Unveiling three-dimensional sea surface signatures caused by internal solitary waves:insights from the surface water ocean topography mission

Internal solitary waves(ISW),characterized by large amplitude and long propagation distance,are widespread in global oceans.While remote sensing images have played an essential role in studying ISWs,they mainly exploit two-dimensional image information.However,with the launch of the surface water ocean topography(SWOT)satellite on December 16,2022,a unique opportunity has emerged to capture wide-swath three-dimensional ISW-induced sea surface information.In this study,we examine ISWs in the Andaman Sea using data from the Ka-band Radar Interferometer(KaRIN),a crucial sensor onboard SWOT.KaRIN not only provides backscattering satellite images but also employs synthetic aperture interferometry techniques to retrieve wide-swath two-dimensional sea surface height measurements.Our observations in the Andaman Sea revealed the presence of ISWs characterized by dark-bright strips and surface elevation solitons.The surface soliton has an amplitude of 0.32 m,resulting in an estimation of ISW amplitude of approximately 60 m.In contrast to traditional two-dimensional satellite images or nadir-looking altimetry data,the SWOT mission’s capability to capture threedimensional sea surface information represents a significant advancement.This breakthrough holds substantial promise for ISW studies,particularly in the context of ISW amplitude inversion.

Study of the ability of SWOT to detect sea surface height changes caused by internal solitary waves

Surface Water and Ocean Topography(SWOT)is a next-generation radar altimeter that offers high resolution,wide swath,imaging capabilities.It has provided free public data worldwide since December 2023.This paper aims to preliminarily analyze the detection capabilities of the Ka-band radar interferometer(KaRIn)and Nadir altimeter(NALT),which are carried out by SWOT for internal solitary waves(ISWs),and to gather other remote sensing images to validate SWOT observations.KaRIn effectively detects ISW surface features and generates surface height variation maps reflecting the modulations induced by ISWs.However,its swath width does not completely cover the entire wave packet,and the resolution of L2/L3 level products(about 2 km)cannot be used to identify ISWs with smaller wavelengths.Additionally,significant wave height(SWH)images exhibit blocky structures that are not suitable for ISW studies;sea surface height anomaly(SSHA)images display systematic leftright banding.We optimize this imbalance using detrending methods;however,more precise treatment should commence with L1-level data.Quantitative analysis based on L3-level SSHA data indicates that the average SSHA variation induced by ISWs ranges from 10 cm to 20 cm.NALTs disturbed by ISWs record unusually elevated SWH and SSHA values,rendering the data unsuitable for analysis and necessitating targeted corrections in future retracking algorithms.For the normalized radar cross section,Ku-band and four-parameter maximum likelihood estimation retracking demonstrated greater sensitivity to minor changes in the sea surface,making them more suitable for ISW detection.In conclusion,SWOT demonstrates outstanding capabilities in ISW detection,significantly advancing research on the modulation of the sea surface by ISWs and remote sensing imaging mechanisms.

Strip segmentation of oceanic internal waves in SAR images based on TransUNet

The development of oceanic remote sensing artificial intelligence has made possible to obtain valuable information from amounts of massive data.Oceanic internal waves play a crucial role in oceanic activity.To obtain oceanic internal wave stripes from synthetic aperture radar(SAR)images,a stripe segmentation algorithm is proposed based on the TransUNet framework,which is a combination of U-Net and Transformer,which is also optimized.Through adjusting the number of Transformer layer,multi-layer perceptron(MLP)channel,and Dropout parameters,the influence of over-fitting on accuracy is significantly weakened,which is more conducive to segmenting lightweight oceanic internal waves.The results show that the optimized algorithm can accurately segment oceanic internal wave stripes.Moreover,the optimized algorithm can be trained on a microcomputer,thus reducing the research threshold.The proposed algorithm can also change the complexity of the model to adapt it to different date scales.Therefore,TransUNet has immense potential for segmenting oceanic internal waves.

Dispersion relation of internal waves in thewestern equatorial Pacific Ocean

Based mainly on TOGA-COARE data, that is, the CTD data from R/V Xiangyanghong No. 5 (Pu et al., 1993), the temperature and current data from the Woods Hole mooring and other deep current data, the layered numerical profiles of buoyancy frequency and mean current components are figured out. A numerical method calculating internal wave dispersion relation without background shear current, used by Fliegel and Hunkins (1975), is improved to be fit for the internal wave equation with mean currents and their second derivatives. The dispersion relations and wave functions of the long crested internal wave progressing in any direction can be calculated conveniently by using the improved method. A comparison between the calculated dispersion relation in the paper and the dispersion relation in GM spectral model of ocean internal waves (Garret and Munk, 1972) is performed. It shows that the mean currents are important to the dispersion relation of internal waves in the western equatorial Pacific Ocean and that the currents make the wave progressing co-directional with (against) the currents stretched (shrink). The influence of the mean currents on dispersion relation is much stronger than that of their second derivatives, but that on wave function is less than that of their second derivatives. The influences on wave functions result in the change of vertical wavenumber, that is, making the wave function stretch or shrink. There exists obvious turning depth but no significant critical layer absorption is found.

Dynamical analysis of mesoscale eddy-induced ocean internal waves using linear theories

This study aims to explore generation mechanisms of the ocean internal wave using the dynamical analysis methods based on linear theories. Historical cruise measurements and recent synthetic aperture radar （SAR） observations of mesoscale eddies with diameter of several tens of kilometers to hundreds of kilometers show that the internal wave packets with wavelength of hundreds of meters to kilometer exist inside the mesoscale eddies. This coexistence phenomenon and inherent links between the two different scale processes are revealed in the solutions of governing equations and boundary conditions for the internal wave disturbance with a horizontally slowly variable amplitude in a cylindrical coordinate system. The theoretical solutions indicate that the instability of eddy current field provides the dynamical mechanism to internal wave generation. The derived dispersion relation indicates that the internal wave propagation is modified by the eddy current field structure. The energy equation of the internal waves clearly shows the internal wave energy increment comes from the eddy. The theoretical models are used to explain the observation of the mesoscale eddy-induced internal waves off the Norwegian coast. The two-dimensional waveform solution of the anticyclonic eddy-induced internal wave packet appears as ring-shaped curves, which contains the typical features of eddy stream lines. The comparison of theoretical solutions to the structure of the internal wave packets on SAR image shows a good agreement on the major features.

A parameterization scheme of vertical mixing due to inertial internal wave breaking in the ocean general circulation model

Based on the theoretical spectral model of inertial internal wave breaking （fine structure） proposed previ- ously, in which the effects of the horizontal Coriolis frequency component f-tilde on a potential isopycnal are taken into account, a parameterization scheme of vertical mixing in the stably stratified interior be- low the surface mixed layer in the ocean general circulation model （OGCM） is put forward preliminarily in this paper. Besides turbulence, the impact of sub-mesoscale oceanic processes （including inertial internal wave breaking product） on oceanic interior mixing is emphasized. We suggest that adding the inertial inter- hal wave breaking mixing scheme （F-scheme for short） put forward in this paper to the turbulence mixing scheme of Canuto et al. （T-scheme for short） in the OGCM, except the region from 15°S to 15°N. The numeri- cal results ofF-scheme by usingWOA09 data and an OGCM （LICOM, LASG/IAP climate system ocean model） over the global ocean are given. A notable improvement in the simulation of salinity and temperature over the global ocean is attained by using T-scheme adding F-scheme, especially in the mid- and high-latitude regions in the simulation of the intermediate water and deep water. We conjecture that the inertial internal wave breaking mixing and inertial forcing of wind might be one of important mechanisms maintaining the ventilation process. The modeling strength of the Atlantic meridional overturning circulation （AMOC） by using T-scheme adding F-scheme may be more reasonable than that by using T-scheme alone, though the physical processes need to be further studied, and the overflow parameterization needs to be incorporated. A shortcoming in F-scheme is that in this paper the error of simulated salinity and temperature by using T-scheme adding F-scheme is larger than that by using T-scheme alone in the subsurface layer.

Is the small-scale turbulence an exclusive breaking product of oceanic internal waves

On the basis of the theoretical research results by the author and the literature published up to date, the analysis and the justification presented in this paper show that the breaking products of oceanic internal waves are not only turbulence, but also the fine-scale near-inertial internal waves （the oceanic reversible finestructure） for inertial waves and the internal solitary waves for internal tides respectively. It was found that the oceanic reversible finestructure may be induced by the effect of the horizontal component f （f = 2Ωcosφ） of the rotation vector on inertial waves. And a new instability of the theoretical shear and strain spectra due to the effect of f occurs at critical vertical wavenumber β c ≈ 0.1 cpm. It happens when the levels of shear and strain of the reversible finestructure are higher than those of inertial waves, which is induced by the effect of f along an ＂iso-potential-pycnal＂ of internal wave. If all breaking products of internal waves are taken into account, the average kinetic energy dissipation rate is an order of magnitude larger than the values of turbulence observed by microstructure measurements. The author’s theoretical research results are basically in agreement with those observed in IWEX, DRIFTER and PATCHEX experiments. An important impersonal fact is that on the mean temporal scale of thermohaline circulation these breaking products of internal waves exist simultaneously with turbulence. Because inertial waves are generated by winds at the surface, and internal tides are generated by strong tide-topography interactions, the analysis and justification in this paper support in principle the abyssal recipes Ⅱ：energetics of tidal and wind mixing by Munk Wunsch in 1998, in despite of the results of microstructure measurements for the turbulent kinetic energy dissipation rate and the diapycnal turbulent eddy diffusivity.

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 different conditions are analyzed.This paper lays a foundation for detecting ocean internal waves using convolutional neural networks.

The first quantitative remote sensing of ocean internal waves by Chinese GF-3 SAR satellite

Quantitative analysis and retrieval is given by the State Key Laboratory of Satellite Ocean Environment Dynamics（SOED）,Second Institute of Oceanography（SIO）,State Oceanic Administration（SOA）,China,from the first batch of GF-3 synthetic aperture radar（SAR）data with ocean internal wave features in the Yellow Sea.

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.

Internal solitary wave generation by the tidal flows beneath ice keel in the Arctic Ocean

A series of non-hydrostatic,non-linear numerical simulations were carried out to investigate the generation and evolution of internal solitary waves(ISWs)through the interaction of a barotropic tidal current with an ice keel in the Arctic Ocean.During the interaction process,the internal surge was generated at first,and then the wave gradually steepened due to non-linearity during its propagation away from the ice keel.The internal surge eventually disintegrated into multi-modal and rank-ordered ISW packets with the largest having an amplitude of O(10)m.Sensitivity experiments demonstrated that the ISWs’amplitudes and energy were proportional to the varying ice keel depths and barotropic tidal fl ow amplitudes,but were insensitive to the changing ice keel widths.Typical ISWs can enhance the turbulent dissipation rate of O(10^(-6))W/kg along their propagation path.Further,heat entrainment induced by the wave-ice interaction can reach O(10)MJ/m per tidal cycle.This study reveals a particular ISW generation mechanism and process in the polar ice environment,which could be important in impacting the energy transfer and heat balance in the Arctic Ocean.

Ocean internal waves interpreted as oscillation travelling waves in consideration of ocean dissipation

Most studies of the synthetic aperture radar remote sensing of ocean internal waves are based on the solitary wave solutions of the Korteweg-de Vries （KdV） equation, and the dissipative term in the KdV equation is not taken into account. However, the dissipative term is very important, both in the synthetic aperture radar images and in ocean models. In this paper, the traveling-wave structure to characterize the ocean internal wave phenomenon is modeled, the results of numerical experiments are advanced, and a theoretical hypothesis of the traveling wave to retrieve the ocean internal wave parameters in the synthetic aperture radar images is introduced.

Characteristics of Semi-diurnal Internal Tides in the Western Equatorial Pacific Ocean Around 1°45′S,156°E

The analyses of a data series obtained during TOGA- COARE show the existence of remarkable semi-diurnal intemal tides in the western equatorial Pacific Ocean around 1°45＇S, 156°E. Some characteristic parameters of the internal tides are vertical wavenumber -1.6×10^-3 m^-1, horizontal wavenumber （wavelength） 3.3×10^-2 km^-1 （210 km）, vertical propagation speed -3.8 cm/s and horizontal propagation speed 2.0 m/s. The waveforms propagate downwards slantingly, that is, the wave energy transfers upwards slantingly. Depth-distribution of the＇rotary spectral levels is a saddle-shape. The depths of the trough and the deeper peaks are almost coincident with those of the south boundaries of the South Equatorial Current and the Equatorial Undercurrent, respectively. The mean orientation of the rotary spectral ellipse changes with depth： 30° from north to east at 40 m, and changes into 14° from east to south at 324 m, and generally, it points to northeastward, which indicates ＂that waves come from the southwest.

An Estimation of Internal Soliton Forces on a Pile in the Ocean

Internal soliton forces on oil-platform piles in the ocean are estimated with the Morison Formula. Different from sur- face wave forces, which change only in magnitude along a pile, internal soliton forces can be distributed over the entire pile in the water and they change not only in magnitude but also in direction with depth. Our calculations show that the maximum total force caused by a soliton with its associated current of 2.1 m s-1 is nearly equal to the maximum total force exerted by a surface wave with a wavelength of 300 m and a wave-height of 18 m. The total internal soliton force is large enough to affect the operations of marine oil platforms and other facilities. Therefore, the influence of internal solitons should not be neglected in the design of oil platforms.

On generation source sites of internal waves in the Luzon Strait

This effort aims to determine the generation source sites in the Luzon Strait for energetic, long-crest, transbasin internal waves （IW） observed in the northern South China Sea （NSCS）. The roles of islands distributed on eastern side of the strait, Kuroshio, submarine ridges, shoaling thennocline, and strait configuration played in the IW generation are examined using the cruise data analysis, satellite data interpretation, and dynamical analysis. The islands and channels on eastern side of the strait are excluded from a list of possible IW source sites owing to their unmatched horizontal dimensions to the scale of IW crest line length, and the relative low Reynolds number. The Kuroshio has a potential to be a radiator for the long-crest IW disturbances, meanwhile, the Kurosbio west （east） wing absorbs the eastward （westward） propagating IW disturbance. Namely, the Kuroshio blockades the outside west-east propagating IW disturbances. The 3-D configuration of the Luzon Strait is characterized by a sudden, more than one order widening of the cross-section areas at the outlets on both sides, providing a favorable condition for IW type initial disturbance formation. In the Luzon Strait, the thermocline is featured by a westward shoaling all the year around, providing the dynamical conditions for the amplitude growth （declination） to the westward （eastward） propagating IW type disturbance. Thus, the west slope of western submarine ridge at the western outlet of the Luzon Strait is a high possibility source sites for energetic, long-crest, transbasin IWs in the NSCS. The interpretation results of satellite SAR images during a 13 a period from 1995 to 2007 provide the convincing evidence for the conclusions.

The slanting property of semi-diurnal internal tide propagation in the Pacific Ocean at 1°45′S,156°E

By analyzing a data set collected using a moored instrument array and CTD during TOGA-COARE, it is found that there exist remarkable internal tides in the western equatorial Pacific Ocean around 1°45′S, 156°E, whose horizontal wavenumber （wavelength）, vertical wavenumber, h 156° orizontal propagation speed and vertical propagation speed are 3.3×10^-2 km^-1 （210 km）, - 1.6×10^-3m, 2.0 m/s and -3.8 cm/s, respectively, that is, the waveform propagates downwards slantingly. Moreover, the propagating direction rotates statistically clockwise as the depth increases and its cause is unclear.

Numerical investigation of wake-collapse internal waves generated by a submerged moving body

The state-of-the-art OpenFOAM technology is used to develop a numerical model that can be devoted to numerically investigating wake-collapse internal waves generated by a submerged moving body.The model incorporates body geometry,propeller forcing,and stratification magnitude of seawater.The generation mechanism and wave properties are discussed based on model results.It was found that the generation of the wave and its properties depend greatly on the body speed.Only when that speed exceeds some critical value,between 1.5 and 4.5 m/s,can the moving body generate wake-collapse internal waves,and with increases of this speed,the time of generation advances and wave amplitude increases.The generated wake-collapse internal waves are confirmed to have characteristics of the second baroclinic mode.As the body speed increases,wave amplitude and length increase and its waveform tends to take on a regular sinusoidal shape.For three linearly temperature-stratified profiles examined,the weaker the stratification,the stronger the wake-collapse internal wave.

The Dispersion Relation of Internal Wave Extended-Korteweg-de Vries Equation in a Two-Layer Fluid

To understand the characteristics of ocean internal waves better, we study the dispersion relation of extended-Korteweg-de Vries (EKdV) equation with quadratic and cubic nonlinear terms in a two-layer fluid by using the Poincaré-Lighthill-Kuo (PLK) method which is one of the perturbation methods. Starting from the partial differential equation, the PLK method can be used to solve the dispersion relation of the equation. In this paper, we use PLK method to solve the equation and derive the dispersion relation of EKdV equation which is related to wave number and amplitude. Based on the dispersion relation obtained in this paper, the expressions of group velocity and phase velocity of the equation are obtained. Under the actual hydrological data, the influence of hydrological parameters on the dispersion relation for descending internal wave is discussed. It is hope that the obtained results will be helpful to the study of energy transfer and other internal wave parameters in the future.

PROPAGATION OF INTERNAL INERTIO-GRAVITY WAVE SPECTRA IN VERTICAL WIND SHEAR ENVIRONMENTS

The variation of the spectral structure of the internal inertio-gravity waves (ⅡGWs) propagating in the atmospheric wind shear environments is discussed in this paper. From the hydrodynamic equation set in Boussinesq approximation, a spectral propagation equation ⅡGWs satisfy is derived, then the spectral correspondence in the upper atmosphere is numerically calculated, after a forced spectrum is given as a Van- Zandt one at the lower boundary. The results show that if ⅡGWs do not encounter the critical-layer absorp- tion, then their spectral structure may be not changed significantly; otherwise it may be changed greatly, and a few of spectral components are filtered. Also the isotropy of the assumed VanZandt spectrum is distorted in upward-propagating process. That is the directional filtering effect of the atmospheric wind on the gravity wave spectrum.

INFLUENCE OF OCEAN INTERNAL WAVE ON PROPAGATION OF UNDER-WATER RADIATION NOISE

The underwater acoustic field influenced by a selected ocean internal wavewas computed using the Parabolic Equation (PE) method and split-step difference algorithm in thispaper. Acoustic field is formed by sound source with different frequency covering the range ofradiation noise of ships and submarines. Owing to the adoption of complex variables, sparse matrix,Gaussian source and analysis on the grid size, numerical results are achieved smoothly. The resultsshow that internal wave''s influence on underwater sound can''t be neglected, especially for highersound frequency. So it'' s necessary to take internal wave into account in identifying radiationnoise of ships and submarines, namely for sound intensity, transmission loss and spectra shape.