PROGRESS OF STUDIES ON THE INTERNAL TIDE GENERATED BY THE PASSAGE OF BAROTROPIC TIDE OVER CONTINENTAL SHELF/SLOPE

Various aspects of studies on internal tides are reviewed .Both beam-like structure and modal structure of internal tides may exist in the ocean . Bottom intensifications are caused by many factors .e.g. upstream blocking , which is the result of nonlinear interaction among waves . The energy may decay very fast so that internal tides are mostly locally generated .Internal tides may have considerable residual currents.In a 3-D frame, numerical study revealed that internal waves may interfere with each other to cause strong motions fer from the generation sources.The mechanism that determines how the lee waves break to form various nonlinear waves such as solitary waves, hydraulic jumps and internal surges or bores remains unclear. Analytic study is difficult , so numerical method may be effective . A radiation condition on the open boundary must be employed. A complete 3-D model may gain interesting result.Study on internal tides in China is limited to field observations and data analysis .     

Distribution of vertical turbulent mixing parameter caused by internal tidal waves and solitary waves in the South Yellow Sea

Many observations show that in the Yellow Sea internal tidal waves (ITWs) possess the remarkable characteristics of internal Kelvin wave, and in the South Yellow Sea (SYS) the nonlinear evolution of internal tidal waves is one of the mechanisms producing internal solitary waves (ISWs), which is different from the generation mechanism in the case where the semidiurnal tidal current flows over topographic drops. In this paper, the model of internal Kelvin wave with continuous stratification is given, and an elementary numerical study of nonlinear evolution of ITWs is made for the SYS, using the generalized KdV model (GKdV model for short) for a continuous stratified ocean, in which the different effects of background barotropic ebb and flood currents are considered. Moreover, the parameterization of vertical turbulent mixing caused by ITWs and ISWs in the SYS is studied, using a parameterization scheme which was applied to numerical experiments on the breaking of ISWs by Vlasenko and Hutter in 2002. It is found that the vertical turbulent mixing caused by internal waves is very strong within the upper layer with depth less than about 30m, and the vertical turbulent mixing caused by ISWs is stronger than that by ITWs.     

STATISTICAL PROPERTIES OF HIGH-FREQUENCY INTERNAL WAVES IN QINGDAO OFFSHORE AREA OF THE YELLOW SEA

Densely-sampled thermistor chain data obtained from a shallow-water acoustics experiment in the Yellow Sea off the coast of Qingdao were analyzed to examine the statistical properties of the 6 to 520 cpd frequency band internal waves observed. The negative skewness coefficients and the greaterthan-3 kurtosis coefficients indicated non-Gaussianity of the internal waves. The probability distributions were negatively skewed and abnormally high peaks. Nonlinear properties, as exemplified by the asymmetric waveshapes of the internal waves in the offshore area are described quantitatively.     

Propagation of internal waves up continental slope and shelf

In a two-dimensional and linear framework, a transformation was developed to derive eigensolutions of internal waves over a subcritical hyperbolic slope and to approximate the continental slope and shelf. The transformation converts a hyperbolic slope in physical space into a flat bottom in transform space while the governing equations of internal waves remain hyperbolic. The eigensolutions are further used to study the evolution of linear internal waves as it propagates to subcritical continental slope and shelf. The stream function, velocity, and vertical shear of velocity induced by internal wave at the hyperbolic slope are analytically expressed by superposition of the obtained eigensolutions. The velocity and velocity shear increase as the internal wave propagates to a hyperbolic slope. They become very large especially when the slope of internal wave rays approaches the topographic slope, which is consistent with the previous studies.     

AN EXACT SOLUTION OF SUB-INERTIAL FREQUENCY BAROCLINIC WAVES

By using a coordinate transformation, an exact solution of internal tides with sub-inertial frequency isobtained when the bottom slope is linear and the Vaisala frequency is constant. Accordingly thedispersion relations of free waves are presented. This solution is suitable for general coastal low-frequencybaroclinic waves with zero alongshore wavenumber.     

Depression and elevation internal solitary waves in a two-layer fluid and their forces on cylindrical piles

Both large amplitude depression and elevation internal solitary waves (ISWs) were observed on the continental shelf of the northwest South China Sea (SCS) during the Wenchang Internal Wave Experiment. In this study, we investigate the characteristics of depression and elevation ISWs based on comparisons between observational results and internal wave theories. It is suggested that the large amplitude depression wave is better represented by the extended Korteweg-de Vries (EKdV) theory than by the KdV model, whereas the large amplitude elevation wave is in better agreement with the KdV equation than with the EKdV theory. Wave-induced forces on a supposed small-diameter cylindrical pile by depression and elevation waves are also estimated using the internal wave theory and Morison formula. The wave-induced force by elevation ISWs is rarely reported in the literature. It is found that the force induced by the elevation wave differs significantly from that by the depression wave, and the elevation wave generally produces greater force on the pile in the lower water column than the depression wave. These results show that ISWs in the study area can present a serious threat to ocean engineering structures, and should not be ignored in the design of oil platforms and ocean operations.     

INTERNAL WAVE EIGENMODES AND THEIR WEAK NONLINEAR RESONANT INTERACTION IN A NONLINEARLY STRATIFIED FLUID- A PRELIMINARY THEORETICAL AND EXPERIMENTAL STUDY

A preliminary theoretical and experimental study was conducted on internal wave modes and their weak nonlinear resonant interaction in a nonlinearly stratified fluid . An asymptotical solution of the modes and a dispersion relation of internal waves in a stratified fluid with density profile similar to that in our experiment were obtained theoretically . The resonant-interaction mechanism to 2nd order approximation is also discussed . The resonant interaction of the 3rd and 4th mode internal waves excited by the unstable 1st mode wave is analyzed on the basis of data obtained by conductivity probes. The resonant-interaction condition, , is examined . It is shown that the resonant instability increases with pycnocline thickness and wave maker driving frequency .     

Scattering process of internal waves propagating over a subcritical strait slope onto a shelf region

The scattering process, which means the redistribution of energy fluy in modenumber space, is analyzed for internal waves propagating from the abyssal ocean onto a subcritical strait slope and then a shelf region. In light of Wunsch＇s work, the waves are analytically expressed as superimposition of eigensolutions distribution of energy flux in the shelf region： one is the ratio of water depth in and the other is the ratio of the slope of the internal tide rays to the topographic energy flux distribution： the energy flux is focused around one modenumber or case, the range of modenumbers where energy flux is distributed is narrow. Two parameters have evident effects on the the shelf region to that in the abyssal ocean slope. Generally, there are two patterns of focused around two modenumbers. In any case, the range of modenumbers where energy flux is distributed is narrow.     

AN EXACT SOLUTION OF INTERNAL TIDES GENERATED AT CONTINENTAL SLOPE

By using a coordinate transformation,an exact solution of internal tides is obtained when the bot- tom slope is linear and the V(?)is(?)la frequency is constant.Consequently the dispersion relations of free waves are presented.Compared with Baines solution,the solution derived here is more consistent with experiment     

Stress analysis of top tensioned riser under random waves and vessel motions

The bending stresses of top tensioned riser(TTR)under combined excitations of currents, random waves and vessel motions are presented in this paper, and the effect of the internal flowing fluid on the riser stresses is also considered. The computation programs which are used to solve the differential equations in the time domain are compiled and the principal factors of concern including the angular movements at the upper and lower ends of the riser, lateral displacements and bending stresses are presented. Then the effects of current velocity, random wave, top tension, vessel mean offset, low frequency motion and internal flow velocity on the bending stresses of the riser are analyzed in detail.     

Detection of ocean internal waves based on Faster R-CNN in SAR images

Ocean internal waves appear as irregular bright and dark stripes on synthetic aperture radar(SAR) remote sensing images. Ocean internal waves detection in SAR images consequently constituted a difficult and popular research topic. In this paper, ocean internal waves are detected in SAR images by employing the faster regions with convolutional neural network features(Faster R-CNN) framework; for this purpose, 888 internal wave samples are utilized to train the convolutional network and identify internal waves. The experimental results demonstrate a 94.78% recognition rate for internal waves, and the average detection speed is 0.22 s/image. In addition, the detection results of internal wave samples under dif ferent conditions are analyzed. This paper lays a foundation for detecting ocean internal waves using convolutional neural networks.     

A continuously stratified nonlinear model for internal solitary waves in the northern South China Sea

A continuously stratified nonlinear model is set up to study the impact of topographical character on the generation of internal solitary waves over a sill by tidal flow. One of the reasons why almost all of the generated internal solitary waves propagate westward in the northern South China Sea is explained. The model simulations describe the generation and propagation of internal waves well. When the strength of imposed barotropic tides and the water stratification stay unchanged, the steepness of the sill slope can control both (a) whether or not the waves induced over a sill by tidal flow are linear internal waves or nonlinear internal solitary waves, and (b) the amplitude of the internal solitary waves generated. If the steepness of the sill is asymmetric, the nonlinear internal solitary waves may be induced on the steeper side of the sill. These conclusions are supported by a numerical experiment with a monthly-mean stratification and an actual seafloor topography from the Luzon Strait.     

An investigation of the properties of low-frequency internal waves in the northeastern China Seas

A simple and practical method for separating low-frequency internal waves from low-frequency barotropic waves was employed to analyze the observation data. Analysis of some data gathered in the northestern China Seas revealed strong semidiurnal internal tides and near-inertial internal waves at the stations in the East China Sea and near-inertial waves but no semidiurnal internal tides at the station in the centre of the Yellow Sea. The geographic properties of low-frequency internal waves in the region are discussed primarily on the basis of the mechanism of internal tide generation on the continental shelfbreak, and the mechanisms of local generation and global generation. Project supported by the National Natural Science Foundation of China.     

A TWO-DIMENSIONAL VORTICITY MODEL OF INTERNAL TIDES GENERATED ON THE CONTINENTAL SHELF/SLOPE

A two-dimensional spectral-difference mode (with vorticity and density equations) of internal tides isdeveloped for studying the genration and propagration of internal tides generated at the continentalshelf/slope. In general, internal tides propagate seaward in deep sea regions and shoreward on the shelf,and are dissipated rapidly. When the Vaisala frequency decreases vertically, waves may be mostly limited to thecontinental slope region. in deep sea region, motions may have either boam-like structure or modal structure,depending on the stratification strerigth and structure, whereas a modal structure may always exist onthe shelf. Waves show strong bottom intensification on the slope when strong stratification exists on thebottom. The barotropic tidal advection may affed the temporal character of internal tides at thecontinental slope, shelf break and shelf regions. but may have little influence on the energy density and energy flux of internal tides. ln the case of strong stratification, waverforms of     

Modification on Lynett and Liu’s model for internal solitary wave propagation over variable bathymetry

1 INTRODUCTION As an important wave phenomenon, taking place inside the ocean, the internal wave has drawn attentions of many scientists. More and more in- formation about it have been provided by both CTD and ADCP data and the images captured by the synt…     

Internal wave eigenmodes and their weak nonlinear resonant interaction in a nonlinearly stratified fluid—A preliminary theoretical and experimental study

A preliminary theoretical and experimental study was conducted on internal wave modes and their weak nonlinear resonant interaction in a nonlinearly stratified fluid. An asymptotical solution of the modes and a dispersion relation of internal waves in a stratified fluid with density profile similar to that in our experiment were obtained theoretically. The resonant-interaction mechanism to 2nd order approximation is also discussed. The resonant interaction of the 3rd and 4th mode internal waves excited by the unstable 1st mode wave is analyzed on the basis of data obtained by conductivity probes. The resonant-interaction condition, i.e., ,k ₁+k ₃+k ₄=0, is examined. It is shown that the resonant instability increases with pycnocline thickness and wave maker driving frequency. This work is supported by the National Natural Science Foundation of China.     

Study on internal waves generated by tidal flow over critical topography

Resonance due to critical slope makes the internal wave generation more effectively than that due to supercritical or subcritical slopes(Zhang et al., 2008). Submarine ridges make a greater contribution to ocean mixing than continental margins in global oceans(Müller, 1977; Bell, 1975; Baines, 1982; Morozov, 1995). In this paper, internal wave generation driven by tidal flow over critical topography is examined in laboratory using Particle Image Velocimetry(PIV) and synthetic schlieren methods in synchrony. Non-tidal baroclinic velocities and vertical isopycnal displacements are observed in three representative regions, i.e., critical, outward-propagating, and reflection regions. Temporal and spatial distributions of internal wave rays are analyzed using the time variations of baroclinic velocities and vertical isopycnal displacement, and the results are consistent with those by the linear internal wave theory. Besides, the width of wave beam changes with the outward propagation of internal waves. Finally, through monitoring the uniformly-spaced 14 vertical profiles in the x-z plane, the internal wave fields of density and velocity fields are constructed. Thus, available potential energy, kinetic energy and energy fluxes are determined quantitatively. The distributions of baroclinic energy and energy fluxes are confined along the internal wave rays. The total depth averaged energy and energy flux of vertical profiles away from a ridge are both larger than those near the ridge.     

A numerical study on the generation of a distinct type of nonlinear internal wave packet in the South China Sea

A distinct type of nonlinear internal-wave packet, with the largest internal solitary wave in the middle of the packet, was regularly observed in the South China Sea during the Asian Seas International Acoustics Experiment in 2001. Data analysis shows that the occurrence of the distinct internal wave packet is closely related with the occurrence of lower-high internal tides; the internal tides are mixed in the experimental area and, thus, there is diurnal inequality between the heights of two neighboring internal tides. Modeling of internal tides and internal solitary waves in a shoaling situation suggests that this type of wave packet can be generated in the South China Sea by the large shoaling of internal solitary waves and internal tides. Both the internal solitary waves and the internal tides come from the direction of Luzon Strait. The initial large internal solitary waves contribute to the occurrence of the largest internal solitary wave in the middle of the packet and the waves behind the largest internal solitary wave, while the shoaling internal tides bring about the nonlinear internal waves in front of the largest internal solitary wave via interaction with the local shelf topography.     

NLS EQUATION OF INTERNAL WAVES IN WEAKLY STRATIFIED OCEAN

The NLS (Non-Linear Schr(?)dinger) equation of internal waves in a wekly stratified ocean is der-ived in phase coordnates in terms of the RPM (Reductive Perturbation Method). It was shown thatwhen AB>0 there exist modulation forms of envelope soliton and dn, and tha when AB<0 there arethree modulation forms dark soliton, sn and cn. Only if K~2>B/A(?) . the side-band perturbation is stable,otherwise unstable. For the stable side-band perturbation there ekisis a modulation form of MdV soliton.     

Thermal lenses and internal solitons in Chapala Lake, Mexico

INTRODUCTIONThelargestlakeinMexicoandthirdlargestinLatinAmerica,ChapalaLake(approximately2 0°N) ,is 1 50 0mabovesealevel,measures 75× 2 5km ,hasaveragedepthof6m (maximumdepthcloseto 1 1m)andamountainchainalongitsnorthernandsouthernshores (Fig .1a) .TheLermaRiverflowsintoit;theSantiagoRiverflowsoutofit.Thebeautifullandscape,andwarmclimateconducivetobreezecirculationalongitsshore ;absenceofabrupttemperaturevariations,andthemoderateairhumidityat tractmanytouriststothelake .Manyretirees…