Internal Solitary Waves Research Articles

Energy transfer from internal solitary waves to turbulence via high-frequency internal waves: seismic observations in the northern South China Sea

Abstract. The shoaling and breaking of internal waves (IWs) are critical processes in the ocean's energy cascade and mixing. Using seismic data, we observed high-frequency internal waves (HIWs), which were primarily distributed in the depth range of 79–184 m. Their amplitude scale is O (10 m), with half-height widths ranging from 154 to 240 m. The shoaling thermocline and gentle slope with a low internal Iribarren number suggest that observed high-frequency internal waves are likely a result of fission. The remote sensing data support this point. Instability estimations showed that, due to the strong vertical shear, the Richardson number (Ri) in the range of 20–30 km was less than 0.25, and Kelvin–Helmholtz (KH) billows can be found in the seismic transect, suggesting that these waves were unstable and might dissipate rapidly. We used the seismic data to estimate diapycnal mixing, and we found that the HIWs can enhance diapycnal mixing, averaging 10−4 m2 s−1. The maximum mixing value is up to 10−3 m2 s−1, and it is associated with the breaking of IWs caused by the strong shear. The results show a new energy cascade route from shoaling internal solitary waves (ISWs) to turbulence, i.e., the fission of ISWs into HIWs, which improves our knowledge of ISW energy dissipation and their roles in improved mixing in the northern South China Sea.

Graph theoretic methods for assessing the effects of a background shear current on internal solitary waves

Internal solitary waves are a widely observed phenomenon in natural waters. Mathematically, they are fundamentally a nonlinear phenomenon that differs from the paradigm of turbulence, in that energy does not move across scales. Internal solitary waves may be computed from the Dubreil–Jacotin Long equation, which is a scalar partial differential equation that is equivalent to the stratified Euler equations. When a background shear current is present the algebraic complexity of the problem increases substantially. We present an alternative point of view for characterizing the situation with a shear current using Lagrangian (particle-like) models analysed with graph theoretic methods. We find that this yields a novel, data-centric framework for analysis that could prove useful well beyond the study of internal solitary waves.

Modulation of Internal Solitary Waves by One Mesoscale Eddy Pair West of the Luzon Strait

Abstract The characteristics of modulated internal solitary waves (ISWs) under the influence of one mesoscale eddy pair in the Luzon Strait, involving one anticyclonic eddy (AE) and one cyclonic eddy (CE) induced by the Kuroshio intrusion, were investigated using a nested high-resolution numerical model in the northeastern South China Sea (SCS). The presence of mesoscale eddies greatly impacts the nonlinear evolution of type-a and type-b ISWs. The eddy pair contributes to distinct wave properties and energy evolutions. Compared to type-b waves, type-a waves display more pronounced modulatory characteristics with a larger spatial scale. CE currents and horizontal inhomogeneous stratification are crucial in modulating the wave behaviors, which induce extremely large-amplitude depression ISWs. The AE thereafter yields retardation effects on the wave energy evolution. The average depth-integrated available potential and kinetic energy showed relative growth rates of −66.12% and −46.07%, respectively, for type-a waves, and −24.26% and −20.15%, respectively, for type-b waves along the propagation path up to the AE core. The deformed and distorted ISW crest lines propagating further northward exhibit a more dramatic shoaling evolution. The maximum total energies of type-a and type-b waves at the north station are approximately 13.5 and 3.5 times, respectively, greater than those at the south station on the continental shelf of the Dongsha Atoll. This work provides essential insights into modulated ISW dynamics under the mesoscale eddy pair within the northeastern SCS deep basin.

Deflection and drag on flexible marine structures in steady currents and internal solitary waves

This study investigates the deflection and drag on flexible marine structures under steady-flow conditions and internal solitary waves (ISWs) using free-hanging risers as a representative example. We examine the relationship between the Cauchy number (Ca), buoyancy parameter (B), deflected height (hd), and effective length (le). Our findings reveal that flow fields influenced by ISWs closely resemble steady flow. This similarity enables the use of steady-flow analyses as a proxy in extreme motion studies of flexible marine structures. We also discover that an inclined configuration of flexible marine structures, such as free-hanging risers, diminishes the horizontal forces exerted by both steady currents and ISWs. Additionally, for both scenarios, increasing the weight of longer flexible marine structures is more effective than increasing stiffness in reducing deflection. The proposed method accurately predicts the deformation of flexible marine structures caused by ship motion in deep-sea mining and the movements of ocean risers with floating platforms. This finding is important for the design and optimization of these structures.

Mechanisms of Reappeared Period Shifts of Internal Solitary Waves Based on Mooring Array Observations in the Northern South China Sea

AbstractMooring observations have revealed that the daily reappeared time (DRt) of internal solitary waves (ISWs) in the northern South China Sea (SCS) manifests systematic shifts. This study aims to reveal the dynamic mechanisms behind this phenomenon using the theory of modulation of shear flow to the internal tide wave (IT) propagation. Approximate solutions for the frequency modulation function (FMF) and the amplitude modulation function (AMF) of ITs are derived and validated by the mooring array measurements on the northern SCS continental shelf in 2019 and 2020. Namely, the mechanisms of the ISW reappeared period shift (RPS derived from DRt) and amplitude variation are attributed to the modulation of low‐frequency flow with a period of about 7 days to ITs. The FMF is induced by the vorticity of the low‐frequency flow (FS1) and the Doppler shift (FS2). Thus, the sign of the FMF value may be positive (blue shift) and negative (red shift), depending on the algebraic summation of the two terms. The FS2 derived from mooring observed velocities confirms the modulation effects of mean current on the frequency shift and the amplitude variation of ITs and ISWs.

Loads and Dynamic Response Characteristic on FPSO Under Internal Solitary Waves

Loads and Dynamic Response Characteristic on FPSO Under Internal Solitary Waves

Study on the Load Characteristics of Submerged Body Under Internal Solitary Waves on the Continental Shelf and Slope

Study on the Load Characteristics of Submerged Body Under Internal Solitary Waves on the Continental Shelf and Slope

Generation characteristics of internal solitary waves in the Northern Andaman sea based on MODIS observations and numerical simulations

The generation characteristics of internal solitary waves (ISWs) in the northern Andaman Sea are studied using remote sensing data and numerical simulations. The dataset comprises 230 images taken by the Moderate Resolution Imaging Spectroradiometer (MODIS) from 2020 to 2023, which reveal two distinct propagation directions of ISWs: southeastward (type-SE) and southwestward (type-SW). Generation hotspots are identified at the southern sill of the Preparis South Channel for type-SE ISWs and over the eastern shelf break for type-SW ISWs. Here, ISWs are intermittently generated, resulting in wave-free spatial gaps. The observed gaps motivate the hypothesis that ISWs are phase-locked with semidiurnal tides, resulting in specific generation time windows around slack tides. This study also reveals that the generation of ISWs is closely related to tidal ranges, with larger tidal ranges leading to more frequent ISWs. Specifically, type-SE and type-SW ISWs are detected only when the tidal range exceeds 1.3 m and 1.4 m, respectively. Numerical simulations with the MIT general circulation model further show that both types of ISWs are generated by nonlinear steepening of internal tides. The influence of background currents on ISW generation is also examined, which supports the proposed generation time window hypothesis. These findings highlight spatial gaps are attributable to the synergistic effects of MODIS observation times and intermittent generation of ISWs.

On the three-dimensional structure of instabilities beneath shallow-shoaling internal waves

The stimulation of instability and transport in the bottom boundary layer by internal solitary waves has been documented for over twenty years. However, the challenge of shallow slopes and a disparity of scales between the large-scale wave and the small-scale boundary layer has proven challenging for simulations. We present laboratory scale simulations that resolve the three-dimensionalisation in the boundary layer during the entire shoaling process. We find that the late stage, in which the incoming wave fissions into boluses, provides the most consistent source of three-dimensionalisation. In the early stage of shoaling, three-dimensionalisation occurs not so much due to separation bubble instability, but due to the interaction of vortices shed from the separation bubble with the overlying pycnocline. This interaction overturns the pycnocline, and creates bursts in kinetic energy and viscous dissipation, suggesting that the shed vortices induce turbulent motion and sediment resuspension in the water column above and behind the separation bubble.

A modified experimental approach for generating internal solitary waves using the dual paddle technique

A modification to the dual paddle wave generation method for internal solitary waves (ISWs) has been achieved through the implementation of the adjusted high-order unidirectional (aHOU) model and the Miyata–Choi–Camassa (MCC) model. This modified method utilizes layer-averaged horizontal velocities from ISWs in both the upper and lower fluid layers to control the operational velocities of the corresponding paddles. Experimental investigations conducted in a two-layer fluid with varied stratification conditions were employed to evaluate the applicability of the aHOU and MCC models. The validation of this approach involved examining the stability of generated ISWs by comparing experimental waveforms with theoretical predictions, demonstrating good agreement with prior research. Furthermore, evaluation of the modified wave generation method included an analysis of dimensionless phase velocity and characteristic frequency. The study also explored the quasi-linear relationship between the designed wave amplitude and the actual wave amplitude, establishing a polynomial fit between the actual wave amplitude and the layer thickness ratio. This approach offers a new method for stable and controllable laboratory generation of ISWs. Under finite water depth conditions, the method can produce ISWs that propagate stably over long distances and effectively control parameters such as wave amplitude and wave profile across a broad range of wave amplitudes and stratifications. These results confirm the effectiveness of the modified method and underscore its practical applicability in ISWs generation.

A novel variable-coefficient extended Davey–Stewartson system for internal waves in the presence of background flows

We propose a novel variable-coefficient Davey–Stewartson type system for studying internal wave phenomena in finite-depth stratified fluids with background flows, where the upper- and lower-layer fluids possess distinct velocity potentials, and the variable-coefficient terms are primarily controlled by the background flows. This realizes the first application of variable-coefficient DS-type equations in the field of internal waves. Compared to commonly used internal wave models, this system not only describes multiple types of internal waves, such as internal solitary waves, internal breathers, and internal rogue waves, but also aids in analyzing the impact of background flows on internal waves. We provide the influence of different background flow patterns on the dynamic behavior and spatial position of internal waves, which contribute to a deeper understanding of the mechanisms through which background flows influence internal waves. Furthermore, the system is capable of capturing variations in the velocity potentials of the upper and lower layers. We discover a connection between internal waves under the influence of background flows and velocity potentials. Through the variations in velocity potentials within the flow field, the dynamic behaviors of internal waves can be indirectly inferred, their amplitude positions located, and different types of internal waves distinguished. This result may help address the current shortcomings in satellite detection of internal wave dynamics and internal rogue waves.

Assessment of unidirectional internal solitary wave models in a two-layer fluid system through an improved experimental method

The suitability of unidirectional internal solitary wave (ISW) models in a two-layer fluid system is evaluated using an improved experimental method. A new method for generating internal solitary waves in the laboratory tank is proposed, utilizing a piston-type wave maker in a density stratified two-layer fluid. The prescribed velocities of the pistons are determined by the mean velocities derived from the adjusted High-order Unidirectional (aHOU) model for the upper and lower layers. Experimental conditions encompass a range of wave Reynolds numbers between 1.8×105 and 2.3×105. The repeatability and amplitude control of the proposed wave-making method are verified. The unidirectional models considered in this study encompass the Korteweg–de Vries (KdV), Gardner and aHOU model. Laboratory experiments and theoretical computations have been systematically compared in this study to examine the wave characteristics inherent in typical unidirectional internal solitary wave models. It is found that Reynolds number (Re) and nonlinear parameter (α=|a|/h) serve as suitable criteria for delineating the range of applicability of unidirectional models. According to these criteria, the KdV theory is suitable for ISWs with amplitudes α<0.02 across all Reynolds number cases, while the Gardner model is valid for cases where α<0.02 and Reω>2.2×105, with α<LimG, where LimG represents the non-dimensional limiting amplitude. The aHOU model exhibits the capability to capture fully nonlinear ISWs across all Reynolds numbers considered in this study.

Dynamic response of seabed in wind power of deep-shallow sea induced by internal solitary waves

With the development of offshore wind power projects worldwide, the stability of deep and shallow sea wind power sites has become a crucial concern. Internal solitary waves (ISWs) are nonlinear and large amplitude waves in the stratified ocean. Their strong vertical and horizontal motion and vorticity and turbulence caused by fragmentation have an important impact on the marine environment, seabed sediments, and marine engineering. This study focuses on the interaction between ISWs and the seabed of wind power sites in deep and shallow seas. Specifically, we investigate the interaction between ISWs and monopile foundations or floating fan plate anchor structures in the seabed. Through the simulation of CFD software and Comsol software, a law of seabed pore pressure variation during the effect of ISWs on the structure can be well demonstrated. Our results demonstrate that ISWs induce the accumulation of excess pore water pressure around the structures. The monopile foundation experiences negative excess pore water pressure at its bottom and the plate anchor at its top. The pore water pressure at the bottom of the monopile foundation initially decreases and then increases. In contrast, the pore water pressure at the right side of the monopile foundation increases, decreases, and then increases. This phenomenon promotes the settlement of the structure. At the bottom of the plate anchor, there is a sharp increase in positive excess pore water pressure by ISW. The pore water pressure above the plate anchor structure initially decreases and then increases, while below the plate anchor, it increases and then decreases. This phenomenon leads to the movement of the anchorage structure and instability of the surrounding soil. The influence of ISWs on the seabed bottom intensifies with the obstruction of the structure, resulting in significant positive pressure at the bottom. Between the two anchoring structures, there is increased seepage of pore water, making the seabed more prone to instability. Through the study of this article, we know that ISW has different effects on the force of monopile foundation and plate anchor structure, which provides a favorable basis for its design and maintenance.

Sediment remobilization over subaqueous sand waves: In-situ observation in the northern South China Sea

High-resolution tripod observations were conducted in a subaqueous sand-wave field in the northern South China Sea. The objective was to gain insight into the dynamic mechanism by which sandy sediments are remobilized by oceanic dynamic processes, in particular internal solitary waves and internal tides. Daily-recurring high suspended sediment concentrations were observed, likely due to lateral transport of sediments resuspended by critical reflection of diurnal internal tides at the shelf break. The passage of extreme internal solitary waves results in resuspension of sediments from the seabed and ejection of these sediments out of the boundary layer. The resuspension of sediments from the seabed is controlled by current-induced strong bed shear stress, while the ejection of sediments out of the bottom boundary layer is driven by the compression and subsequent expansion of the mixing layer, together with the developments of the separation bubbles behind the internal solitary waves. These findings provide new insights into understanding the dynamic mechanism of sediment remobilization by internal solitary waves. Moreover, they contribute to our understanding of the migration of subaqueous sand waves.

Insights Into Internal Solitary Waves East of Dongsha Atoll From Integrating Geostationary Satellite and Mooring Observations

AbstractUnderstanding of internal solitary wave (ISW) behavior has been limited due to sparse observations. We used high‐resolution Himawari‐8 satellite imagery and mooring observations to reveal the two‐dimensional (x–y) propagation process of ISWs in the South China Sea as they westward propagate onto the Dongsha plateau and encounter Dongsha Atoll. The 2D depiction of wave speed distribution, derived from detected wave crest positions every 10 min, shows the wave speeds range from 3 m s−1 to 1 m s−1 and have a tight correspondence to the local water depth. The correlation coefficient between the wave speeds and the Dubreil–Jacotin–Long (DJL) solutions is around 0.7, with a root mean squared value of 0.26 m s−1, and the representative available potential energy for this region is considered to be 130 MJ m−1. However, diffusions of wave speed in the ISW's lateral direction, particularly around abrupt topography, contribute to occurrences of outliers. Pairs of incident and reflected waves are well recognized east of Dongsha Atoll. The incident wave packet is known to be classified into a‐type and b‐type waves. The reflected waves associated with the b‐wave, identifiable as mode‐1 depression ISWs, are traced back to their generation site at depths of 100–200 m. In contrast, the reflected waves of the a‐wave remain elusive in shallower waters (&lt;300 m), likely due to interference from their longer incident counterparts. The reflected wave, however, is slower and decelerates toward deeper water, deviating from the DJL prediction. These comprehensive observations can help refine models for improved accuracy.

Numerical investigation of interaction of two internal solitary waves with different initial wave amplitudes

The present study investigates the collision of two internal solitary waves with different initial amplitudes using a multi-domain boundary element method. It calculates and discusses wave profiles, residence time, and phase shifting. Observations reveal that tail waves are induced during the collision process, with the amplitude of the tail wave increasing as the initial amplitude of the internal solitary wave increases. Residence time, defined in terms of the interaction between waves of different initial amplitudes, decreases as wave amplitudes increase, eventually stabilizing at a constant value. Additionally, phase shifting increases with wave amplitude, with the rate of increase slowing down as the wave profile becomes relatively large.

Qualitative difference between large waves in deep and shallow fluid formulations

The note addresses a qualitative difference between shallow (vertically confined) and deep (vertically non-confined) fluid geometries for stationary internal solitary waves. It is shown that in a deep fluid, the propagation velocity of large amplitude wave (with a vortex inside) is greater than the velocity predicted by small but finite amplitude theory, known as the Benjamin-Ono model. This effect has been found both asymptotically and experimentally. For the case of a shallow fluid, the situation is qualitatively different. The speed of a wave with vortex inside is smaller than that predicted by the Korteweg-de Vries theory. The reported observation could distinguish wave motions in shallow (confined) and deep (non-confined) geometries and seems to be important in a variety of applications.

The boundary layer instability beneath internal solitary waves and its sensitivity to vortex wakes

We investigated the stability of the bottom boundary layer (BBL) beneath periodic internal solitary waves (ISWs) of depression over a flat bottom through two-dimensional direct numerical simulations. We explored the convective versus absolute/global nature of the BBL instability in response to changes in Reynolds number, and the sensitivity of the instability to seeding noise in the front of the ISW – spanning laboratory to geophysical scales. The BBL was laminar at $Re_{ISW}=90$ and convectively unstable at $Re_{ISW}=300$ . At laboratory-scale $Re_{ISW}=300$ , the convective wave packet was periodically amplified by each successive ISW, until vortex shedding occurred. The associated noise-amplification behaviour potentially explains the discrepancies of the critical $Re_{ISW}$ between the lock–release laboratory experiments and our Dubreil–Jacotin–Long-initialized numerical simulations as the result of the difference in background noise. Instability energy decreased under the front shoulder of the ISW, analogous to flow relaminarization under a favourable pressure gradient. At geophysical-scale $Re_{ISW}=900$ , the BBL was initially convectively unstable, and then the instability tracked with the ISW, appearing phenomenologically similar to a global instability. The simulated initial convective instability at both $Re_{ISW}=300$ and $Re_{ISW}=900$ is in agreement with local linear stability analysis which predicts that the instability group speed is always lower than the ISW celerity. Increased free stream perturbations in front of the ISW and larger $Re_{ISW}$ shift the location of vortex shedding (and enhanced bed shear stress) beneath the wave, closer to the ISW trough, thereby potentially changing the location of maximum sediment resuspension, in agreement with field observations at higher $Re_{ISW}$ .

Tuning control parameters of underwater vehicle to minimize the influence of internal solitary waves

ISWs (Internal solitary waves) are waves that occur in stratified oceans, generating strong shear near the pycnocline. Encountering ISWs can cause a vehicle to experience the phenomenon of “falling deep”. Therefore, it is quite necessary to exert control on the vehicle in order to effectively avoid this phenomenon. This study establishes a numerical wave tank for ISWs based on the mKdV (modified Korteweg de Vries) theory. Additionally, a PD (Proportional Derivative) control method is developed for vehicles encountering ISWs in stratified fluids. The PD control parameters are designed and tuned, and the vehicle's control effectiveness, motion response and hydrodynamic characteristics, are analysed. The results suggest that this control method can effectively reduce the heave and pitch motions of the vehicle in different submergence depths and wave amplitudes. The pitch angle can be controlled within 0.2 rad for different control parameters. Better control can suppress changes within a range of 0.1 rad. To better evaluate the control effect, a new evaluation parameter σ is proposed, which takes into account both heave and pitch motions. After implementing control, the value of σmax significantly decreases. Optimal control parameters can reduce the value of σmax by about 90% compared to an uncontrolled vehicle.

Seismic oceanography of internal solitary waves offshore the South Island, New Zealand

Seismic oceanography has been widely used in the study of internal solitary waves (ISWs) in recent years, and has achieved remarkable results. In this paper, we analyzed the multi-channel seismic reflection data in the Canterbury Basin offshore New Zealand from January 9 to January 29, 2000, collected by R/V Maurice Ewing. We observed 4 groups of ISWs (labeled ISW1s to ISW4s) on 4 seismic survey lines. We studied their waveforms and propagation speeds in detail. There are two theoretical structures used to describe the vertical waveform of ISWs: the first-order nonlinear vertical structure and the linear vertical structure. We found that ISW1s fit the nonlinear structure well, ISW3s and ISW4s fit the linear structure, and ISW2 does not fit either one. As the water depth increases, the waveforms of all ISWs gradually widen. Two satellite SAR images reveal that all ISWs generally travel shoreward across the isobaths. However, the propagation direction of ISW1s is about 354°-360° (clockwise from due north), different from the propagation directions of other ISWs (about 22°-26°), which explains why ISW1s have the largest characteristic half-height width. The estimated propagation speeds are close to the theoretical speeds, confirming our speed correction method. In the end, we also discuss the interaction of ISWs and eddies.