Statistical properties of the internal solitary wave ensemble

2021 ◽  
Author(s):  
Tatiana Talipova ◽  
Ekaterina Didenkulova ◽  
Anna Kokorina ◽  
Efim Pelinovsky
Keyword(s):  
Wave Propagation ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Internal Solitary Wave ◽  
Statistical Moments ◽  
Nonlinear Propagation ◽  
Positive Sign ◽  
Cubic Nonlinearity ◽  
Gardner Equation ◽  
Water Stratification

<p>Internal solitary wave ensembles are often observed on the ocean shelves. The long internal baroclinic tide is generated by a barotropic tide on the shelf edges, and then transforms into the soliton-like wave packets during the nonlinear propagation to the beach. The tide is a periodic process and the solitary wave ensemble appears on the shelf usually each semi-diurnal period of 12.4 hours. This process is very sensitive to the variation of the tide characteristics and the hydrology.</p><p>We study the propagation of the soliton ensembles numerically in the framework of the spatial form of the Gardner equation (i.e., the Korteweg-de Vries equation with both, quadratic and cubic nonlinearities) assuming horizontally uniform background and applying periodic conditions in time. The water stratification and the local depth are taken similar to the conditions of the north-western Australian shelf, where the stratification admits the existence of solitons but not breathers. The numerical simulation is performed using the Gardner equation with the negative sign of the cubic nonlinearity. For the study of the statistic properties of the solitary waves we use the ensemble of 50 realizations with the same set of 13 solitary waves which are located randomly. The histograms of the wave amplitudes change as the waves travel. The histogram variations become significant after 50 km of the wave propagation. The third (skewness) and the fourth (kurtosis) statistical moments are computed versus the travel distance. It is shown that the both moments decrease by 20% when the solitary wave groups travel for about 150 km.</p><p>A similar simulation is conducted for a variable background within the framework of the variable-coefficient Gardner equation. At some location the water stratification corresponds to the positive sign of the local coefficient of the cubic nonlinearity, and then internal breathers may exist. The wave propagation in horizontally inhomogeneous hydrology leads to the occurrence of complicated patterns of solitons and breathers; in the course of the transformation they can disintegrate or form internal rogue waves. Under these conditions the statistical moments of the wave field are essentially different from case when the breather-like waves cannot occur.</p><p>The research was supported by the RFBR grants No 19-05-00161 (TT and EP) and 19-35-60022 (ED). The Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS” (№ 20-1-3-3-1) is also acknowledged by ED</p>

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 The transformation of an interfacial solitary wave of elevation at a bottom step

2009 ◽  
Vol 16 (1) ◽  
pp. 33-42 ◽  
Author(s):  
V. Maderich ◽  
T. Talipova ◽  
R. Grimshaw ◽  
E. Pelinovsky ◽  
B. H. Choi ◽  
...  
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Numerical Study ◽  
Nonlinear Effects ◽  
Ocean Model ◽  
Gardner Equation ◽  
Fully Nonlinear ◽  
Layer Flow ◽  
The One ◽  
Bottom Step

Abstract. In this paper we study the transformation of an internal solitary wave at a bottom step in the framework of two-layer flow, for the case when the interface lies close to the bottom, and so the solitary waves are elevation waves. The outcome is the formation of solitary waves and dispersive wave trains in both the reflected and transmitted fields. We use a two-pronged approach, based on numerical simulations of the fully nonlinear equations using a version of the Princeton Ocean Model on the one hand, and a theoretical and numerical study of the Gardner equation on the other hand. In the numerical experiments, the ratio of the initial wave amplitude to the layer thickness is varied up one-half, and nonlinear effects are then essential. In general, the characteristics of the generated solitary waves obtained in the fully nonlinear simulations are in reasonable agreement with the predictions of our theoretical model, which is based on matching linear shallow-water theory in the vicinity of a step with solutions of the Gardner equation for waves far from the step.

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.

scholarly journals Internal solitary wave propagation observed by tandem satellites

2014 ◽  
Vol 41 (6) ◽  
pp. 2077-2085 ◽  
Author(s):  
Bingqing Liu ◽  
Hong Yang ◽  
Zhongxiang Zhao ◽  
Xiaofeng Li
Keyword(s):  
Wave Propagation ◽  
Solitary Wave ◽  
Internal Solitary Wave

Effects of mesoscale eddies on the internal solitary wave propagation

2012 ◽  
Vol 31 (5) ◽  
pp. 26-40 ◽  
Author(s):  
Guanghong Liao ◽  
Chenghao Yang ◽  
Xiaohua Xu ◽  
Xingang Shi ◽  
Yaochu Yuan ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Solitary Wave ◽  
Mesoscale Eddies ◽  
Internal Solitary Wave

Vortex generation due to internal solitary wave propagation past a sidewall constriction

2021 ◽  
Vol 913 ◽  
Author(s):  
David Deepwell ◽  
Cameron Clarry ◽  
Christopher Subich ◽  
Marek Stastna
Keyword(s):  
Wave Propagation ◽  
Solitary Wave ◽  
Internal Solitary Wave ◽  
Vortex Generation

Abstract

Experimental investigation of elevation internal solitary wave propagation over a ridge

2021 ◽  
Vol 33 (4) ◽  
pp. 042108
Author(s):  
Hui Du ◽  
Shao-Dong Wang ◽  
Xin-Long Wang ◽  
Jun-Nan Xu ◽  
Hai-long Guo ◽  
...  
Keyword(s):  
Experimental Investigation ◽  
Wave Propagation ◽  
Solitary Wave ◽  
Internal Solitary Wave

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.

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