Large-amplitude Internal Waves Research Articles

Numerical research on internal solitary waves in stratified fluid

Internal solitary waves are a common nonlinear large amplitude internal wave in nature, which can cause strong divergence and sudden strong currents in seawater during propagation, thus having great destructive effects on marine structures. The paper focuses on numerical wave generation based on three types of internal solitary wave theories. The waves are numerical simulated by RANS method in the paper. The numerical results of internal solitary wave theories are compared and analyzed. It shows that under the same numerical water tank scale and calculation conditions, the mKdV theory can obtain the largest wave amplitude, followed by the eKdV theory and the KdV theory. In addition, background currents will accelerate the propagation speed of internal solitary waves and increase their amplitude slightly.

Discrimination of Internal Solitary Waves from Coarse Time Resolution Field Observational Data by Using Wavelet Analysis

Internal solitary waves (ISWs) are large-amplitude internal waves which would destroy underwater engineering. Finding an easy way to discriminate ISWs from field observational data is crucial. Two time--series datasets, one contained ISWs and another only containing internal tides, were obtained from filed observations. Based on single-layer velocity data, wavelet spectrum shows significant high value in short time-scale domain when ISWs pass, whilst having no signal in that domain when only internal tides exist, indicating the capability of wavelet analysis on ISWs detection. Wavelet variances of the dataset with ISWs has a bimodal distribution versus periods with two peaks around 40 min and 110 min, which can also be reproduced by a numerical model, indicating that the energy within period band of 10–120 min is caused by ISWs. By using the conceived signal processing techne, data reconstruction can precisely obtain the arrival time of ISWs and retain about 91.4% of the original signal. It is found that, based on a field observational dataset with even a coarse sampling interval for up to 20 min, the existence of ISWs can be easily discriminated by using wavelet analysis, which provides us an economic method for the early warning of ISWs in ocean engineering.

Multi-Sensor Observations Reveal Large-Amplitude Nonlinear Internal Waves in the Kara Gates, Arctic Ocean

We present multi-sensor measurements from satellites, unmanned aerial vehicle, marine radar, thermal profilers, and repeated conductivity–temperature–depth casts made in the Kara Gates strait connecting the Barents and the Kara Seas during spring tide in August 2021. Analysis of the field data during an 18-h period from four stations provides evidence that a complex sill in the Kara Gates is the site of regular production of intense large-amplitude nonlinear internal waves. Satellite data show a presence of a relatively warm northeastward surface current from the Barents Sea toward the Kara Sea attaining 0.8–0.9 m/s. Triangle-shaped measurements using three thermal profilers revealed pronounced vertical thermocline oscillations up to 40 m associated with propagation of short-period nonlinear internal waves of depression generated by stratified flow passing a system of shallow sills in the strait. The most intense waves were recorded during the ebb tide slackening and reversal when the background flow was predominantly supercritical. Observed internal waves had wavelengths of ~100 m and traveled northeastward with phase speeds of 0.8–0.9 m/s. The total internal wave energy per unit crest length for the largest waves was estimated to be equal to 1.0–1.8 MJ/m.

Analysis of the Force Characteristics of Two Tandem Cylinders by Internal Waves over Slope Topography

Large-amplitude internal waves (IWs) with strong lateral shear forces can cause destructive effects on marine engineering structures. In this study, a large eddy simulation (LES) method was employed to simulate the generation and propagation of IWs in a three-dimensional numerical wave tank, and the pressure distribution, flow field characteristics, and force behaviors of two tandem cylinders under the coupling effect of the IWs and slope terrain were studied. The influence mechanism of the normalized value of center-to-center spacing (L) and the diameter of the cylinder (D), i.e., (L/D), on the strength of the vortex disturbance between cylinders was studied by comparing the simulation results of two tandem cylinders with those of a single cylinder (SC) to further explore the mechanical response characteristics of the upstream cylinder (P1) and downstream cylinder (P2). The simulation results showed that the vortex interaction between cylinders is the critical factor that affects the forces acting on the cylinders. The strength of the vortex disturbance could be distinguished by the dimensionless critical center-to-center spacing between cylinders (Lc/D = 3.0). When L/D ≤ Lc/D, the vortex disturbance was severe, causing P1 and P2 to experience significant horizontal positive forces and negative forces, respectively. In the case of L/D > Lc/D, the forces acting on both cylinders gradually returned to those on a single cylinder.

Ocean Turbulence Observation Techniques and Data Processing Algorithms based on SAR Sequence Images

Waves in the ocean are a widespread phenomenon and their effective detection requires the use of high-resolution, large-area detection devices. Synthetic aperture radar (SAR), with its all-weather performance and high resolution, is often used for the detection and imaging of both land and ocean, as well as large-area, high-resolution SAR and interferometric SAR, which are all based on SAR enhancements. This has become an important area of research in marine sensors, and the use of multiple-input multiple-output (MIMO) reception modes for detection and imaging of large-area, high-resolution SAR data has become one of the research priorities for obtaining large-area, high-resolution SAR data. Oceanic internal waves generate internal mixing of seawater through unstable fragmentation, which is an important mechanism for maintaining the meridional overturning circulation within the ocean, and the strong currents and strong mixing processes generated by large amplitude internal waves carry enormous energy. The main objective of this paper is to investigate ocean turbulence observation techniques and data processing algorithms based on SAR sequence images. The research is of great significance for the development of marine science, and the technical areas studied are of great research significance for the development of the marine economy, breakthroughs in marine research technology, and the development of the marine industry.

Strongly non-linear Boussinesq-type model of the dynamics of internal solitary waves propagating in a multilayer stratified fluid

We propose a system of first-order balance laws that describe the propagation of internal solitary waves in a multilayer stratified shallow water with non-hydrostatic pressure in the upper and lower layers. The construction of this model is based on the use of additional variables, which make it possible to approximate the Green–Naghdi-type dispersive equations by a first-order system. In the Boussinesq approximation, the governing equations allow one to simulate the propagation of non-linear internal waves, taking into account fine density stratification, a weak velocity shear in the layers, and uneven topography. We obtain smooth steady-state soliton-like solutions of the proposed model in the form of symmetric and non-symmetric waves of mode-2 adjoining to a given multilayer constant flow. Numerical calculations of the generation and propagation of large-amplitude internal waves are carried out using both the proposed first-order system and Green–Naghdi-type equations. It is established that the solutions of these models practically coincide. The advantage of the first-order equations is the simplicity of numerical implementation and a significant reduction in the calculation time. We show that the results of numerical simulation are in good agreement with the experimental data on the evolution of mode-2 solitary waves in tanks of constant and variable height.

Internal solitary waves generated by a moving bottom disturbance

The strongly nonlinear Miyata–Choi–Camassa model under the rigid lid approximation (MCC-RL model) can describe accurately the dynamics of large-amplitude internal waves in a two-layer fluid system for shallow configurations. In this paper, we apply the MCC-RL model to study the internal waves generated by a moving body on the bottom. For the case of the moving body speed $U=1.1c_{0}$ , where ${c_0}$ is the linear long-wave speed, the accuracy of the MCC-RL results is assessed by comparing with Euler's solutions, and very good agreement is observed. It is found that when the moving body speed increases from $U=0.8c_{0}$ to $U=1.241c_{0}$ , the amplitudes of the generated internal solitary waves in front of the moving body become larger. However, a critical moving body speed is found between $U=1.241c_{0}$ and $U=1.242c_{0}$ . After exceeding this critical speed, only one internal wave right above the body is generated. When the moving body speed increases from $U=1.242c_{0}$ to $U=1.5c_{0}$ , the amplitudes of the internal waves become smaller.

Analysis on Causes of the “4·21” Indonesian Submarine “Nanggala” Crash Based on Satellite Images

In view of the “4·21” Indonesian submarine “Nanggala” crash event, an analysis of the marine environmental factors that may lead to the crash is carried out. The results show that the ocean internal wave is one possible cause of the disappearance of Indonesian submarines. The event is most likely that the submarine was subject to the so called “sea cliff” when encountering large-amplitude ocean internal waves, and at the same time, the officers and soldiers on board failed to take reasonable evasive measures in time, resulting in the submarine losing control and falling below the maximum safe diving depth, making the submarine crack under the pressure of the huge sea, resulting in a submarine accident. This conclusion is obtained based on the analysis of integrated ocean internal wave satellite images and numerical simulations.

High-order strongly nonlinear long wave approximation and solitary wave solution. Part 2. Internal waves

A strongly nonlinear long-wave approximation is adopted to obtain a high-order model for large-amplitude long internal waves in a two-layer system by assuming the water depth is much smaller than the typical wavelength. When truncated at the first order, the model can be reduced to the regularized strongly nonlinear model of Choiet al.(J. Fluid Mech., vol. 629, 2009, pp. 73–85), which lessens the Kelvin–Helmholtz instability excited by the tangential velocity jump across the interface in the inviscid Miyata–Choi–Camassa (MCC) equations. Using the second-order model, the next-order correction to the internal solitary wave solution of the MCC equations is found and its validity is examined with the Euler solution in terms of the wave profile, the effective wavelength and the velocity profile. It is shown that the correction greatly improves the comparison with the Euler solution for the whole range of wave amplitudes and no further correction is necessary for practical applications. Based on a local stability analysis, the region of stability for the second-order long-wave model is identified in the physical parameter space so that the efficient numerical scheme developed for the first-order model can be used for the second-order model.

Projected climate variability of internal waves in the Andaman Sea

The Andaman Sea, in the northeast Indian Ocean, is renowned for large-amplitude internal waves. Here, we use a global climate model (CanESM5) to investigate the long-term variability of internal waves in the Andaman Sea under a range of shared socioeconomic pathway (SSP) scenarios. SSPs are future societal development pathways related to emissions and land use scenarios. We project that mean values of depth-averaged stratification will increase by approximately 6% (SSP1-2.6), 7% (SSP2-4.5), and 12% (SSP5-8.5) between 1871-1900 and 2081-2100. Simulating changes in internal tides between the present (2015-2024) and the end-century (2091-2100), we find that the increase in stratification will enhance internal tide generation by approximately 4 to 8%. We project that the propagation of internal tides into the Andaman Sea and the Bay of Bengal will increase by 8 to 18% and 4 to 19%, respectively, under different SSP scenarios. Such changes in internal tides under global warming will have implications for primary production and ecosystem health not only in the Andaman Sea but also in the Bay of Bengal.

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.

Short timescale variability in large-amplitude internal waves on the western Portuguese shelf

Timescales in the ocean can range from the transient turbulence to the long-term climate scales. Quantifying its changes involves establishing meaningful background states, but that can be challenging if an extensive array of wave phenomena is masking the ocean's variability. Internal Waves (IWs) are a fundamental part of these wave phenomena, which are now widely acknowledged as major contributors in ocean dynamics. In this study we use satellite imagery from Synthetic Aperture Radars (SAR) and moored temperature records to assess the variability scales and magnitudes of coastal IW systems propagating onshore off the western Portuguese shelf. The data shows significant variability in timescales of just a few days, and hence within the waves' typical propagation lifespan. A regional ocean circulation model is used together with linear theory to assess how mesoscale variability is contributing to the observed variability patterns observed in the IWs in the SAR and in situ data. According to linear theory, the IW variability is mostly owing to variable mesoscale currents, which off the Portuguese coast typically result from geostrophic flows, eddies and upwelling dynamics. IW variability owing to changes in stratification is found to amount to about half of that in background flows, but their effect can go unnoticed within the largest contributions from mesoscale currents. One extreme event is highlighted in which IWs from consecutive tidal cycles could possibly decouple from (i.e. not traceable back to) their originating tides in just a few days and hence within their typical lifespans.

Generation of Underwater Noise by the Rip Zone of a Large-Amplitude Internal Wave in the Ocean

Generation of Underwater Noise by the Rip Zone of a Large-Amplitude Internal Wave in the Ocean

A high-order spectral method for effective simulation of surface waves interacting with an internal wave of large amplitude

In this study, we propose a new method for simulating complex surface waves interacting with a large amplitude internal solitary wave. Our model is based on a high-order spectral method for surface waves with the bottom boundary conditions computed from an internal wave solver. The convergence of the model is first tested using an internal wave case without surface waves. We then perform simulations of a canonical nonlinear wave interaction case involving two surface wave components and a prescribed internal wave component. The initial wave energy growth rate of the resonant wave component is found to agree with the analytical value predicted by the perturbation theory. We also use the model to simulate the interaction between surface waves and a weakly nonlinear internal wave, and the result is nearly identical to that calculated using a two-layer model. Finally, we show the application of our model in a multiscale nested modeling framework, where the internal wave parameters are extracted from the mesoscale simulation using a nonhydrostatic ocean model. The evolution of the spatial variations of the surface roughness is captured and the surface wave orbital velocity also changes in space due to the surface motions induced by the internal wave. Our phase-resolved model provides a computationally efficient tool for simulating complex surface wave fields in the background of internal waves of large amplitudes.

Oceanic internal wave amplitude retrieval from satellite images based on a data-driven transfer learning model

Internal waves (IW) are characterized by a large-amplitude, long-wave crest, and long-propagation distance. They are widespread in the global ocean. Amplitude is an essential IW parameter and is difficult to derive from the IW surface signatures in satellite images. A laboratory experiment and combined satellite/in-situ measurements were carried out to build two internal wave datasets (888 pairs of lab data and 121 pairs of synchronous in-situ data and satellite images). To efficiently use the lab data, we implemented a transfer learning model to retrieve IW amplitude from satellite images. The model is a purely data-driven model pre-trained with lab data and re-trained with satellite/in-situ data. A short connection was incorporated into the transfer learning framework to reduce information loss. Bias correction was adopted to improve the model performance. After the correction, the root mean square error (RMSE) of the estimated IW amplitude decreased from 12.09 m (17.84 m) to 9.59 m (11.59 m), the mean relative error decreased from 21% (27%) to 18% (16%), and the correlation coefficients improved from 0.81 (0.72) to 0.89 (0.90) on the test (training) dataset. For IWs with amplitude exceeding 100 m, the model can be expected to get an absolute error of 10 m. The mean relative error decreased with the increase in IW amplitudes. Comparisons with other algorithms demonstrate that the proposed model is efficient for IW studies. We applied the model to 156 satellite images containing IW signatures in the Andaman Sea, finding that large-amplitude IWs were mainly located at the water depth between 200 m and 1000 m on the continental slope. When considering one-pixel input errors for the peak-to-peak (PP) distance, the model shows large tolerance with the errors. Compared with the KdV equation-based method, the developed model was more accurate.

Estimating the Pycnocline Depth From the SAR Signature of Internal Waves in the Alboran Sea

In the Alboran Sea, west of the Straits of Gibraltar, the pycnocline depth has been assessed from the signature of a Large Amplitude Internal Wave (LAIW) captured by a Sensing Aperture Radar (SAR) image. First, the coefficients of the extended Korteweg-deVriès model were expressed using two different models of ocean stratification : an interfacial model and a continuously stratified ocean model. Then, via a Backscattering model, the same extended Korteweg-deVri‘es coefficients were computed. This latter calculation was performed along several transects extracted from the Large Amplitude Internal Wave surface signature and through an improved CARMA-derived method. Using the values of the coefficients for the ocean stratification model and those calculated from the SAR image, we obtained solutions for the pycnocline depth and thickness. This method was applied to a LAIW event on October 1st, 2008, for which SAR data and stratification measurements by an in-situ experiment were available jointly. The results are that the interfacial stratification model provides only few solutions for the pycnocline depth, while the continuous stratification model allows an interval of solutions for the pycnocline depth and thickness. These models are nevertheless complementary. Extra applications of this method on other ocean regions would be of interest.

Mean and Turbulent Characteristics of a Bottom Mixing‐Layer Forced by a Strong Surface Tide and Large Amplitude Internal Waves

AbstractWe present 15 days of both mean and turbulent field observations bottom mixing‐layer at a gently sloping 250 m deep continental shelf site, energized by tides and nonlinear internal waves (NLIWs). The tidal frequency forcing was due to the combined effects of the barotropic tide and a mode‐1 internal tide (IT), while the NLIWs were predominantly mode‐1 waves of depression. The bottom mixing‐layer thickness varied at both semidiurnal and sub‐tidal ∼O(10)d frequencies, with an average thickness of around 10 m. Compression and expansion of the mixing‐layer by both the IT and NLIWs affected the mean velocity profiles in the mixing‐layer, while the phasing between the barotropic and baroclinic flows led to an asymmetry in mean velocity profiles between periods of rising and falling isotherms. With the exception of periods of flow reversal, the turbulent kinetic energy balance and turbulent stress observations were consistent with the existence of an inertial‐sublayer with thickness of approximately 10%–15% of the mixing‐layer thickness ( ∼1 m), even beneath NLIWs. In the outer portion of the mixing‐layer—that is, above the inertial‐sublayer—NLIWs modulated the local turbulence spectra. We discuss the observations in the context of a predictive model for mixing‐layer thickness. The analysis suggests that the high‐frequency variability in mixing‐layer thickness was dominated by internal wave pumping, though strength of the ambient stratification and the frequency of the forcing were important controls on the time‐averaged (sub‐tidal) variation.

Applicability of high-order unidirectional internal solitary wave theoretical model

Internal solitary waves exist widely in the oceans, and their generations, propagation evolutions, and dissipations have profound effects on the ocean environment, topography, and marine structures. Typically, two basic theoretical models are now being developed to govern the evolutions of internal solitary waves at the interface of two immiscible inviscid fluids. One is a unidirectional wave propagation model described by the KdV (Korteweg-de Vries) equation, and the other is a bidirectional wave propagation model depicted by the Miyata-Choi-Camassa (MCC) equation. Neither of them, however, can effectively characterize the course of the evolution of large-amplitude internal solitary wave. In this paper, a modified unidirectional internal solitary wave model is established by adjusting the coefficients of the original unidirectional model. The adjusted coefficients are determined through asymptotic analysis by matching with the MCC model. The efficacy of the modified coefficients is investigated by comparing the modified model with the original model. The experiments on the generation of internal solitary waves with varying amplitudes are carried out by comparing the internal solitary wave solution of the modified equation. It is shown that the modified model is suitable for describing the waveform of internal solitary waves with small, medium, and large amplitudes within the limiting amplitude of the MCC model. By quantitatively analyzing the agreement of the effective wavelength, wave speed, and waveform of steady-state internal solitary waves between the unidirectional model and the MCC model, the applicability of the modified model in characterization of the properties of steady-state internal solitary waves is further investigated. In addition, the stability of unidirectional theoretical model is analyzed for simulating the propagation of large-amplitude internal solitary wave under flat bottom condition. It is found that the unidirectional model is suitable for initiating its own internal solitary solution provided that the numerical scheme is stable. It is shown that the modified unidirectional model can be used to characterize large-amplitude internal solitary waves, and is also expected to be applied to the study of marine structure hydrodynamics.

The effect of strong shear on internal solitary-like waves

Abstract. Large-amplitude internal waves in the ocean propagate in a dynamic, highly variable environment with changes in background current, local depth, and stratification. The Dubreil–Jacotin–Long, or DJL, theory of exact internal solitary waves can account for a background shear, doing so at the cost of algebraic complexity and a lack of a mathematical proof of algorithm convergence. Waves in the presence of shear that is strong enough to preclude theoretical calculations have been reported in observations. We report on high-resolution simulations of stratified adjustment in the presence of strong shear currents. We find instances of large-amplitude solitary-like waves with recirculating cores in parameter regimes for which DJL theory fails and of wave types that are completely different in shape from classical internal solitary waves. Both are spontaneously generated from general initial conditions. Some of the waves observed are associated with critical layers, but others exhibit a propagation speed that is very near the background current maximum. As such they are not freely propagating solitary waves, and a DJL theory would not apply. We thus provide a partial reconciliation between observations and theory.

Dynamics of currents and biological scattering layers around Senghor Seamount, a shallow seamount inside a tropical Northeast Atlantic eddy corridor

Biophysical interactions of the mesopelagic fauna and hydrodynamic features were investigated at a shallow, tall seamount in the tropical Northeast Atlantic based on data from three inter-disciplinary surveys collected between 2009 and 2015. Senghor Seamount is located close to the equator in a unique but underexplored oceanographic setting, where classical seamount effects are expected to be small. Shipboard Acoustic Doppler Current Profiler (ADCP) and remote sensing data revealed flow phenomena strongly varying over different temporal and spatial scales. The quasi-steady, longer period flow at the seamount was largely unchanged by flow-topography interaction with the exception of a persistent and recurring shadow zone of weaker currents downstream of the summit. Senghor Seamount is exposed to energetic mesoscale eddy activity in surrounding waters with potentially large physical and biological implications. At higher frequencies, tidal currents interacting with the seamount generated large-amplitude internal waves propagating horizontally and vertically away from the summit. Analysis of acoustic backscatter data and micronekton biomass displayed prominent near-surface night time and deep (>400 m) day time scattering layers associated with the diurnal vertical migration of the mesopelagic fauna. An intense and previously unreported aggregation of acoustic scatterers was detected in the depth range 150–300 m inside a radius of 3 km along the upper slopes of the seamount summit. ADCP measurements over a full semi-diurnal tidal cycle suggest that biophysical interactions were present in near-seafloor waters around the upper seamount as evidenced by plankton distributions that were modified by topographic blocking during descent and aggregation in waters characterised by internal waves and enhanced tidally-driven energy dissipation.