scholarly journals The evolution of mode-2 internal solitary waves modulated by background shear currents

2018 ◽  
Vol 25 (2) ◽  
pp. 441-455 ◽  
Author(s):  
Peiwen Zhang ◽  
Zhenhua Xu ◽  
Qun Li ◽  
Baoshu Yin ◽  
Yijun Hou ◽  
...  
Keyword(s):  
Wave Packet ◽  
Shear Layer ◽  
Solitary Waves ◽  
Average Rate ◽  
Propagation Distance ◽  
Internal Solitary Waves ◽  
Long Wave ◽  
Shear Current ◽  
Mode 2 ◽  
Background Shear

Abstract. The evolution of mode-2 internal solitary waves (ISWs) modulated by background shear currents was investigated numerically. The mode-2 ISW was generated by the “lock-release” method, and the background shear current was initialized after the mode-2 ISW became stable. Five sets of experiments were conducted to assess the sensitivity of the modulation process to the direction, polarity, magnitude, shear layer thickness and offset extent of the background shear current. Three distinctly different shear-induced waves were identified as a forward-propagating long wave, oscillating tail and amplitude-modulated wave packet in the presence of a shear current. The amplitudes of the forward-propagating long wave and the amplitude-modulated wave packet are proportional to the magnitude of the shear but inversely proportional to the thickness of the shear layer, as well as the energy loss of the mode-2 ISW during modulation. The oscillating tail and amplitude-modulated wave packet show symmetric variation when the background shear current is offset upward or downward, while the forward-propagating long wave was insensitive to it. For comparison, one control experiment was configured according to the observations of Shroyer et al. (2010); in the first 30 periods, ∼ 36 % of total energy was lost at an average rate of 9 W m−1 in the presence of the shear current; it would deplete the energy of initial mode-2 ISWs in ∼ 4.5 h, corresponding to a propagation distance of ∼ 5 km, which is consistent with in situ data.

scholarly journals The evolution of mode-2 internal solitary waves modulated by background shear currents

2018 ◽  
Author(s):  
Peiwen Zhang ◽  
Zhenhua Xu ◽  
Qun Li ◽  
Baoshu Yin ◽  
Yijun Hou ◽  
...  
Keyword(s):  
Energy Transfer ◽  
Solitary Wave ◽  
Wave Packet ◽  
Solitary Waves ◽  
Transfer Process ◽  
Energy Transfer Process ◽  
Average Rate ◽  
Internal Solitary Waves ◽  
Mode 2 ◽  
Background Shear

Abstract. The evolution process of mode-2 internal solitary waves (ISWs) modulated by the background shear currents was investigated numerically. The forward-propagating long wave, amplitude-modulated wave packet were generated during the early stage of modulation, where the amplitude-modulated wave packet were suggested playing an important role in the energy transfer process, and then the oscillating tail was generated and followed the solitary wave. Five different cases were introduced to assess the sensitivity of the energy transfer process to the Δ, which defined as a dimensionless distance between the centers of pycnocline and shear current. The forward-propagating long waves were found robust to the Δ, but the oscillating tail and amplitude-modulated wave packet decreased in amplitude with increasing Δ. The highest energy loss rate was observed when Δ = 0. In the first 30 periods, ~ 36 % of the total energy lost at an average rate of 9 W m−1, it would deplete the energy of the solitary wave in ~ 4.5 h, corresponding to a propagation distance of ~ 5 km, which is consistent with the hypothesis of Shroyer et al. (2010), who speculated that the mode-2 ISWs are short-lived in the presence of shear currents.

scholarly journals Generation of Internal Solitary Waves by Lateral Circulation in a Stratified Estuary

2017 ◽  
Vol 47 (7) ◽  
pp. 1789-1797 ◽  
Author(s):  
Xiaohui Xie ◽  
Ming Li ◽  
Malcolm Scully ◽  
William C. Boicourt
Keyword(s):  
Solitary Waves ◽  
Tidal Flow ◽  
Tidal Currents ◽  
Internal Solitary Waves ◽  
Deep Channel ◽  
Mode 2 ◽  
Lee Wave ◽  
Salinity Data ◽  
Lateral Circulation ◽  
Stratified Estuary

AbstractInternal solitary waves are commonly observed in the coastal ocean where they are known to contribute to mass transport and turbulent mixing. While these waves are often generated by cross-isobath barotropic tidal currents, novel observations are presented suggesting that internal solitary waves result from along-isobath tidal flows over channel-shoal bathymetry. Mooring and ship-based velocity, temperature, and salinity data were collected over a cross-channel section in a stratified estuary. The data show that Ekman forcing on along-channel tidal currents drives lateral circulation, which interacts with the stratified water over the deep channel to generate a supercritical mode-2 internal lee wave. This lee wave propagates onto the shallow shoal and evolves into a group of internal solitary waves of elevation due to nonlinear steepening. These observations highlight the potential importance of three-dimensionality on the conversion of tidal flow to internal waves in the rotating ocean.

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 Higher-order Korteweg-de Vries models for internal solitary waves in a stratified shear flow with a free surface

2002 ◽  
Vol 9 (3/4) ◽  
pp. 221-235 ◽  
Author(s):  
R. Grimshaw ◽  
E. Pelinovsky ◽  
O. Poloukhina
Keyword(s):  
Free Surface ◽  
Shear Flow ◽  
Solitary Waves ◽  
Vries Equation ◽  
Wave Theory ◽  
Higher Order ◽  
Internal Solitary Waves ◽  
Long Wave ◽  
De Vries ◽  
Stratified Shear Flow

Abstract. A higher-order extension of the familiar Korteweg-de Vries equation is derived for internal solitary waves in a density- and current-stratified shear flow with a free surface. All coefficients of this extended Korteweg-de Vries equation are expressed in terms of integrals of the modal function for the linear long-wave theory. An illustrative example of a two-layer shear flow is considered, for which we discuss the parameter dependence of the coefficients in the extended Korteweg-de Vries equation.

Features of internal solitary waves revealed by seismic oceanography data

2020 ◽  
Author(s):  
Haibin Song ◽  
Wenhao Fan ◽  
Shaoqing Sun ◽  
Yongxian Guan ◽  
Kun Zhang ◽  
...  
Keyword(s):  
Phase Velocity ◽  
Central America ◽  
Solitary Waves ◽  
Sand Dunes ◽  
Maximum Amplitude ◽  
Internal Solitary Waves ◽  
Strait Of Gibraltar ◽  
Seismic Oceanography ◽  
Mode 2 ◽  
Reflection Configuration

<p>In this paper, we used the seismic oceanography method to study the structural characteristics of internal solitary waves (ISWs) near the Strait of Gibraltar in the Mediterranean Sea, South China Sea and offshore Central America.</p><p>The ISWs near the Strait of Gibraltar are the first mode depressional type, mostly medium amplitude and large amplitude internal solitary waves. The maximum vertical amplitude is up to 74.5m, and the amplitude increases with depth，the propagation velocity increases with amplitude. It can be determined that the "true" maximum amplitude position is near the pycnocline. After correction, the maximum half-height-width can reach 1721.8m, but there is somewhat different from the theoretical result，which may be related to the development stability of ISWs. As the solitary wave packet continuously moves eastward, the overall wave width becomes larger, and the vertical velocity becomes smaller. In this paper, seismic oceanography is applied to the analysis of ISWs in the Mediterranean Sea, which further proves the feasibility of using seismic oceanography to study the movement of sea water.</p><p>We reprocess some multi-channel seismic (MCS) data which is acquired recently in the Dongsha region of the northeastern South China Sea and we obtain new seismic oceanography data. The research suggest that there are the mode-2 internal solitary wave(ISWs) not just the mode-1 ISWs and a special reflection pattern (hair-like reflection configuration )usually above sand dunes in the seismic images. In new seismic oceanography data, there are some mode-1 ISWs with amplitudes less than 50m and wavelength of 1~5 km and the biggest mode-1 ISWs have the amplitude about 45m. The internal solitary waves packets are not prototypical rank-ordered ISW packets, their soliton amplitudes are smaller than 40. The mode-2 ISWs is well-shaped and its’ amplitude is approximate 30m, the vertical structure height is about 200m.The reflection configuration of water column above sand dunes usually include weak reflection layer-maybe called turbulent bottom boundary layer, and there is hair reflection configuration that must not appear. Whether there will be hair reflection configuration or not may depend on the angle between the seismic line and the sand dunes.</p><p>In the region offshore Central America, there are lots of mode-2 ISWs revealed from seismic oceanography data. We combine seismic data with hydrographic data to study the features of ISWs in these different regions. The preliminary results show the phase velocity in SCS is the largest, that in the Strait of Gibraltar is the second and that offshore Central America is the last. The phase velocity depends on the amplitude of ISW. Usually the mode-1 depressional ISW has the largest phase velocity, while the mode-1 elevation ISW is the second, and the mode-2 ISW is the last. The location of the maximum amplitude from the characteristic function is consistent with the pycnocline as shown from floating frequency curve. The polarity of ISW is consistent with nonlinear parameter of alpha. Seismic data in global continental margins will provide more and more key evidence to increase our understanding of ISW evolution in the ocean.</p>

Mode-2 internal solitary waves offshore Central America discovered by seismic oceanography method

2020 ◽  
Author(s):  
Wenhao Fan ◽  
Haibin Song ◽  
Yi Gong ◽  
Shaoqing Sun ◽  
Kun Zhang
Keyword(s):  
Phase Velocity ◽  
Central America ◽  
Solitary Waves ◽  
Kdv Equation ◽  
Seismic Survey ◽  
Internal Solitary Waves ◽  
Acquisition Time ◽  
Apparent Velocity ◽  
Seismic Oceanography ◽  
Mode 2

<p>In the past, most of the internal solitary waves (ISWs) found by seismic oceanography (SO) method were mode-1 ISWs. We discover many mode-2 ISWs in the Pacific coast of Central America by using SO method for the first time. These mode-2 ISWs are convex mode-2 ISWs with the maximum amplitudes of about 10 m, and most of them are ISWs with smaller amplitudes. The pycnocline for the mode-2 ISWs on the shelf (ISW3) is displaced 6.4% of the total seawater depth from the mid-depth of the total seawater. The deviation is large, and it shows a strong asymmetry feature of the peaks and troughs on the seismic profile. This is consistent with the results of previous numerical simulation. Observing the changes in the fine structure of mode-2 ISWs packet through pre-stack migration, it was found that the overall waveform of the three mode-2 ISWs (ISW1, ISW2, and ISW3) on the shelf during the acquisition time period of about 40 seconds is stable. The apparent phase velocity of these mode-2 ISWs calculated by the pre-stack migration section using the Common Offset Gathers is about 0.5 m/s, and their apparent propagation directions are from SW to NE along the seismic line (44 ° N, 0° pointing north). The vertical amplitude distribution and estimated apparent velocities of these mode-2 ISWs are basically consistent with the theoretical values ​​calculated from the KdV equation. By analyzing the apparent velocities of the three mode-2 ISWs (ISW1, ISW3, and ISW5) with relatively small apparent velocity errors, it is found that the apparent velocity of mode-2 ISWs generally increases with the increasing depth of seawater. In addition, the apparent phase velocity of the mode-2 ISWs with a larger maximum amplitude is generally larger. Based on the analysis of hydrological data in the study area, it was found that a strong anticyclone developed on the northwest side of the seismic survey line and a weaker anticyclone developed on the southeast side. These anticyclones will increase the depth of the thermocline in the surrounding seawater. According to previous studies, the deepening of the thermocline (pycnocline) maybe conducive to the generation of mode-2 ISWs.</p>

Mooring observed mode-2 internal solitary waves in the northern South China Sea

2020 ◽  
Vol 39 (11) ◽  
pp. 44-51
Author(s):  
Liang Chen ◽  
Xuejun Xiong ◽  
Quanan Zheng ◽  
Yeli Yuan ◽  
Long Yu ◽  
...  
Keyword(s):  
South China Sea ◽  
Solitary Waves ◽  
South China ◽  
Northern South China Sea ◽  
Internal Solitary Waves ◽  
China Sea ◽  
Mode 2
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