Distribution Of Internal Waves Research Articles

On the steady-state interfacial waves with two-dimensional type-A double exact resonance

Steady-state interfacial waves under two-dimensional (2D) type-A exact triad resonance and other related resonances are researched in a two-layer liquid model with a free surface in contact with air. Five groups (groups 1–5) of convergent series solutions are achieved via the homotopy analysis method. It is found that the phenomenon of double exact resonance could exist in periodic interfacial waves if physical parameters correspond to the intersection of two exact resonance curves. The double exact resonance considered here contains a 2D type-A triad resonance and an other resonance. Under the 2D type-A exact triad resonance, the other resonant triad could obviously enlarge or reduce the wave amplitudes and energy proportions of primary and resonant components. Nevertheless, other resonant quartet, quintet, sextet, and septet all produce no influence on interfacial waves when the 2D type-A exact triad resonance occurs. The above-mentioned results indicate that in the neighborhood of the double exact triad resonance, small perturbations of wave vector of a primary component can cause huge changes on wave profiles of free surface and interface, wave amplitude spectrum, and energy distribution of internal waves in real ocean. In addition, the closer the interfacial waves are to the double exact triad resonance, the more possible energy combinations exist in the wave system, and the greater the number of steady-state interfacial wave solutions. All of this should deepen our understanding of nonlinear resonance interactions in short-crested internal waves.

The Close Relationship between Internal Wave and Ocean Free Surface Wave

A numerical model was used to simulate the propagation of internal waves (IW) along the surface layer. The results show that strong water exchange during IW propagation results in strong free surface flow and produces small but distinct free surface waves. We found a close relationship between the internal and ocean surface waves. Our intuitive reaction is that by training the relationship between the water surface wave height and the internal wave waveform, the internal wave waveform can be reversed from the water surface wave height value. This paper intends to validate our intuition. The artificial neural network (ANN) method was used to train the Fluent simulated results, and then the trained ANN model was used to predict the inner waves below by the free surface wave signal. In addition, two linear internal wave equations (I and II) were derived, one based on the Archimedes principle and the other based on the long wave and Boussinesq approximation. The prediction by equation (II) was superior to the prediction of equation (I), which is independent of depth. The predicted IW of the proposed ANN method was in good agreement with the simulated results, and the predicted quality was much better than the two linear wave formulas. The proposed simple method can help researchers infer the magnitude of IW from the free surface wave signal. In the future, the spatial distribution of IW below the sea surface might be obtained by the proposed method without costly field investigation.

A study of the spatial-temporal distribution and propagation characteristics of internal waves in the Andaman Sea using MODIS

This paper describes investigations of the internal waves in the Andaman Sea using Moderate Resolution Imaging Spectroradiometer (MODIS) imagery over the period of June 2010 to May 2016. Results of the spatial and temporal distribution, generation sources and propagation characteristics of internal waves are presented. The statistical analysis shows that internal waves can be observed in almost the entire area of the Andaman Sea. Most internal waves are observed in the northern, central and southern regions of the Andaman Sea. A significant number of internal waves between 7°N and 9°N in the East Indian Ocean are also observed. Internal waves can be observed year-round in the Andaman Sea, while most of internal waves are observed between February and April, with a maximum frequency of 15.03% in March. The seasonal distribution of the internal waves shows that the internal waves have mostly been observed in the dry season (February to April), and fewer internal waves are observed in the rainy season (May to October). The double peak distribution for the occurrence frequency of internal waves is found. With respect to the lunar influence, more internal waves are observed after the spring tide, which implies the spring tide may play an important role in internal wave generation in the Andaman Sea. Generation sources of internal waves are explored based on the propagation characteristics of internal waves. The results indicate that six sources are located between the Andaman Islands and the Nicobar Islands, and one is located in the northern Andaman Sea. Four regions with active internal wave phenomenon in the Andaman Sea were presented during the MODIS survey, and the propagation speed of internal waves calculated based on the semidiurnal generation period is smaller than the results acquired from pairs of the images with short time intervals.

Studies of Internal Waves in the Strait of Georgia Based on Remote Sensing Images

This paper analyzes over 500 sets of internal waves in the Strait of Georgia (British Columbia, Canada) based on a large number of satellite remote sensing images. The spatial and temporal distribution of internal waves in the central region of the strait are discussed via statistical analysis. Possible generation origins of the observed internal waves are divided into three categories based on their different propagation directions and geographical locations: (1) the interaction between the narrow channels to the south of the Strait and the tidal currents, leading to the formation of mainly eastward and northward propagating waves; (2) the interaction between the tidal currents and the topography near Point Roberts, resulting in mainly westward propagating waves; (3) excitation by river plume, mainly near Fraser River mouth, leading to the formation of mainly westward waves along the direction of the river plume. The relation between the occurrence of internal waves in remote sensing images and wind or tide level is also discussed. It is found that most of the observed internal waves occur at low tides. However, due to the influence of the river, the eastward propagating internal waves near the river mouth seldom occur at the lowest tide. Also, internal waves are captured more easily by remote sensing images in summer due to the lower wind speed than winter and therefore the seasonal distribution of internal waves in remote sensing images may not be able to completely represent the real situation in the study area. Finally, combining the in situ measured data and model output data, the Benjamin-Ono equation is found to satisfyingly simulate the characteristic parameters of the studied internal waves.

Spatial-Temporal Distribution and Characteristics of Internal Waves in the Lombok Strait Area Studied by Alos-Palsar Images

Numerous packets of internal waves were revealed in Advanced Land Observing Satellite Phased Array L-band Synthetic Aperture Radar (ALOSPALSAR) images of the Lombok Strait area, and high-resolution and quick look images were used for their detection and analysis. The parameters of internal waves, such as the number of waves in a packet, crest length, and propagation velocity were estimated from the images. This paper describes the use of PALSAR imagery for internal wave frequency detection and presents the results of a survey that detected 90 internal wave occurrences with ScanSAR and Fine Mode PALSAR imagery over the period May 2006 to April 2011. The paper also discusses the spatial and temporal distribution of internal wave occurrences in the Lombok Strait area.

Influence of stratification and topography upon internal wave spectra in the region of sills

A non‐hydrostatic model in vertical cross section form is used to examine the role of sill width and buoyancy upon the energy cascade into the internal tidal band and higher frequencies in sill regions. Power spectra analysis of computed time series show that as sill width is reduced the energy transfer from the baroclinic tide to its higher harmonics is reduced. However, there is an increase in energy at higher frequencies corresponding to lee wave periods. In addition internal mixing on the lee side of the sill increases. The addition of small scale topography on the sill slope produces a similar spectral change in the internal wave distribution and mixing. For a narrow sill the addition of a surface buoyant layer with a higher buoyancy frequency, significantly reduces the energy cascade to higher frequencies with a corresponding reduction in mixing. The associated spectra have characteristics resembling wide sill topography.

A Case Study of Internal Solitary Wave Propagation During ASIAEX 2001

During the recent Asian Seas International Acoustics Experiment (ASIAEX), extensive current meter moorings were deployed around the continental shelf-break area in the northeastern South China Sea. Thirteen RADARSAT SAR images were collected during the field test to integrate with the in situ measurements from the moorings, ship-board sensors, and conductivity/temperatire/depth (CTD) casts. Besides providing a synoptic view of the entire region, satellite imagery is very useful for tracking the internal waves, locating surface fronts, and identifying mesoscale features. During ASIAEX in May 2001, many large internal waves were observed at the test area and were the major oceanic features studied for acoustic volume interaction. Based on the internal wave distribution maps compiled from satellite data, the wave crests can be as long as 200 km with an amplitude of 100 m. Environmental parameters have been calculated based on extensive CTD casts data near the ASIAEX area. Nonlinear internal wave models have been applied to integrate and assimilate both synthetic aperture radar (SAR) and mooring data. Using SAR data in deep water as an initial condition, numerical simulations produced the wave evolution on the continental shelf and compared reasonably well with the mooring measurements at the downstream station. The shoaling, turning, and dissipation of large internal waves at the shelf break have been studied and are very important issues for acoustic propagation.

Internal wave study in the South China Sea using Synthetic Aperture Radar (SAR)

Internal wave distribution maps have been compiled from more than one hundred ERS-1/2, RADARSAT and Space Shuttle SAR images in the South China Sea (SCS) from 1993 to 2000. Based on these distribution maps, most of the internal waves in the north-east part of the SCS were propagating westward. The wave crest can be as long as 200 km with an amplitude of 100 m, due to strong current from the Kuroshio branching out into the SCS. In a recent SCS internal wave study, moorings were deployed in April 1999 and 2000. Simultaneous SAR coverage from ERS-2 and RADARSAT were also collected. The ERS-2 high-resolution SAR images collected from the Taiwan ground station were processed in near real-time to coordinate the field test. SAR data are then used to compare with mooring data. SAR data and Acoustic Doppler Current Profiler (ADCP) data show internal solitons induced by the semi-diurnal tides with a wave speed of 2.4 m s−1.

Nonlinear internal waves in the South China Sea during ASIAEX

Internal wave distribution maps have been compiled from more than 100 ERS-1/2, RADARSAT and Space Shuttle SAR images in the South China Sea (SCS) from 1993 to 2000. Based on these distribution maps, most of the internal waves in the northeast part of the SCS were propagating westward. The wave crest can be as long as 200 km with an amplitude of 100 m, due to strong current from the Kuroshio branching out into the SCS. In the recent Asian Seas International Acoustics Experiment (ASIAEX), moorings have been deployed in April 2000 and May 2001. Simultaneous RADARSAT ScanSAR images have been collected during the field test to integrate with the model and the in-situ measurements in the SCS. During ASIAEX in May 2001, many large internal waves were observed at the test area and were the major features for acoustic volume interaction. The evolution and dissipation of huge internal waves on the shelf break, mode-two waves, and wave–wave interaction are very important issues for acoustic propagation. Numerical simulations have been performed to produce the wave evolution on the continental shelf and compared with the field measurements. The implication of internal wave effects on acoustic propagation will also be discussed. [Work supported by ONR.]

Moments of internal gravity waves

Observations have revealed the widespread distribution of internal waves in deep oceans, shallow seas, lakes and reservoirs. Much theoretical, numerical, laboratory and field work has studied their generation and propagation, and in particular significant progress has been made in internal solitary wave research. However, statistical properties of internal waves, especially in shallow water, are still little understood. This paper is to investigate the second-, third- and fourth-order moments of internal waves. Results of internal waves in a strong seasonal thermocline of the Yellow Sea are presented and analyzed. It is found that the skewness coefficients are nonzero and the kurtosis coefficients are greater than 3, indicating skewed waveshapes and non-Gaussian distributions of the internal wave elevations. Statistics have been widely used to describe nonbreaking shoaling sea surface waves. It is suggested that the present study on internal gravity waves could be extended to construct nonlinear models for shallow-water internal waves. [Work supported by NSFC.]

Resonance of internal waves in fjords: A finite-difference model

After the time periodicity is removed from the problem, the spatial distribution of internal waves in a stratified fluid is governed by a hyperbolic equation. With boundary conditions specified all along the perimeter of the domain, information is transmitted in both directions (forward and backward) along every characteristic, and, unlike the typical temporal hyperbolic equation, the internal-wave equation is not amenable to a simple forward integration. The problem is tackled here with a finite-difference, relaxation technique by constructing a time-dependent, dissipative problem, the final steady state of which yields the solution of the original problem. Attempts at solving the problem for arbitrary topography then reveal multiple resonances, each resonance being caused by a ray path closing onto itself after multiple reflections. The finite-difference formulation is found to be a convenient vehicle to discuss resonances and to conclude that their existence renders the problem not only singular but also extremely sensitive to the details of the topography. The problem is easily overcome by the introduction of friction. The finite-difference representation of the problem is instrumental in serving as a guide for the investigation of the resonance problem. Indeed, it keeps the essence of the continuous problem and yet simplifies the analysis enormously. Although straightforward, robust and successful at providing a numerical solution to a first few examples, the relaxation component of the integration technique suffers from lack of efficiency. This is due to the particular nature of the hyperbolic problem, but it remains that numerical analysts could improve or replace the present scheme with a faster algorithm.

Interpretation of Internal Wave Measurements in the Presence of Fine-Structure

Abstract Philips has pointed out that the measurement of the internal wave spectrum and coherence in a stratified medium is distinctly altered when the profile contains fine-scale layers. Garrett and Munk demonstrated that the measured spectrum can be explicitly calculated in terms of the internal wave distribution and the statistics of the layered medium with the result P0=P+F, where P is the true spectrum and F the fine-structure contamination. The present study is based on a formal modification of the Garrett and Munk method, tailored to describe a medium for which the layers occur, in effect, as a nonstationary Poisson process in the vertical dimension, i.e., a randomly layered ocean. The fine-structure contamination is discussed in detail for the case of a Gaussian internal wave distribution, with a band-limited power law spectrum P=ω−q for ω1<ω<ωn. Above the cutoff (Vaisala) frequency, ωn, the result is F≈omega;−2, in agreement with Phillips and the “fine-structure approximation” of Garrett and Munk...