Internal Solitary Waves Research Articles

Influence of the internal solitary waves on the deep sea mining system

The South China Sea is rich in mineral resources, and the prospect of developing seabed mineral resources in the South China Sea is bright. However, the South China Sea is also famous for the active internal solitary waves, the researchers detected an internal solitary waves with an amplitude of 240 m and a peak velocity of 2.55 m/s in this area, which may severely impact the deep sea mining system. In this paper, we first simplify the vector finite element method's calculation process. Then the improved vector form intrinsic finite element method is used to simulate the installation process and normal working state of the deep sea mining systems under the action of internal solitary waves. The influence of the internal solitary waves on the deep sea mining systems in the installed state is limited, and its displacement and internal force changes are controllable. Still, the internal solitary waves may cause extensive movement or 180° bends in deep sea mining systems during installation. Necessary measures must be taken during installing deep sea mining systems to reduce the effects of internal solitary waves.

High-resolution, non-hydrostatic simulation of internal tides and solitary waves in the southern East China Sea

The slope area northeast of Taiwan Island in the southern East China Sea (ECS) is well known as a hotspot for both internal tides and internal solitary waves (ISWs) despite uncertainties regarding their specific source and generation mechanism. This study investigates the generation and evolution processes of internal tides and ISWs northeast of Taiwan Island in the southern ECS, based on a super-high-resolution and non-hydrostatic numerical simulation. ISWs create a complex spatial pattern in both satellite images and our simulation, with wave propagation in multiple directions, including onshore and offshore. These ISWs, with the largest amplitudes reaching ∼50 m, are mainly generated by two mechanisms: local tide-topography interactions and disintegration of internal tides remotely generated over I-Lan Ridge. Locally generated ISWs propagate in various directions owing to the complex topography, whereas ISWs generated by the disintegration of remote internal tides are more consistent in their pathways. Strong barotropic to baroclinic energy conversions occur over both Mien-Hua Canyon and North Mien-Hua Canyon. For the baroclinic tidal energy fluxes, the advection flux is comparable to the pressure-work term in shallow water, while the pressure-work flux dominates in deep water. The nonlinear energy flux terms in shallow water are more important for the supertidal than the tidal signals. The semidiurnal energy flux features a clockwise pattern over the double-canyon region, indicating the formation of partial standing waves.

Detection of an internal solitary wave by the underwater vehicle based on machine learning

A new hydrodynamic artificial intelligence detection method is proposed to realize the accurate detection of internal solitary waves (ISWs) by the underwater vehicle. Two deep convolution neural network structures are established to predict the relative position between the underwater vehicle and ISW and the flow field around the underwater vehicle. By combining field observation data and the computational fluid dynamics method, accurate numerical simulation of the motion of the underwater vehicle in a real ISW environment is achieved. The training process for the neural network is implemented by building a dataset from the above results. It is shown that the position prediction accuracy of the network for ISW is larger than 95%. For the prediction of the flow field around the underwater vehicle, it is found that the addition of the convolutional block attention module can increase the prediction accuracy. Moreover, the reduction of the number of sensors by the dynamic mode decomposition method and k-means clustering method is realized. The accuracy can still reach 92% even when the number of sensors is reduced. This study is the first to use hydrodynamic signals for the detection of ISW, which can enhance the navigation safety of underwater vehicles.

Satellite data-driven and knowledge-informed machine learning model for estimating global internal solitary wave speed

Internal solitary waves (ISW) are widely distributed worldwide and significantly affect the ocean environment and offshore activities. ISW propagation speed is important for ISW forecasts and varies largely globally. This study collected 810 quasi-synchronous optical satellite images with clear ISW signatures in 13 global hotspots to build a large ISW dataset. ISW speed was calculated using extracted ISW wave crest locations and the time difference between satellite image pairs. The dataset contains 57,196 samples, including extracted ISW wave crests and corresponding ISW phase speed. We developed an ISW propagation speed (IPS) model based on the dataset using machine learning techniques. The model structure includes clustering and regression algorithms. The model adopts two tailored modifications to incorporate the ISW domain knowledge and solve the ISW sample distribution imbalance problems. Implementation domain knowledge (IDK) includes selecting relevant ocean factors and ISW properties based on oceanography theory and remote sensing imaging mechanisms. The second tailored modification is adopting advanced model architecture (AMA) by introducing the Gaussian clustering algorithm to classify ISW samples into several groups beyond the limitation of space and time. The extreme gradient boosting regression algorithm was applied in each group to build the IPS model. We used 47,425 samples as the training dataset and the remaining 9771 samples as the test dataset. The model-predicted ISW speed shows good accuracy, with a root mean square error/relative error rate (RER) of 0.16 (7.9) and 0.30 m/s (12.7%) on the training and test dataset. Analysis shows that IDK and AMA improve the model performance by 19.4% and 13.1%, respectively. With a one-pixel error in the peak-to-peak distance of input parameters, the model results degraded from 0.30 m/s to 0.33 m/s. The IPS model was applied to estimate ISW speeds in ocean regions besides the 13 hotspots, and the average RER is 6.0%. ISW forecast in seven ocean areas was tested, and the results indicate that the IPS model can describe ISW propagation patterns. The model results reveal that the ISW phase speed strongly correlates with the spring and neap tide. The IPS model results show that ISW speed is decreased with a deepening stratification. Model-predicted global ISW propagation speed comparison shows that the Celebes Sea and North-West of South America has the fastest and slowest propagating ISWs all year around, respectively. Discussion on the background current's influence on the IPS model results is presented.

Three-dimensional structures of internal solitary waves in the northern south China sea revealed by mooring array observations

The data collected from an array of five subsurface moorings, which are deployed along the direction of internal solitary wave (ISW) crests in the northern South China Sea (SCS) from October 2013 to June 2014, are used to investigate the three-dimensional structures of ISWs and their temporal variabilities. The measurements reveal that the ISWs are asymmetric along their crests, with the average amplitude in the southern portion being 70% larger than that in the northern portion. The observed three-dimensionally integrated energy and flux of ISWs are accurately calculated for the first time, reaching 53 TJ and 0.82 GW, respectively, on average. Over the whole observation period, the pattern of ISW crests was dominantly convex, accounting for 76.2% of all observed episodes. However, due to the changes in propagation speeds along the direction of ISW crests caused by either single or combined effects of mesoscale eddies and intruded Kuroshio, the ISW crests could deform into S-shaped and concave patterns, which accounted for 19.6% and 4.2%, respectively. Moreover, during November and December, the positions of the largest amplitude along ISW crests mostly shifted from the southern portion to the northern portion due to the energy refraction caused by mesoscale eddies, leading to the increase/decrease in wave intensity in the northern/southern portion. In early February, the intruded Kuroshio remarkably shifted ISW energy southward, which increased the wave amplitude in the southern portion by as much as 96%. These results clearly demonstrate that the intensities of three-dimensional ISWs could temporally vary out of phase between the northern and southern portions of crests due to the remarkable modulations by intense background processes.

Prediction of shear stress induced by shoaling internal solitary waves based on machine learning method

Recently, the interactions between internal solitary waves (ISWs) and the seabed have directed increasing attention to ocean engineering and offshore energy. In particular, ISWs induce bottom currents and pressure fluctuations in deep water. In this paper, we propose a method for predicting the shear stress induced by shoaling ISWs based on machine learning, and the developed approach can be used to quickly determine the safety and stability of ocean engineering. First, we provided a basic dataset for model training. Four machine learning models were selected to predict the shear stress induced by shoaling ISWs under different trim conditions. The results indicated that the performance of the convolutional neural network-long short-term memory (CNN-LSTM) forest prediction model was significantly better than the three other tested models, including long short-term memory (LSTM), support vector regression (SVR) and deep neural network (DNN) models. Therefore, the CNN-LSTM forest prediction model was the optimal model for predicting the shear stress induced by shoaling ISWs. Specifically, each metric of the CNN-LSTM model was smaller than that of the other three, and the root mean squared error to the standard deviation ratio was closest to 0.7. In addition, the CNN-LSTM model significantly outperformed the SVR and DNN models in terms of the length of prediction time. The predicted values by the CNN-LSTM model were consistent with the experimental values. The method for predicting shear stress based on machine learning in this paper can be used to predict the shear stress induced by shoaling ISWs, guide future field experiment designs, reduce damage to the seabed caused by ISWs, and promote the development of ocean engineering in deep water.

Submarine Trenches and Wave-Wave Interactions Enhance the Sediment Resuspension Induced by Internal Solitary Waves

Submarine Trenches and Wave-Wave Interactions Enhance the Sediment Resuspension Induced by Internal Solitary Waves

Internal Solitary Waves in the White Sea: Hot-Spots, Structure, and Kinematics from Multi-Sensor Observations

A detailed picture of internal solitary waves (ISWs) in the White Sea is presented based on an analysis of historical spaceborne synthetic aperture radar (SAR) data and field measurements. The major hot-spot of ISW generation locates in the southwestern (SW) Gorlo Strait (GS), characterized by the presence of strong tides, complex topography, and two distinct fronts. Here, pronounced high-frequency isopycnal depressions of 5–8 m were regularly observed during flood and flood/ebb slackening. Other regions of pronounced ISW activity are found near Solovetsky Islands and in the northwestern Onega Bay. The spatial and kinematic properties of the observed ISWs are linked to water depth, with larger wave trains and higher propagation speeds being observed over the deep regions. Direct estimates of ISW propagation speeds from sequential and single SAR images agree well, while theoretical ones obtained using a two-layer model overestimate the observed values by 2–3 times. This is explained by the effective modulation of ISW propagation speed during the tidal cycle by background currents that are not accounted for in the model. Enhanced values of diapycnic diffusion coefficient in the pycnocline layer were registered near the frontal zones, where intense 14–17 m high ISWs were regularly observed.

Large-Amplitude Internal Wave Transformation into Shallow Water

Abstract Large-amplitude internal solitary wave (ISW) shoaling, breaking, and run-up was tracked continuously by a dense and rapidly sampling array spanning depths from 500 m to shore near Dongsha Atoll in the South China Sea. Incident ISW amplitudes ranged between 78 and 146 m with propagation speeds between 1.40 and 2.38 m s−1. The ratio between wave amplitude and a critical amplitude A0 controlled breaking type and was related to wave speed cp and depth. Fissioning ISWs generated larger trailing elevation waves when the thermocline was deep and evolved into onshore propagating bores in depths near 100 m. Collapsing ISWs contained significant mixing and little upslope bore propagation. Bores contained significant onshore near-bottom kinetic and potential energy flux and significant offshore rundown and relaxation phases before and after the bore front passage, respectively. Bores on the shallow forereef drove bottom temperature variation in excess of 10°C and near-bottom cross-shore currents in excess of 0.4 m s−1. Bores decelerated upslope, consistent with upslope two-layer gravity current theory, though run-up extent Xr was offshore of the predicted gravity current location. Background stratification affected the bore run-up, with Xr farther offshore when the Korteweg–de Vries nonlinearity coefficient α was negative. Fronts associated with the shoaling local internal tide, but equal in magnitude to the soliton-generated bores, were observed onshore of 20-m depth.

Remote sensing survey and research on internal solitary waves in the South China Sea-Western Pacific-East Indian Ocean (SCS-WPAC-EIND)

Remote sensing survey and research on internal solitary waves in the South China Sea-Western Pacific-East Indian Ocean (SCS-WPAC-EIND)

Effects of barotropic tides and ocean stratification on the generation and propagation of internal solitary waves in the deep south Andaman Sea

The Andaman Sea is one of the sea areas with the most internal solitary waves (ISWs) observed in the world and an ideal experimental site for studying the generation and propagation characteristics of ISWs. In this paper the generation and propagation characteristics of the ISWs in the deep south Andaman Sea are investigated based on the results of Massachusetts Institute of Technology General Circulation Model (MITgcm) numerical models. The reliability of the model is verified. The sea surface current gradient of 3D model is consistent with Terra MODIS and Sentinel-1A SAR remote sensing images. The turbulent kinetic energy dissipation rate of 2D model is also consistent with in-situ mooring measurements in other sea areas. The variation of temperature, energy and current field caused by barotropic tides and oceanic stratification are analyzed and compared. The results show that ISWs cannot be generated directly by the individual diurnal tides in our 2D model, and ISWs are mainly generated by the semidiurnal tides in the deep south Andaman Sea. Ocean stratification affects the waveform, the velocity and the generation position of ISWs. ISWs are easier to form in the hot season because of a larger Ursell number and stronger nonlinearity.

Dense pulses formed from fissioning internal waves

Cold pulses generated by the fission of internal solitary waves over gentle slopes are an important source of nutrients and relief from excess heat to benthic ecosystems. This numerical study investigates the effect of stratification form on pulses produced by fission of internal solitary waves propagating over a smooth, gentle, linear topographic slope in 2D simulations. Three stratification types are investigated, namely (i) thin tanh (homogeneous upper and lower layers separated by a thin pycnocline), (ii) surface stratification (linearly stratified layer overlaying a homogeneous lower layer) and (iii) broad tanh (continuous density gradient throughout the water column). Incident wave amplitude was varied. In the thin tanh stratification, good agreement is seen with past studies, whilst the dynamics observed in the surface stratification are very similar to those in the thin tanh stratification. However, in the broad tanh stratification, due to the different form of incident waves, the fission dynamics differ, but produce pulses similar in form to those produced by fission in the other stratifications. Pulse amplitude, wavelength and propagation velocity are found to strongly depend on incident wave amplitude, and each degenerate linearly as the pulse propagates upslope.

The nonlinear evolution of internal tides. Part 1: the superharmonic cascade

In non-uniform stratification, horizontally propagating internal waves with the vertical structure of a single mode self-interact to excite superharmonics. Baker & Sutherland (J. Fluid Mech., vol. 891, 2020, R1) showed that a vertical mode-1 parent wave of sufficiently small amplitude dominantly excites a vertical mode-1 superharmonic with double the horizontal wavenumber. Through theory, assuming a parent wave of sufficiently small amplitude, they showed that the superharmonics grew and decayed periodically due to the parent forcing frequency being off-resonant with the natural frequency of the superharmonic. Here, we extend this theory to allow for larger parent wave amplitudes and/or stronger resonant forcing, as would occur at lower latitudes, where the influence of background rotation is small. The resulting coupled system of nonlinear ordinary differential equations is shown to well predict the evolution of the internal tide as determined in fully nonlinear numerical simulations. With strong nonlinear forcing, successive superharmonics grow to non-negligible amplitudes in what we call the ‘superharmonic cascade’. The phase relationship between the superharmonics is such that when superimposed, the internal tide transforms into a solitary wave train, consistent with the predictions of well-established shallow-water models, particularly that of the Ostrovsky equation, which is an extension of the Korteweg–de Vries equation accounting for background rotation. This work thus gives new insight into internal solitary wave generation. The model equations have less restrictive assumptions than models based upon shallow-water theory, and because they are quickly solved, these provide a potentially powerful new tool to examine the nonlinear evolution of the internal tide.

A new method to estimate the speed of internal solitary waves based on a single optical remote sensing image

ABSTRACT It is imperative to estimate the energy of internal solitary waves (ISWs) in the real ocean. The energy of ISW is related to speed and amplitude. It is a problem to obtain the propagation speed of ISW from a single optical remote sensing image. Generally, the nonlinear phase speed (NPS) of ISW can be regarded as the propagation speed of ISW. This paper proposes a new inversion approach for NPS of ISW based on an optical remote sensing image. The simulation platform of optical remote sensing was used to conduct the ISW experiment in the laboratory, and the data were obtained by a series of experiments. Three NPS inversion models of ISW are investigated by support vector regression (SVR), Random forest (RF) and Deep neural network (DNN) based on a single optical remote sensing image. The accuracy of the inversion models was verified by the in-situ data of GF-1 satellite images, GF-4 satellite images and Moderate-resolution Imaging Spectroradiometer (MODIS) images. In the verification results, the SVR inversion model has high accuracy in different sea areas and water depths. The RF and DNN inversion models both have high inversion accuracy in the water depth range of 93–299 m in the South China Sea. Compared with the other two traditional methods for calculating ISW NPS, the SVR inversion model still has the highest accuracy. The results showed that the NPS models of ISW are suitable and effective.

The Generation of Linear and Nonlinear Internal Waves Forced by Subinertial Tides over the Yermak Plateau, Arctic Ocean

Abstract The propagation of internal waves (IWs) of tidal frequency is inhibited poleward of the critical latitude, where the tidal frequency is equal to the Coriolis frequency (f). These subinertial IWs may propagate in the presence of background vorticity, which can reduce rotational effects. Additionally, for strong tidal currents, the isopycnal displacements may evolve into internal solitary waves (ISWs). In this study, wave generation by the subinertial K1 and M2 tides over the Yermak Plateau (YP) is modeled to understand the linear response and the conditions necessary for the generation of ISWs. The YP stretches out into Fram Strait, a gateway into the Arctic Ocean for warm Atlantic-origin waters. We consider the K1 tide for a wide range of tidal amplitudes to understand the IW generation for different forcing. For weak tidal currents, the baroclinic response is predominantly at the second harmonic due to critical slopes. For sufficiently strong diurnal currents, ISWs are generated and their generation is not sensitive to the range of f and stratifications considered. The M2 tide is subinertial yet the response shows propagating IW beams with frequency just over f. We discuss the propagation of these waves and the influence of variations of f, as a proxy for variations in the background vorticity, on the energy conversion to IWs. An improved understanding of tidal dynamics and IW generation at high latitudes is needed to quantify the magnitude and distribution of turbulent mixing, and its consequences for the changes in ocean circulation, heat content, and sea ice cover in the Arctic Ocean.

Experimental investigation of vortex-induced vibration of a flexible pipe in bidirectionally sheared flow

The existence of a bidirectionally sheared flow field caused by internal solitary waves has recently been confirmed according to a field survey in the South China Sea. A model test of a tensioned flexible pipe in bidirectionally sheared flow was performed in an ocean basin. The model was 28.41mm in diameter and 7.64m in length. The purpose of the model test was to understand the response performance and obtain benchmark data of vortex-induced vibration (VIV) in bidirectionally sheared flow. The test was performed on a rotating test rig to simulate bidirectionally sheared flow conditions. Fiber Bragg Grating (FBG) strain sensors were arranged along the test pipe to measure bending strains, and the modal analysis approach was used to determine the VIV response. Reduced velocities based on the tested first natural frequency in water reached 30.79. The cross-flow and in-line VIV amplitudes, response frequencies in statistics and time-domain analysis, traveling wave characteristics, phase synchronization and trajectories are presented in this article. The maximum root mean square (RMS) VIV amplitudes in the test reached 0.51 diameters and 0.18 diameters in the cross-flow and in-line directions, respectively. A relative low Strouhal number of 0.10 was found in the CF direction.

Effects of the coupling between slope morphology and bottom currents on flow erosion and sedimentation at the Dongsha Continental Margin, South China Sea

Abstract The Dongsha Continental Margin (DCM) projects seaward and is situated in the path of bottom currents coming through the only deep-water exchange passage, the Luzon Strait between the South China Sea (SCS) and the western Pacific Ocean. This provides an opportunity to observe the different interaction between the two wings of the convex margin and the bottom currents, and help understand the corresponding implications for provenance, debris transportation, and sedimentation in such an environment. The convexity of the DCM causes its eastern flank to shrink against upcoming bottom currents and internal solitary waves (ISWs), producing a funneling effect and forming strong erosion grooves or strips, remnant seamounts, and large seafloor coarse debris dunes. The concavity of the western flank induces the expansion of bottom currents that flow around the plateau, resulting in a depositional zone with weak erosion that mainly interacts with bottom currents and gravity flow. The strong erosion on the DCM caused by the bottom current forms the primary provenance of the deep-water environment, while the nepheloid layer that entraps the fine debris of the gravity flow that derives from Taiwan and that is transported by the bottom current is the secondary provenance. The different coupling patterns between the bottom currents and the two flanks determine the different modes of debris transportation and deposition. Debris eroded by the currents is mainly transported by the gravity flow on the eastern flank while sweeping of the outer shelf and upper slope by eddy currents, progradation of the gravity flow, and reworking by the bottom current mainly occur on the western flank. Two types of morphological breaks, namely, continental slope break and bottom-current slope break, have developed on the DCM. They control the evolution of the flow regime of the multi-layer bottom currents and the gravity flow of the DCM as well as the effects of erosion and deposition. These two types of slope breaks are coupled and form an area in front of Dongsha Island with the highest deposition rate in the SCS.

Characteristics of internal solitary waves in the Maluku Sea, Indonesia

The appearance of internal solitary waves (ISWs) in the Maluku Sea is often captured by satellite imagery. However, no study has revealed details on this phenomenon to date. Here, the characteristics of such ISWs were investigated based on their appearance in synthetic aperture radar (SAR) imagery on 20 February 2015. Two different sources of ISW packets were observed: one packet propagating from the Lifamatola Passage and another from the Sangihe Passage. The vertical structure of the waves was constructed using the Korteweg-de Vries (KdV) model, which suggests an average phase speed of ∼2.8 and 2.7 m s−1 for the first and the second sources, respectively. ISWs originating from the first source had a typical amplitude of O(80 m), while those from the second source were characterized by a lower amplitude of O(40 m). The waves generated horizontal and vertical currents with typical magnitudes of O(1 m s−1) and O(10 cm s−1) for the first source and O(0.6 m s−1) and O(4 cm s−1) for the second source, respectively. The mean energy densities of the first and second sources reached 461 MJ m−1 and 185 MJ m−1, respectively. Single leading solitary wave contained a fraction of approximately 20% and 15% of the baroclinic tidal energy generated in the Lifamatola Passage and Sangihe Passage, respectively.

Experiment-based coupled dynamic analysis of submerged production platform-mooring system in internal solitary waves

As a competitive alternative to the conventional dry tree and wet tree concepts, the next generation subsea production system, with a focus on the critical issues of well access and riser design, is designed to utilize shallow-water rated subsea production systems for the development of large oil and gas fields in deep and ultra-deep water. This study focuses on the crucial component of the next generation subsea production system, referred to as the submerged production platform-mooring system, and investigates its nonlinear coupled dynamic responses to internal solitary waves. A time-domain coupled dynamic analysis method is developed. Specifically, based on the load experiment in a large gravitationally stratified fluid flume, the applicability conditions of internal solitary wave theories and the determination method of hydrodynamic coefficients are quantitatively characterized, and the internal solitary wave load model for the submerged production platform is developed and validated. The fully coupled dynamic analysis model for the submerged production platform-mooring system is established and solved by the Generalized-α integration algorithm in combination with the Newton iterative method. The coupling effects, dynamic response characteristics, and security weaknesses of the submerged production platform-mooring system are analyzed. The effects of various key factors on the dynamic responses of the submerged production platform-mooring system are systematically analyzed. The results demonstrate that the dynamic responses of the submerged production platform-mooring system to internal solitary waves are characterized by the large amplitude surge and heave motions, and the significant fluctuation in the mooring tension, particularly when the submerged production platform is located at the density pycnocline. The developed method also has its applicability to the dynamic analysis of the deepwater free standing hybrid riser system in internal solitary waves.

On Characteristics and Mixing Effects of Internal Solitary Waves in the Northern Yellow Sea as Revealed by Satellite and In Situ Observations

This study examines the characteristics, statistics, and mixing effects of internal solitary waves (ISWs) observed in the northern Yellow Sea (YS) during the summers of 2018 and 2019. The mooring stations are located between offshore islands with rough topographic features. Throughout the observation period, the ISWs with vertical displacements of up to 10 m induced prevailing high-frequency (3–10 min period) temperature variations. Synthetic aperture radar (SAR) images showed that the observed ISWs propagate in zonal directions generated around the islands where internal-tide-generating body force is strong. The estimated ISW propagation speed ranges from 0.16 to 0.25 m s−1, which agrees with the Korteweg-de Vries (KdV) model. The ISW intensity exhibits a clear spring-neap cycle corresponding to the local tidal forcing. The constant occurrence of ISWs at low tide suggests an important generation site where the ISWs are tidally generated. The ray-tracing result indicates that this generation site appears to be located at a strait between Dahao and Xiaohao islands. A generalized KdV model successively reproduces the propagation process from the generation site to the mooring station. Following the passage of ISWs, microstructure profiling observations reveal a high turbulent kinetic energy dissipation rate (10−6 W kg−1). The prevalence of ISWs in the study area is believed to play a crucial role in regulating vertical heat and nutrient transport, thereby modulating the biogeochemical cycle.