scholarly journals Observations of Internal Structure Changes in Shoaling Internal Solitary Waves Based on Seismic Oceanography Method

2021 ◽  
Vol 8 ◽  
Author(s):  
Haibin Song ◽  
Yi Gong ◽  
Shengxiong Yang ◽  
Yongxian Guan
Keyword(s):  
Fine Structure ◽  
Solitary Wave ◽  
Phase Velocity ◽  
Shallow Water ◽  
Solitary Waves ◽  
Deep Water ◽  
Internal Solitary Wave ◽  
Internal Solitary Waves ◽  
Structure Changes ◽  
Different Depths

High spatial resolution and deep detection depths of seismic reflection surveying are conducive to studying the fine structure of the internal solitary wave. However, seismic images are instantaneous, which are not conducive to observing kinematic processes of the internal solitary waves. We improved the scheme of seismic data processing and used common-offset gathers to continuously image the same location. In this way, we can observe internal fine structure changes during the movement of the internal solitary waves, especially the part in contact with the seafloor. We observed a first-mode depression internal solitary wave on the continental slope near the Dongsha Atoll of the South China Sea and short-term shoaling processes of the internal solitary wave by using our improved method. We found that the change in shape of waveform varies at different depths. We separately analyzed the evolution of the six waveforms at different depths. The results showed that the waveform in deep water deforms before that in shallow water and the waveform in shallow water deforms to a greater degree. We measured four parameters of the six waveforms during the shoaling including phase velocity, amplitude, wavelength, and slopes of leading and trailing edge. The phase velocity and amplitudes of waveforms in shallow water increase, the wavelengths decrease, and the slopes of trailing edge gradually become larger than that of the leading edge, while the amplitudes of the deep water waveforms do not change significantly and the phase velocities decrease. Our results are consistent with previous studies made by numerical simulations, which suggest the effectiveness of the new processing scheme. This improved scheme cannot only study the internal solitary waves shoaling, but also has great potential in the study of other ocean dynamics.

Observations of fine structure changes in shoaling internal solitary waves based on seismic oceanography method

2021 ◽  
Author(s):  
Haibin Song ◽  
Yi Gong ◽  
Yongxian Guan ◽  
Wenhao Fan ◽  
Yunyan Kuang
Keyword(s):  
Fine Structure ◽  
Solitary Wave ◽  
Phase Velocity ◽  
Shallow Water ◽  
Solitary Waves ◽  
Internal Solitary Wave ◽  
Internal Solitary Waves ◽  
Seismic Events ◽  
Velocity Amplitude ◽  
Seismic Oceanography

<p>In the study of shoaling internal solitary waves, the observation and research on the internal fine structure and the effect of the topography are still insufficient. We try to make up for such insufficiency by seismic oceanography method. A first-mode depression internal solitary wave was observed propagating on the continental slope in the northeast South China Sea near Dongsha Atoll. We used common offset gathers (COGs) to obtain a series of images of this internal solitary wave that evolved over time, and studied the changes in internal fine structure by analyzing the seismic events in COG migrated sections. We found that the seismic events were broken during the shoaling, which was caused by the instability induced by internal solitary wave. We picked six events which represent six waveform and analyzed their evolution. It was found that the change in shape of waveform at different depths is different. The waveform in deep water deforms before that in shallow water, and the waveform in shallow water deforms to a greater degree. In addition, we also counted four parameters of phase velocity, amplitude, wavelength, and slopes of front and rear during the shoaling. The results show that the phase velocity and amplitude of waveform in shallow water increases, the wavelength decreases, and the slope of rear gradually becomes larger than that of the front. We have compared the observed changes with previous study made by numerical simulation.</p>

scholarly journals Energetics of internal solitary waves in a background sheared current

2010 ◽  
Vol 17 (5) ◽  
pp. 553-568 ◽  
Author(s):  
K. G. Lamb
Keyword(s):  
Solitary Wave ◽  
Surface Waves ◽  
Solitary Waves ◽  
Deep Water ◽  
Pressure Change ◽  
Boussinesq Approximation ◽  
Internal Solitary Wave ◽  
Internal Solitary Waves ◽  
Deep Basin ◽  
Internal Seiche

Abstract. The energetics of internal waves in the presence of a background sheared current is explored via numerical simulations for four different situations based on oceanographic conditions: the nonlinear interaction of two internal solitary waves; an internal solitary wave shoaling through a turning point; internal solitary wave reflection from a sloping boundary and a deep-water internal seiche trapped in a deep basin. In the simulations with variable water depth using the Boussinesq approximation the combination of a background sheared current, bathymetry and a rigid lid results in a change in the total energy of the system due to the work done by a pressure change that is established across the domain. A final simulation of the deep-water internal seiche in which the Boussinesq approximation is not invoked and a diffuse air-water interface is added to the system results in the energy remaining constant because the generation of surface waves prevents the establishment of a net pressure increase across the domain. The difference in the perturbation energy in the Boussinesq and non-Boussinesq simulations is accounted for by the surface waves.

scholarly journals Enhanced diapycnal mixing by polarity-reversing internal solitary waves in the South China Sea

2021 ◽  
Author(s):  
Yi Gong ◽  
Haibin Song ◽  
Zhongxiang Zhao ◽  
Yongxian Guan ◽  
Kun Zhang ◽  
...  
Keyword(s):  
South China Sea ◽  
Solitary Wave ◽  
Solitary Waves ◽  
South China ◽  
The South China Sea ◽  
Internal Solitary Wave ◽  
Internal Solitary Waves ◽  
Diapycnal Mixing ◽  
Dongsha Atoll ◽  
Diapycnal Diffusivity

Abstract. Shoaling internal solitary waves near the Dongsha Atoll in the South China Sea dissipate their energy and thus enhance diapycnal mixing, which have an important impact on the oceanic environment and primary productivity. The enhanced diapycnal mixing is patchy and instantaneous. Evaluating its spatiotemporal distribution requires comprehensive observation data. Fortunately, seismic oceanography meets the requirements, thanks to its high spatial resolution and large spatial range. In this paper, we studied three internal solitary waves in reversing polarity near the Dongsha Atoll, and calculated the spatial distribution of resultant diapycnal diffusivity. Our results show that the average diffusivities along three survey lines are two orders of magnitude larger than the open-ocean value. The average diffusivity in the internal solitary wave with reversing polarity is three times that of the non-polarity-reversal region. The diapycnal diffusivity is higher at the front of one internal solitary wave, and gradually decreases from shallow to deep water in the vertical direction. Our results also indicates that (1) the enhanced diapycnal diffusivity is related to reflection seismic events; (2) convective instability and shear instability may both contribute to the enhanced diapycnal mixing in the polarity-reversing process; and (3) the difference between our and previous diffusivity profiles is about 2–3 orders of magnitude, but their vertical distribution is almost the same.

scholarly journals Combined Effect of Rotation and Topography on Shoaling Oceanic Internal Solitary Waves

2014 ◽  
Vol 44 (4) ◽  
pp. 1116-1132 ◽  
Author(s):  
Roger Grimshaw ◽  
Chuncheng Guo ◽  
Karl Helfrich ◽  
Vasiliy Vlasenko
Keyword(s):  
Solitary Wave ◽  
Wave Packet ◽  
Numerical Simulations ◽  
Solitary Waves ◽  
Combined Effect ◽  
Internal Solitary Wave ◽  
Internal Solitary Waves ◽  
De Vries ◽  
Ostrovsky Equation ◽  
Variable Topography

Abstract Internal solitary waves commonly observed in the coastal ocean are often modeled by a nonlinear evolution equation of the Korteweg–de Vries type. Because these waves often propagate for long distances over several inertial periods, the effect of Earth’s background rotation is potentially significant. The relevant extension of the Kortweg–de Vries is then the Ostrovsky equation, which for internal waves does not support a steady solitary wave solution. Recent studies using a combination of asymptotic theory, numerical simulations, and laboratory experiments have shown that the long time effect of rotation is the destruction of the initial internal solitary wave by the radiation of small-amplitude inertia–gravity waves, and the eventual emergence of a coherent, steadily propagating, nonlinear wave packet. However, in the ocean, internal solitary waves are often propagating over variable topography, and this alone can cause quite dramatic deformation and transformation of an internal solitary wave. Hence, the combined effects of background rotation and variable topography are examined. Then the Ostrovsky equation is replaced by a variable coefficient Ostrovsky equation whose coefficients depend explicitly on the spatial coordinate. Some numerical simulations of this equation, together with analogous simulations using the Massachusetts Institute of Technology General Circulation Model (MITgcm), for a certain cross section of the South China Sea are presented. These demonstrate that the combined effect of shoaling and rotation is to induce a secondary trailing wave packet, induced by enhanced radiation from the leading wave.

Internal solitary waves in a two-fluid system with a free surface

2016 ◽  
Vol 804 ◽  
pp. 201-223 ◽  
Author(s):  
Tsubasa Kodaira ◽  
Takuji Waseda ◽  
Motoyasu Miyata ◽  
Wooyoung Choi
Keyword(s):  
Free Surface ◽  
Solitary Wave ◽  
Surface Waves ◽  
Solitary Waves ◽  
Silicone Oil ◽  
Internal Solitary Wave ◽  
Internal Solitary Waves ◽  
Weakly Nonlinear ◽  
Two Fluids ◽  
Strongly Nonlinear

Internal solitary waves in a system of two fluids, silicone oil and water, bounded above by a free surface are studied both experimentally and theoretically. By adjusting an extra volume of silicone oil released from a reservoir, a wide range of amplitude waves are generated in a wave tank. Wave profiles as well as wave speeds are measured using multiple wave probes and are then compared with both the weakly nonlinear Korteweg–de Vries (KdV) models and the strongly nonlinear Miyata–Choi–Camassa (MCC) models. As the density difference between the two fluids in the experiment is relatively small (approximately 14 %), but non-negligible, special attention is paid to the effect of the boundary condition at the top surface. The nonlinear models valid for rigid-lid (RL) and free-surface (FS) boundary conditions are considered separately. It is found that the solitary wave of the FS model for a given amplitude is consistently narrower than that of the RL model and it propagates at a slightly lower speed. Due to strong nonlinearity in the internal-wave motion, the weakly nonlinear KdV models fail to describe the measured internal solitary wave profiles of intermediate and large wave amplitudes. The strongly nonlinear MCC-FS model agrees better with the measurements than the MCC-RL model, which indicates that the free-surface boundary condition at the top surface is crucial in describing the internal solitary waves in the experiment correctly. Leaving the top surface free in the experiment allows us to observe small and relatively short wave packets on the top surface, particularly when the amplitude of the internal solitary wave is large. Once excited, the wave packet is located above the front half of the internal solitary wave and propagates with a speed close to that of the internal solitary wave underneath. A simple resonance mechanism between short surface waves and long internal waves without and with nonlinear effects is examined to estimate the characteristic wavelength of modulated short surface waves, which is found to be in good agreement with the observed wavelength when nonlinearity is taken into account. Using ray theory, the evolution of short surface waves in the presence of a background current induced by an internal solitary wave is also investigated to examine the location of the modulated surface wave packet.

Internal Solitary Waves with shear: beyond DJL theory

2020 ◽  
Author(s):  
Marek Stastna ◽  
Aaron Coutino ◽  
Ryan Walter
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Wave Train ◽  
Theoretical Description ◽  
Internal Solitary Wave ◽  
Shear Instability ◽  
Internal Solitary Waves ◽  
Wave Trains ◽  
Set Up ◽  
Background Shear

<p>While background shear is ubiquitous in the natural environment, the vast majority of theoretical and numerical studies of internal solitary waves do not include a background shear.  Walter et al 2016, Continental Shelf Research reported on measurements in Monterey Bay in which large amplitude internal solitary wave trains were observed but corresponding waves could not be computed from DJL theory due to the strength of the background shear.  In this talk I will revisit this issue using a classical stratified adjustment set up.  For the case of an exponential, surface trapped background current I will demonstrate that internal solitary wave trains with and without trapped cores coexist with a substantial region dominated by stratified shear instability and/or Rayleigh Taylor instability.  I will then demonstrate the type of internal wave train that results in cases when the the variational formulation of the DJL equation fails to converge. I will speculate on implications for theoretical description of such waves and for more realistic simulations in the coastal ocean.</p>

scholarly journals Numerical Simulation for the Evolution of Internal Solitary Waves Propagating over Slope Topography

2021 ◽  
Vol 9 (11) ◽  
pp. 1224
Author(s):  
Yingjie Hu ◽  
Li Zou ◽  
Xinyu Ma ◽  
Zhe Sun ◽  
Aimin Wang ◽  
...  
Keyword(s):  
Numerical Model ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Wave Amplitude ◽  
Domain Boundary ◽  
Internal Solitary Wave ◽  
Internal Solitary Waves ◽  
Initial Amplitude ◽  
Nonlinear Potential ◽  
Slope Topography

In this study, the propagation and evolution characteristics of internal solitary waves on slope topography in stratified fluids were investigated. A numerical model of internal solitary wave propagation based on the nonlinear potential flow theory using the multi-domain boundary element method was developed and validated. The numerical model was used to calculate the propagation process of internal solitary waves on the topography with different slope parameters, including height and angle, and the influence of slope parameters, initial amplitude, and densities jump of two-layer fluid on the evolution of internal solitary waves is discussed. It was found that the wave amplitude first increased while climbing the slope and then decreased after passing over the slope shoulder based on the calculation results, and the wave amplitude reached a maximum at the shoulder of the slope. A larger height and angle of the slope can induce larger maximum wave amplitude and more obvious tail wave characteristics. The wave amplitude gradually decreased, and a periodic tail wave was generated when propagating on the plateau after passing the slope. Both frequency and height of the tail wave were affected by the geometric parameters of the slope bottom; however, the initial amplitude of the internal solitary wave only affects the tail wave height, but not the frequency of the tail wave.

Transformation of the first mode internal solitary wave over topography in three-layer flow

2020 ◽  
Author(s):  
Kateryna Terletska ◽  
Tatiana Talipova ◽  
Roger Grimshaw ◽  
Zihua Liu ◽  
Vladimir Maderіch
Keyword(s):  
Solitary Wave ◽  
Wave Field ◽  
Solitary Waves ◽  
Internal Solitary Wave ◽  
Wave Transformation ◽  
Internal Solitary Waves ◽  
Wave Characteristics ◽  
Second Mode ◽  
Layer Flow ◽  
Bottom Step

<p>Transformation of the first mode internal solitary wave over the underwater bottom step in three-layer fluid is studied numerically. In the three layer flow two modes (the first and the second) of the internal waves are existed. It is known that interaction of the first mode internal solitary wave with an underwater obstacle is the mechanisms of second-mode internal solitary waves generation. Different scenarios of transformation are realized under different wave characteristics: wave amplitude, position of the step and thickness of the layers as is the two layer case [1]. Formation of the second mode internal solitary waves during interaction of the first mode internal solitary waves occurs only for special range of wave characteristics and thickness of the layers that was defined in this investigation. The second mode internal solitary waves appear as in the reflected wave field as well as in the transmitted wave field. Transfer of energy from incident mode one wave into reflected and transmitted waves (the first and the second modes) during transformation is also studied. Dependence of the amplitudes of generated solitary waves (transmitted and reflected) from amplitude of the incident wave is obtained.  Comparison of numerical results (reflected and transmitted coefficients) with the theoretical calculations [2] shows good agreement in the range of wave characteristics that corresponds to the weak interaction.  </p><p> </p><p>1. Talipova T., Terletska K., Maderich V., Brovchenko I., Pelinovsky E., Jung K.T., Grimshaw R. Internal solitary wave transformation over a bottom step: loss of energy. Phys. Fluids. 2013. № 25. 032110; doi:10.1063/1.4797455</p><p>2.    Liu Z., Grimshaw R. and Johnson E.  The interaction of a mode-1 internal solitary wave with a step and the generation of mode-2 waves Geophysical & Astrophysical Fluid Dynamics 2019, N 4, V 113, https://doi.org/10.1080/03091929.2019.1636046</p><p> </p>

A regularized model for strongly nonlinear internal solitary waves

2009 ◽  
Vol 629 ◽  
pp. 73-85 ◽  
Author(s):  
WOOYOUNG CHOI ◽  
RICARDO BARROS ◽  
TAE-CHANG JO
Keyword(s):  
Stability Analysis ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Wave Solution ◽  
Wave Amplitude ◽  
Solitary Wave Solution ◽  
Shear Instability ◽  
Internal Solitary Waves ◽  
Strongly Nonlinear ◽  
Regularized Model

The strongly nonlinear long-wave model for large amplitude internal waves in a two-layer system is regularized to eliminate shear instability due to the wave-induced velocity jump across the interface. The model is written in terms of the horizontal velocities evaluated at the top and bottom boundaries instead of the depth-averaged velocities, and it is shown through local stability analysis that internal solitary waves are locally stable to perturbations of arbitrary wavelengths if the wave amplitudes are smaller than a critical value. For a wide range of depth and density ratios pertinent to oceanic conditions, the critical wave amplitude is close to the maximum wave amplitude and the regularized model is therefore expected to be applicable to the strongly nonlinear regime. The regularized model is solved numerically using a finite-difference method and its numerical solutions support the results of our linear stability analysis. It is also shown that the solitary wave solution of the regularized model, found numerically using a time-dependent numerical model, is close to the solitary wave solution of the original model, confirming that the two models are asymptotically equivalent.

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