstrated with the SSP data from an experiment in the South China Sea, and the mean RMSE of SSP prediction is reduced to about 1 m/s.

High-amplitude internal waves southeast of Spitsbergen

We investigate tidal and higher frequency internal waves southeast of Hopen Island of the Svalbard archipelago using shipborne CTD and ADCP data, model simulations, and satellite observations. The experiment was carried out in the marginal ice zone region. Previous numerical simulations predicted high amplitudes of internal tides here. A series of repeated CTD-casts provide estimates of the vertical displacements of water particles caused by internal waves generated over the continental slope. Peak to peak displacements caused by forced non-propagating internal tides were as high as 50 m. Generation of strong internal tides is also shown based on numerical model revealing high amplitudes (50 m) of vertical displacement over the submarine slope. The development of forced internal tides in the vicinity of the M2 critical latitude is accompanied by generation of short-wave trains of internal solitary waves depicted in satellite observations.

Generation of internal solitary waves over a large sill: From Knight Inlet to Luzon Strait

A fully nonlinear, nonhydrostatic numerical model is utilized to investigate the generation of Internal Solitary Waves (ISWs) upstream of the Knight Inlet sill. While an upstream hydraulic jump initiates the ISW generation and both hydraulic jump and upstream influence contribute to the generation, it is found that upstream influence is dominant and the hydraulic jump is not necessary for the ultimate generation of ISWs. Decreasing the tidal forcing or upstream sill width may render the flow subcritical (i.e., the hydraulic jump disappears) and ISWs can be generated by nonlinear steepening of long wave disturbances induced by upstream influence. Increasing the tidal forcing or upstream sill width may generate a hydraulic jump blocking strong upstream propagating disturbances. The jump subsequently becomes a turbulent bore and later disperses into a train of ISWs as the tide relaxes. Further increase in the tidal forcing may sweep the turbulent bore downstream and a train of ISWs is emitted upstream toward the end of waning tide. By reducing the stratification strength by 1 order of magnitude, the near-sill flow is in the transcritical regime and ISWs are resonantly generated over the lee side slope. Connections to the internal tide release mechanism at Luzon Strait and to the unsteady lee wave model are also discussed. The present work provides some more insights into the ISW generation process at Knight Inlet and the connection between the generation mechanism at Knight Inlet and that at Luzon Strait is identified.

On the generation and evolution of internal solitary waves in the southern Red Sea

Satellite observations recently revealed trains of internal solitary waves (ISWs) in the off-shelf region between 16.0°N and 16.5°N in the southern Red Sea. The generation mechanism of these waves is not entirely clear, though, as the observed generation sites are far away (50 km) from the shelf break and tidal currents are considered relatively weak in the Red Sea. Upon closer examination of the tide properties in the Red Sea and the unique geometry of the basin, it is argued that the steep bathymetry and a relatively strong tidal current in the southern Red Sea provide favorable conditions for the generation of ISWs. To test this hypothesis and further explore the evolution of ISWs in the basin, 2D numerical simulations with the non-hydrostatic MIT general circulation model (MITgcm) were conducted. The results are consistent with the satellite observations in regard to the generation sites, peak amplitudes and the speeds of first-mode ISWs. Moreover, our simulations suggest that the generation process of ISWs in the southern Red Sea is similar to the tide-topography interaction mechanism seen in the South China Sea. Specifically, instead of ISWs arising in the immediate vicinity of the shelf break via a hydraulic lee wave mechanism, a broad, energetic internal tide is first generated, which subsequently travels away from the shelf break and eventually breaks down into ISWs. Sensitivity runs suggest that ISW generation may also be possible under summer stratification conditions, characterized by an intermediate water intrusion from the strait of Bab el Mandeb. This article is protected by copyright. All rights reserved.

Sediment resuspension and nepheloid layers induced by long internal solitary waves shoaling orthogonally on uniform slopes

Two-dimensional, nonlinear and nonhydrostatic field-scale numerical simulations are used to examine the resuspension, dispersal and transport of mud-like sediment caused by the shoaling and breaking of long internal solitary waves on uniform slopes. The patterns of erosion and transport are both examined, in a series of test cases with varying conditions. Shoreward sediment movement is mainly within boluses, while seaward movement is within intermediate nepheloid layers. Several relationships between properties of the suspended sediment and control parameters are determined such as the horizontal extent of the nehpeloid layers, the total mass of resuspended sediment and the point of maximum bed erosion. The numerical results provide a plausible explanation for acoustic backscatter patterns observed during and after the shoaling of internal solitary wavetrains in a natural coastal environment. The results may be useful in the interpretation of some sedimentary structures, and suggest an effective mechanism for offshore dispersal of muddy sediments.

Internal solitary waves in Upper Lake Constance

The conceptual hypothesis that internal solitary waves (ISWs) in lakes are generated at fronts of basin-scale internal waves, propagate until they break at the terminal boundary and extend over the lake width in cross-propagation direction is tested using temperature and current profiles measured in Upper Lake Constance. Trains of ISWs of depression propagate in close association with the front of a Kelvin wave at almost constant phase speed from the main basin of Upper Lake Constance to the western shore of a sub-basin, Lake Uberlingen. The trough of the ISWs extends over the entire basin width in narrow Lake Uberlingen but not in the wider main basin. A substantial part of the ISWs propagating towards the western terminal boundary did not return, suggesting wave-energy loss due to wave breaking. Close to the shorelines parallel to their propagation direction the amplitudes of the ISWs are diminished. Temperature inversions suggest that wave breaking is occurring at these boundaries, but also in the open water where breaking events extend along the width of the ISW front. The heterogeneity of ISW breaking suggests that the associated mixing and vertical fluxes of plankton and nutrients across the thermocline are highly variable in space and time.

Experimental study of the effect of rotation on nonlinear internal waves

Nonlinear internal waves are commonly observed in the coastal ocean. In the weakly nonlinear long wave régime, they are often modeled by the Korteweg-de Vries equation, which predicts that the long-time outcome of generic localised initial conditions is a train of internal solitary waves. However, when the effect of background rotation is taken into account, it is known from several theoretical and numerical studies that the formation of solitary waves is inhibited, and instead nonlinear wave packets form. In this paper, we report the results from a laboratory experiment at the LEGI-Coriolis Laboratory which describes this process.

Numerical simulation of mass transport in internal solitary waves

A computational study of mass transport by large-amplitude, mode-2 internal solitary waves propagating on a pycnocline between two layers of different densities was conducted. The numerical model is based on the simulation of a vorticity-based formulation of the two-dimensional Navier-Stokes equations in the Boussinesq limit. Numerical experiments are conducted of the collapse of an initially mixed region, which leads to the generation of a train of internal solitary waves. The peak wave amplitude, a, is achieved by the leading wave, which encloses an intrusional bulge. The wave amplitude decays as it moves away from the collapsing mixing region. When the amplitude drops below a critical value, the wave is no longer able to transport mass and sharp-nosed intrusion is left behind. Mass transport by the leading wave, and by the trailing wave train and intrusion, is analyzed by tracking the motion of Lagrangian particles initially concentrated in the mixed region. Results indicate that for moderate wave amplitudes, a gradual decay in the wave amplitude occurs as the wave propagates, but the structure of the bulge is essentially maintained during this process. In contrast, for large-amplitude waves, the motion around the bulge is substantially more complex, exhibiting periodic shedding of vortex structures in the wake of the bulge and entrainment of external fluid into its core. It is shown that these motions have substantial impact on mass transport by the wave train, which is quantified through detailed analysis of the Lagrangian particle distributions.

A propagation model for the internal solitary waves in the northern South China Sea

A two‐dimensional, regularized long‐wave equation model is developed to study the dynamic mechanisms of the propagation and evolution of the internal solitary waves (ISWs) in the northern South China Sea (SCS). It is shown that the bottom topography would cause the polarity reversal of ISWs, the change of the local wave crestline shape, and some diminution in wave amplitude; even if the ISWs are induced at the small sill channel along the Luzon Strait, they could propagate westward with their crestlines covering a large area in the latitudinal direction in the northern SCS. When there are two trains of ISWs propagating from the same source site with a time lag but different amplitudes of initial solitons, the latter train of ISWs with a larger amplitude may catch then swallow the former one with a smaller amplitude, and the wave amplitude of the merged ISW train decreases while the wave number increases. When there are two trains of ISWs propagating from the different source sites at the same time with the same amplitude of initial solitons, the crestlines of the two ISW trains may meet and a new leading soliton is induced at the connection point. Once the ISW trains collide with the island, before the island, a weak ISW train is reflected; behind the island, the former crestlines of the ISW train are torn by the island into two new trains, which may reconnect after passing around the island. The propagation direction, the wave amplitude, and the reconnection point of the new merged ISW train behind the island depend on the relative orientation of the original soliton source site to the island.

Solitary wave generation dynamics at Luzon Strait

A high resolution modeling study is undertaken, with a 2.5-dimensional nonhydrostatic model, of the generation of internal waves induced by tidal motion over the ridges in Luzon Strait. The model is forced by the barotropic tidal components K1, M2, and O1. These tidal components, along with the initial density field, were extracted from data and models. As the barotropic tide moves over the Luzon Strait sills, there is a conversion of barotropic tidal energy into baroclinic tidal energy. Depressions are generated that propagate towards the Asian Seas International Acoustics Experiment (ASIAEX) test site on the Chinese continental shelf. Nonlinear effects steepen the depressions, frequency and amplitude dispersion set in, and disintegration into large amplitude solitary waves occurs. The effects of varying the initial density field, tidal component magnitudes, as well as adding a steady background current to represent the occasional excursions of the Kuroshio Current into the strait, are considered. Depressions are generated at each of the two sills in Luzon Strait which radiate away, steepening and evolving into internal solitary wave trains. Baroclinic fluxes of available potential energy, kinetic energy and linear are calculated for various parameter combinations. The solitary wave trains produced in the simulations generally consist of large amplitude wave trains alternating with small amplitude wave trains. During strong tidal flow, Kelvin–Helmholtz type instabilities can develop over the taller double-humped sill. The solitary waves propagating towards the ASIAEX test site have been observed to reach amplitudes of 120–250 m, depending on the tidal strength. ASIAEX observations indicate amplitudes up to 150 m and the Windy Island Experiment (WISE) measurements contain magnitudes over 200 m. The model results yield solitary wave amplitudes of 70–300 m and half widths of 0.60–3.25 km, depending on parameter values. These are in the range of observations. Measurements by Klymak et al. (2006), in the South China Sea, exhibit amplitudes of 170 m, half widths of 3 km and phase speeds of 2.9 m s −1. Model predictions indicate that the solitary waves making up the wave packet each experience different background currents with strong near surface shear. The energy in the leading soliton of the large amplitude wave trains ranges between 1.8 and 9.0 GJ m −1. The smaller value, produced using barotropic tidal currents based on the Oregon State University data base, is the same as the energy estimated to be in a solitary wave observed by Klymak et al. (2006). Estimates of the conversion of barotropic tidal energy into radiating internal wave energy yield conversion rates ranging between 3.6% and 8.3%.

Analytical and Observational Studies of Internal Solitary Waves in the Yellow Sea

Abstract This article presents findings regarding the origination and evolution of a large train of internal solitary waves as observed through Synthetic Aperture Radar (SAR). The internal wave train under study propagates into deeper waters away from the coast and, most important, appears to be generated at a well-defined point along a steep topographic variation. The shallow bottom topography revealed itself in the SAR image and provided the opportunity to determine, with a large level of accuracy, the precise area where an internal bore originated. The bore traveled east and broke up into a train of solitary waves. The packet's phase speed, wave amplitude, mixed-layer depth, and density difference for a two-layer structure were remotely estimated based on measurements made from the SAR image, the knowledge of the local bathymetry, historical climatological data, and a two-layer model. Farther along the propagation path the internal waves exhibited an extremely large degree of dispersion, which was rela...

Large-Amplitude Internal Solitary Waves in the North Equatorial Countercurrent

The analysis of high-resolution oceanographic data referring to velocity measurements carried out by means of a vessel-mounted acoustic Doppler current profiler on 12 November 2000 in the equatorial Atlantic, at 44°W between 4.5° and 6°N, reveals the presence of three large-amplitude internal solitary waves superimposed on the velocity field associated with the North Equatorial Countercurrent (NECC). These waves were found in the deep ocean, more than 500 km off the continental shelf and far from regions of topographic variations. They propagated toward the north-northeast, strongly inclined with respect to the main axis of the NECC and perpendicular to the Brazilian shelf, as well as to the North Brazil Current, and were characterized by maximum horizontal velocities of about 2 m s−1 and maximum vertical velocities of about 20 cm s−1. The large magnitudes of the measured velocities indicate that the observed waves represent disturbances evolving in a strongly stratified ocean. The distance separating the waves (about 70 km) indicates that the observed features cannot be considered as elements of a single train of internal solitary waves. The waves consist, instead, of truly disconnected, pulselike intense solitary disturbances. This behavior, which strongly differs from that typically observed for trains of tidally generated internal solitary waves, indicates that different mechanisms were possibly involved in their generation and/or evolution.

A numerical study of the generation and propagation of internal solitary waves in the Luzon Strait

A new composite model, which consists of a generation model of the internal tides and a regularized long wave propagation model, is presented to study the generation and evolution of internal solitary waves in the sill strait. Internal bores in the sill strait are first simulated by the generation model, and then the internal tidal field outside of the sill region is given as input for the propagation model. Numerical experiments are carried out to study the imposing tide, depth profile, channel width and shoaling effect, etc., on the generation and evolution of internal solitary waves. It is shown that only when the amplitude of internal tide at the forcing boundary of the propagation model is large enough that a train of internal solitary waves would be induced. The amplitude of the imposing tide in the generation model, shoaling effect, asymmetry of the depth profile and channel width have some effects on the amplitude of the induced internal solitary wave. The imposing tidal flow superimposed on a constant mean background flow has a great damping effect on the induced internal waves, especially on those propagate against the background flow direction. The generation and propagation of internal solitary waves in three possible straits among the Luzon Strait are simulated, and the reasons for the asymmetry of their propagation are also explained.

Evidence for the Influence of Atlantic–Ionian Stream Fluctuations on the Tidally Induced Internal Dynamics in the Strait of Messina

Abstract On 24 and 25 October 1995, high-resolution oceanographic measurements were carried out in the Strait of Messina by using a towed conductivity-temperature-depth chain and a vessel-mounted acoustic Doppler current profiler. During the period of investigation the surface water of the Tyrrhenian Sea north of the strait sill was heavier than the surface water of the Ionian Sea south of the strait sill. As a consequence, during northward tidal flow surface water of the Ionian Sea spread as a surface jet into the Tyrrhenian Sea, whereas during southward tidal flow heavier surface water of the Tyrrhenian Sea spread, after having sunk to a depth of about 100 m, as a subsurface jet into the Ionian Sea. Both jets had the form of an internal bore, which finally developed into trains of internal solitary waves whose amplitudes were larger north than south of the strait sill. These measurements represent a detailed picture of the tidally induced internal dynamics in the Strait of Messina during the period of i...

Study of the generation and propagation of internal waves in the Strait of Gibraltar using a numerical model and synthetic aperture radar images of the European ERS 1 satellite

A weakly nonhydrostatic, two‐layer numerical model based on the Boussinesq equations is presented which is capable of describing, among others, the generation and propagation of nonlinear weakly dispersive internal waves in the Strait of Gibraltar. The model depends on one space coordinate only, but it retains several features of a fully three‐dimensional model by including a realistic bottom profile, a variable channel width, and a trapezoidal channel cross section. The nonlinear primitive Boussinesq equations include horizontal diffusion, bottom friction, and friction between the two water layers. The model is driven by a height difference of the mean interface depth between the Atlantic and the Mediterranean boundaries and by semidiurnal tidal oscillations of the barotropic transport. The model presented in this paper describes (1) the mean and tidal flow in the Strait of Gibraltar, (2) the variation of the depth of the interface during a tidal cycle, (3) the generation of strong depressions of the interface at the western sides of the Spartel Sill and the Camarinal Sill, (4) the generation of strong eastward propagating internal bores, and (5) their disintegration into trains of internal solitary waves. The surface convergence patterns associated with depressions of the interface at the Camarinal Sill, internal bores, and internal solitary waves are calculated and compared with roughness patterns visible on synthetic aperture radar (SAR) images of the first European Remote Sensing Satellite ERS 1. In total, 155 ERS 1 SAR scenes from 94 satellite overflights over the Strait of Gibraltar, which were acquired in the period from January 1992 to March 1995, have been analyzed. It is shown that the proposed model is capable of explaining the observed temporal and spatial evolution of surface roughness patterns associated with eastward propagating internal waves inside the Strait of Gibraltar as well as the observed east‐west asymmetry of the internal wave field.

Resonant interaction of sound wave with internal solitons in the coastal zone

Naturally occurring internal solitary wave trains (solitons) have often been observed in the coastal zone, but no reported measurements of such solitary waves include low-frequency long-range sound propagation data. In this paper, the possibility that internal waves are responsible for the anomalous frequency response of shallow-water sound propagation observed in the summer is investigated. The observed transmission loss is strongly time dependent, anisotropic and sometimes exhibits an abnormally large attenuation over some frequency range. The parabolic equation (PE) model is used to numerically simulate the effect of internal wave packets on low-frequency sound propagation in shallow water when there is a strong thermocline. It is found that acoustic transmission loss is sensitive to the signal frequency and is a ‘‘resonancelike’’ function of the soliton wavelength and packet length. The strong interaction between acoustic waves and internal waves, together with the known characteristics of internal waves in the coastal zone, provides a plausible explanation for the observed anomalous sound propagation in the summer. By decomposing the acoustic field obtained from the PE code into normal modes, it is shown that the abnormally large transmission attenuation is caused by ‘‘acoustic mode-coupling’’ loss due to the interaction with the internal waves. It is also shown that the ‘‘resonancelike’’ behavior of transmission loss predicted by the PE analysis is consistent with mode coupling theory. As an inverse problem, low-frequency acoustic measurements could be a potential tool for remote-sensing of internal wave activity in the coastal zone.

A numerical algorithm to study internal solitary waves

This paper presents a finite difference method to solve two coupled, one-dimensional, nonlinear, dispersive, and non-dissipative partial differential equations. They describe the generation and propagation of internal solitary wave trains along the interface of an inviscid two-layer fluid over a variable bottom topography. Since the existence of solitary waves requires a balance between dispersion' and nonlinear effects, great care has been taken to minimize the numerical dispersion which could otherwise overwhelm the mild analytic dispersion and thereby alter the shape and propagation characteristics of the solitary waves. Because the equations contain terms representing continuous forcing and arbitrary bottom topography, we can use the numerical algorithm presented here to study internal solitary waves in a natural fluid environment.

Effect of internal solitons on shallow‐water sound propagation

There have been many reports on observations of naturally occurring internal solitary wavetrains (solitons) in the coast zone, especially in the summer. The mechanism for the generation of these nonlinear internal waves has been investigated in the geophysics and fluid mechanics community. Little attention, however, has been focused on their effect on sound propagation with the exception of the work of Baxter and Orr, which was based on ray theory [L. Baxter and M. H. Orr, J. Acoust. Soc. Am. 71, 61–66 (1982)]. In this paper, the parabolic equation (PE) model (IFD or PAREQ code) is used to numerically simulate the effect of internal solitons on low‐frequency sound propagation in the coast zone. The results show that sound transmission loss is sensitive to soliton parameters (such as wavelength, amplitude, etc.) and wave packet parameters (position, number, and propagation direction). The results can be used to explain, at least partly, an interesting experiment phenomena: The frequency response of shallow‐water sound propagation under the condition of a thermocline during the summer is often a strong function of space and time, and sound propagation over certain frequency ranges has an abnormal attenuation that cannot be explained by using conventional models of sound propagation. [Work supported by ONR.]