内孤立波过陆架陆坡地形的数值模拟研究

内波是海洋中普遍存在的波动形式。内孤立波是典型的非线性内波,多发于陆架边缘海,如南海等海域,对陆架海域有重要影响。本文针对内孤立波在陆架地形上的传播问题,先基于弱非线性与全非线性数值模型,模拟了不同振幅、地形高度条件下内孤立波的演化的过程,探讨了动力系数对内孤立波演化过程的影响,对比了两模型的模拟结果在内孤立波演化过程、能量分配以及能量耗散的差异,后分析了南海的动力系数分布特征。结果表明,在内孤立波不发生破碎的情况下,弱非线性模型与全非线性模拟结果相近。当发生破碎过程时,弱非线性模型可准确模拟头波,但无法通过强非线性的破碎过程耗散能量,只能以裂变的方式辐射能量。在弱非线性模型中,随地形高度增加,频散系数减小到零,平方非线性系数由负转正,立方非线性系数绝对值增大一个量级,并主导陆架地形上内孤立波的演化过程。通过对比南海夏季与冬季非线性内波动力系数空间分布,发现内孤立波在传播过程由于夏季平方非线性效应、立方非线性效应与频散效应较强的影响,其在夏季更易发生陡化与裂变,波列发生频率高。     

Seasonal and spatial variations of kinematic parameters of internal solitary waves in the Andaman Sea

The horizontally variable density stratification and background currents are taken into the variable-coefficent extended Korteweg-de Vries(evKdV) theory to obtain the geographical and seasonal distribution of kinematic parameters of internal solitary waves in the Andaman Sea(AS). The kinematic parameters include phase speed,dispersion parameter, quadratic and cubic nonlinear parameters. It shows that the phase speed and dispersion parameter are mainly determined by the topographic feature and ha...     

南海北部内孤立波数学模型

在二层内潮数学模型的基础上,考虑非静力平衡扰动压力的影响,导出潮频内孤立波产生、传播的数学模型。该模型不受小地形假设的限制,并适用于南海。应用该模型能解释说明产生以下现象的物理机制：潮流流过巴坦-萨布坦海脊时,在一定海洋环境条件下,通过潮流与起伏的底地形相互作用可激发产生潮频内孤立波,并西传至东沙群岛附近的海域。     

veKdv方程的若干系数在南海北部的地理分布特征及其季节变化分析

应用中国近海及邻近海域海洋再分析资料(简称CORA)研究南海北部第一模态内波场运动学参数的地理分布特征及其季节变化。首先分析了Brunt-Väisälä频率的统计特征;其次,基于弱非线性变系数扩展Kortewed-de Vries (veKdv)方程模型,计算了它的输入系数,即线性长波相速度,平方和立方非线性系数和频散系数,这些参数可用于定性评估内孤立波传播可能的极性,内孤立波的形态,幅度限制以及传播速度等。分析结果表明,南海北部季节性密度跃层从2月开始出现,最大浮力频率约在20 m。它在6—7月达到最强,自8月开始减弱,在10月消退。另一密度跃层出现在8—11月,最大浮力频率约在80 m,冬季大致在120 m。季节性密度跃层在4—9月十分明显,而8—10月双跃层现象显著,冬季仅出现较弱的第二密度跃层。在1—3月和10—12月海盆深水区最大Brunt-Väisälä频率值要大于陆架浅水区;而在5—9月情况则相反。Brunt-Väisälä频率最大值所在深度随季节变化显著,冬季最深,6—7月则最浅。计算的线性内波相速度、频散系数和幅度放大因子的空间特征主要取决于地形变化;平方(立方)非线性系数与地形关系较小,随季节变化明显,它们主要取决于局地海洋环境特征。通过分析veKdv方程的系数特征,解释了为何在夏季南海北部最容易观测到大振幅内孤立波和在吕宋海峡以东海域难以观测到孤立波的原因。     

基于遥感与现场观测数据的南海北部内波传播速度

南海北部是全球海洋中内波最为活跃、生成和演变机制较为复杂的海域,本文利用多源卫星遥感数据(MODIS、GF-1、ENVISAT ASAR、RADARSAT-2)和现场观测数据开展了南海北部内波传播速度的研究。通过匹配捕获同一条内波的相邻两幅遥感图像,由内波的空间位移和时间间隔反演传播速度,并以0.5°×0.5°网格给出了南海北部内波传播速度的分布图。研究结果表明,内波传播速度受背景流场、水体层结和底地形变化等多因素影响,特别是水深。在南海北部由东至西、由南至北方向,内波传播速度逐渐递减。深海区内波传播速度最大,可达3m/s以上;内波在向西大陆架传播过程中,随着水深变浅速度逐渐减慢,传播速度为1—2m/s;大陆架浅海的内波传播速度较小,仅为零点几米每秒。同时,利用Kd V方程反演了内波传播速度理论值,对遥感数据提取的内波传播速度进行了精度验证,结果较为一致。     

Assessment of theoretical approaches to derivation of internal solitary wave parameters from multi-satellite images near the Dongsha Atoll of the South China Sea

This study assesses the accuracy and the applicability of the Korteweg-de Vries(KdV) and the nonlinear Schr?dinger(NLS) equation solutions to derivation of dynamic parameters of internal solitary waves(ISWs) from satellite images. Visible band images taken by five satellite sensors with spatial resolutions from 5 m to 250 m near the Dongsha Atoll of the northern South China Sea(NSCS) are used as a baseline. From the baseline, the amplitudes of ISWs occurring from July 10 to 13, 2017 are estimate...     

A study of SAR remote sensing of internal solitary waves in the north of the South China Sea:I.Simulation of internal tide transformation

For settlement of the well-known problem of contemporary radar imaging models,i.e.,the pmblem of a general underestimation of radar signatures of hydrodynamic features over oceanic internal waves and underwater bottom topography in tidal watels at at high radar frequency bands(X-band and C-band),the impact of the ocean surface mixed layer turbulence and the significance of strat-ified oceanic model on SAR remote sensing of internal solitary waves are proposed.In the north of the South China Sea by utilizing seme observed data of background field the nonlinearity coefficient,the dispersion coefficient,the horizontal variability coefficient and the phase speed in the generalized K-dV equation are determined approximately.Through simulations of internal tide transfor-mation the temporal evolution and spatial distribution of the vertical displacement and horizontal velocity of intereal wave field are obtained.The simulation results indicate that the maximum amplitudes of internal solitary waves occur at depth 35 m,but the maximum current speeds take place at depth 20 m in this area of the sea(about 20°30'N,114°E)in August.It was noticed that considering the effects of flood current and ebb current respectively is appropriate to investigate influence of the background shear flow on coefficients of the K-dV equation.The obtained results provide the possibility for the simulation of SAR signatures of inter-nal solitary waves under considering the impact of ocean surface mixed layer turbulence in the companion paper.     

基于哨兵一号和高分三号卫星SAR数据的马六甲海峡内孤立波特性研究

漫长狭窄的马六甲海峡是重要的航道,研究该海峡内孤立波特征对潜艇、船只航行和海洋工程都是急需解决的问题。利用高空间分辨率的哨兵1号（Sentinel-1）和高分三号（GF-3）SAR遥感数据,对马六甲海峡的内孤立波特征开展了详细研究。利用哨兵一号2015年6月到2016年12月20景有内孤立波的SAR图像和高分三号2018年4月到2019年3月24景有内孤立波的SAR图像,统计分析了马六甲海峡海域的内孤立波空间分布特征。发现内孤立波多以内孤立波包以及单根内孤立波形式出现,内孤立波头波的波峰线最长可达39km。采用高阶非线性薛定谔方程反演模型可以计算出内孤立波的振幅与群速度,计算得到的内孤立波振幅和波包的传播群速度分别为4.7m ~ 23.9m和0.12m/s ~ 0.40m/s。由KdV方程得到的单根内孤立波的相速度为0.26m/s ~ 0.60m/s。可以得到,马六甲海峡内孤立波的振幅与传播速度与地形密切相关。     

Observation and analysis of solitary internal waves in the coastal zone of the Sea of Okhotsk

Experimental data on the measurement of solitary internal waves in the coastal zone of the Sea of Okhotsk are reported. The non-linear and dispersion coefficients of the Korteweg-de Vries (KdV) equation are determined for weakly non-linear disturbances of the first mode. The shapes and parameters of solitary waves are compared with the corresponding parameters of solitons. It is shown that at least ten observed solitary waves are similar to the KdV solitons. Histograms of the distribution of the amplitudes, duration, and spatial dimensions are plotted for a large number of solitary waves.Translated by Mikhail M. Trufanov.     

A study of SAR remote sensing of internal solitary waves in the north of the South China Sea: Ⅰ. Simulation of internal tide transformation

For settlement of the well-known problem of contemporary radar imaging models, i. e. , the problem of a general underestimation of radar signatures of hydrodynamic features over oceanic internal waves and underwater bottom topography in tidal waters at high radar frequency bands （ X-band and C-band）, the impact of the ocean surface mixed layer turbulence and the significance of strat- ified oceanic model on SAR remote sensing of internal solitary waves are proposed. In the north of the South China Sea by utilizing some observed data of background field the nonlinearity coefficient, the dispersion coefficient, the horizontal variability coefficient and the phase speed in the generalized K-dV equation are determined approximately. Through simulations of internal tide transfor- mation the temporal evolution and spatial distribution of the vertical displacement and horizontal velocity of internal wave field are obtained. The simulation results indicate that the maximum amplitudes of internal solitary waves occur at depth 35 m, but the maximum current speeds take place at depth 20 m in this area of the sea （about 20°30＇N, 114°E） in August. It was noticed that considering the effects of flood current and ebb current respectively is appropriate to investigate influence of the background shear flow on coefficients of the K-dV equation. The obtained results provide the possibility for the simulation of SAR signatures of internal solitary waves under considering the impact of ocean surface mixed layer turbulence in the companion paper.     

苏禄—苏拉威西海内孤立波动力参数时空变化特征

基于弱非线性理论及再分析同化数据,计算了苏禄—苏拉威西海冬季及夏季内孤立波动力参数,包括内孤立波线性速度、一阶和二阶非线性参数及线性色散参数,并研究了这些参数的时空变化特征。我们发现,虽然苏拉威西海域受到更加显著的西北太平洋水入侵,但苏禄海内孤立波动力参数的时空变化特征却比苏拉威西海更为显著。夏季苏禄海内孤立波线性速度总体上比冬季约大0.1m·s^–1;与此相反,夏季苏拉威西海内孤立波线性速度却比冬季约小0.05m·s^–1。无论是一阶或二阶非线性动力参数,其在苏拉威西海的时空变化均比较微弱,但在苏禄海则较为显著。苏禄海夏季一阶非线性动力参数比冬季高出约3×10^–3s^–1,但是夏季二阶非线性动力参数却比1月份低约3×10^–5m^–1·s^–1。此外,相比冬季,夏季苏禄海和苏拉威西海的色散动力参数均有所减弱,但其在苏禄海减弱的幅度更大。综上,苏禄—苏拉威西海环流引起的水体层化最大浮力频率所在深度的时空变化是造成上述内孤立波动力参数时空变化的根本...     

Effects of mesoscale eddies on the internal solitary wave propagation

The mesoscale eddy and internal wave both are phenomena commonly observed in oceans. It is aimed to investigate how the presence of a mesoscale eddy in the ocean affects wave form deformation of the internal solitary wave propagation. An ocean eddy is produced by a quasi-geostrophic model in f-plane, and the one-dimensional nonlinear variable-coefficient extended Korteweg-de Vries (eKdV) equation is used to simulate an internal solitary wave passing through the mesoscale eddy field. The results suggest that the mode structures of the linear internal wave are modified due to the presence of the mesoscale eddy field. A cyclonic eddy and an anticyclonic eddy have different influences on the background environment of the internal solitary wave propagation. The existence of a mesoscale eddy field has almost no prominent impact on the propagation of a smallamplitude internal solitary wave only based on the first mode vertical structure, but the mesoscale eddy background field exerts a considerable influence on the solitary wave propagation if considering high-mode vertical structures. Furthermore, whether an internal solitary wave first passes through anticyclonic eddy or cyclonic eddy, the deformation of wave profiles is different. Many observations of solitary internal waves in the real oceans suggest the formation of the waves. Apart from topography effect, it is shown that the mesoscale eddy background field is also a considerable factor which influences the internal solitary wave propagation and deformation.     

基于机器学习的内孤立波波要素关系研究

内孤立波在海洋中的传播会携带能量和动量,不同振幅的内孤立波对海洋中的能量交换及海上工程等影响也不同,因此,研究内孤立波振幅与半波宽度、水深、分层条件、密度等水文特征参量之间的关系显得尤为重要.以往在研究中建立内孤立波振幅与它们之间的关系时,会受到不同理论有效适用范围的限制.本文借助实验室的水槽方法,设计了不同的水深、分...     

Gerris在海洋大振幅内孤立波数值模拟中的应用

本文运用基于自适应网格的流体动力学开源软件Gerris,来建立基于Boussinesq近似下的二维不可压缩Euler方程组的数值模型,以模拟不同层化条件下稳定状态的完全非线性大振幅内孤立波。文中比较了完全非线性的用Gerris实现的Euler模型与弱非线性的KdV理论模型在刻画大振幅内孤立波结构及特征参数上的差异,说明在模拟大振幅内孤立波时,高阶非线性不应忽略。Euler模型模拟结果表明,完全非线性大振幅内孤立波的等密度面半宽度随深度变化,这使得基于KdV方程解析解、利用卫星SAR(Synthetic Aperture Radar)图像提取内孤立波极值间距来反演内波振幅的可行性存疑,需要重新评估。此外,本文用两组实测数据验证了用Gerris实现的Euler模型模拟大振幅内波的有效性。     

相同尺度地形与背景流共振生成内孤立波机制

为研究内孤立波的地形和背景流共振机制,用地形和背景流共振机制计算了3个潜标观测的内孤立波(不同模态、不同波长)的流速和传播速度,并与观测到的内孤立波进行比较。潜标观测的第一模态内孤立波(波长分别为6.4和3.3km)都是下凹型内孤立波,2个内孤立波的传播速度约为1.4m/s、最大振幅约为48m,水平流向结构都是上层西北向、下层东南向,波长3.3km 的内孤立波波峰前后有更明显的下降流和上升流。用共振机制计算出的第一模态和第二模态纬向流速的垂向结构与观测相同,最大纬向流速出现的深度与观测一致,分别相差5和12m。用共振机制计算出的内孤立波传播速度与用 KdV 方程计算的传播速度相当,共振机制计算波速为0.66~1.21m/s,KdV 方程计算波速为0.79~1.40m/s。     

内孤立波破碎后对斜坡沉积物的动力作用过程及特性实验研究

为完善内孤立波与海底斜坡沉积物相互作用研究,本文着眼于内孤立波破碎后在斜坡上继续运动的阶段,开展物理模拟实验,分析斜坡响应的土压力和超孔隙水压力的变化状况,揭示内波作用过程。研究发现:斜坡沉积物颗粒在内孤立波破碎引起的涡旋和渗流的共同作用下,会发生再悬浮,斜坡坡度变化不改变沉积物产生动力响应的主导动力作用;内孤立波振幅大小影响涡旋与渗流两者的比例,即在小振幅条件下由涡旋作用主导,在大振幅条件下由渗流作用主导;破碎流体在沿斜坡冲出坡顶位置后形成新的涡流,沉积物在新生涡流作用下的动力响应受斜坡坡度的影响。本文结果对于研究内孤立波再悬浮运移海底沉积物、改造海底地形地貌具有参考价值。     

Monthly variation of some parameters about internal solitary waves in the South China sea

In this paper, by non-dimensional analysis, it is found that finite-depth theory is more appropriate to the study of internal solitary waves (ISWs) in the South China Sea (SCS) than shallow-water theory. The 1-degree grid data of monthly mean temperature and salinity data at standard levels in the SCS are used to solve the linearized vertical eigenvalue problem. The nonlinear parameter and the wave phase speed are computed, then the nonlinear phase speed and the characteristic half-width of ISWs are calculated respectively by two different theories to investigate the difference between these two parameters in the SCS. The nonlinearity is the strongest near the continental slope of the SCS or islands where the bottom topography changes sharply, it is stronger in summer than that in winter; it increases (decreases) as pycnocline depth deepens (shallows), stratification strengthens (weakens) and pycnocline thickness thins (thickens). The nonlinear wave phase speed and the characteristic half-width are the largest in deep sea area, they then reduce peripherally in shallower water. The nonlinear wave phase speed in the SCS changes slightly with time, but the characteristic half-width changes somewhat larger with time. In most of the SCS basin, the nonlinear wave phase speed derived from shallow-water theory is very close to that derived from finite-depth theory, but the characteristic half-width derived from shallow-water theory is about 0.2–0.6 times larger than that derived from finite-depth theory. The ISW induced horizontal current velocity derived from shallow-water theory is larger than that derived from finite-depth theory. Some observed and numerical modeled ISW characteristic half-widths are compared with those derived from shallow-water and finite-depth theories, respectively. It is shown that, the characteristic half-widths derived from finite-depth theory agree better with observational and numerical modeled results than those derived from shallow-water theory in most cases, finite-depth theory is more applicable to the estimation of ISW characteristic half-widths in the northern SCS. It is also suggested that, to derive the precise ISW parameters in further study, the physical non-dimensional ratios which are related with ISW characteristic half-width, amplitude, thermocline and water depths should be calculated, so that an appropriate theory can be chosen for estimation.     

Run-Up of a Solitary Tsunami Wave on a Sloping Coast

Within the framework of the nonlinear theory of long waves, we perform the numerical analysis of the one-dimensional run-up of solitary tsunami waves upon a plane sloping coast. We study the dependences of the run-up heights on the parameters of waves at the entrance of the shelf zone and on the slope of the coast. The run-up heights of tsunami waves are estimated for the bottom topography typical of the south coast of the Crimean Peninsula. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 4, pp. 11–18, July–August, 2005.     

THE NONLINEAR INTERNAL GRAVITY WAVES IN STRATIFIED FLUID

In this paper, starting from the equations of the nonlinear internal gravity waves in stratified fluid, using the method of the Taylor expansion nearby the equilibrium point for the nonlinear terms, we find the analytical solutions for nonlinear internal gravity waves. The linear internal gravity waves and solitary waves are its special cases. The nonlinear internal gravity waves satisfy the well-known KdV (Karteweg-de Vries) equation. The nonlinear internal gravity waves are different from linear waves in character. The former dispersive relation contains the amplitude, but the latter does not. The larger the amplitude and the wavelength the faster are waves for the nonlinear internal gravity waves. The smaller the stability of the stratification, the larger is the wavelength (or the width). Some phenomena such as squall line, cumulus, turbulent mass structure in atmosphere, and thermocline in ocean have these natures.     

基于调制不稳定性的吕宋海峡内孤立波生成机理探讨

The South China Sea (SCS) is a hot spot for oceanic internal solitary waves due to many factors, such as the complexity of the terrain environment. The internal solitary waves in the northern SCS mainl...