南海北部内潮与非线性内波：观测与数值模拟研究
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摘要
基于水文观测和数值模拟研究了南海北部内潮和非线性内波现象，主要内容有：吕宋海峡的测流观测与线性内波配极关系的比较；南海北部非线性内波背景环境及运动学参数的地理特征及其季节变化；中尺度涡旋对内孤立波传播影响的数值模拟；南海北部陆坡区内孤立波极性转换的数值模拟和吕宋海峡双屋脊上内波产生的数值模拟。
1.吕宋海峡内潮的观测分析
鉴于吕宋海峡观测流的稀少，开展了该海域的海流锚定观测。运用统计和经验正交函数分析方法研究了观测流特征。谱分析和能量计算均显示全日潮和半日潮为主要的能量频带，近惯性频率峰值仅出现在斜压分量。在66m以浅，显著分潮和近惯性频率分量都基本符合线性内波能量一致性关系式E+(ω)/E-(ω)=(ω-f)~2/(ω+f)~2；在其它观测深度，并非所有的主要分潮都满足上述关系。正压潮和内潮均为混合潮，潮日不等现象明显。全日分潮平行与垂直于陆架方向的分量几乎相等；而半日分潮垂直于陆架方向分量远大于平行于陆架方向分量；M2和S2潮垂向结构主要表现为第一模态，而K1和O1潮则接近于第二模态；在主温跃层附近，它们的短轴与长轴之比与比值f/ω接近。
2.南海北部非线性内波背景环境及运动学参数的地理特征及其季节变化
从遥感图像的统计分析表明，南海北部内波呈现显著的季节变化。基于海洋再分析资料研究了南海北部的层化特征和非线性内波运动学参数的地理分布特征和季节变化。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20m；它在6-7月达到最强，自8月开始减弱，在10月消退。在8-11月出现另一较深的密度跃层，最大浮力频率约在80m，冬季大致在120m。季节性密度跃层在4-9月十分明显，在8-10月出现双跃层现象，而在冬季仅出现较弱的第二密度跃层。在1-3月和10-12月深水区最大浮力频率值要大于浅水区，而在5-9月情况则相反。浮力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。线性内波相速度、频散系数和幅度放大因子的空间分布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，随季节变化较大，它们主要取决于局地海洋环境特征。分析了变系数扩展KdV方程中出现的系数特征，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。
3.中尺度涡旋对内孤立波传播影响的数值模拟
内波和中尺度涡都是海洋中出现的普遍现象，中尺度涡对内波的传播具有怎样的影响呢？应用准地转模型假定得到中尺度涡旋场，变系数扩展KdV方程用于模拟内孤立波通过中尺度涡的形变。计算结果表明，中尺度涡旋修改了线性内波的垂直模态结构，而且气旋涡和反气旋涡对内波传播的背景环境具有不同的影响。仅考虑第一模态垂直结构背景场，则中尺度涡对小振幅内孤立波的传播几乎不存在影响。但是，对高模态的垂直结构背景场，对内孤立波的传播的影响十分明显。在观测中，通常在不同位置观测到的内孤立波波形各异,研究结果表明除了地形影响因素外，中尺度涡背景场对内孤立波的传播和形变也是一个重要的影响因素，且不同的中尺度涡对内孤立波具有不同的影响。
4.南海北部陆坡区内孤立波极性转换的数值模拟
卫星图像经常观测到南海北部陆坡区内波的极性转换现象，采用数值模拟研究了南海北部陆坡区内孤立波极性转换的物理过程。深水区的下降型内孤立波在向陆坡传播过程中，受地形变浅的影响，波形尾部加陡，并在尾部分裂出孤立子列，逐渐出现上凸型的内孤立波；随着水深越来越浅，上凸型内孤立波幅度也逐渐增大，且头波与后面波列的距离也逐渐增大，体现了内波的频散特性。
5.吕宋海峡双屋脊上内波产生的数值模拟
卫星图像观测表明吕宋海峡是南海北部内波产生的重要源区，数值模拟吕宋海峡双屋脊上内波的产生，表明在表层难以追踪到内波信号，这与从卫星图像观测到的内波信号也主要出现在120.5°E以西海域相一致。落潮阶段在吕宋海脊的西侧形成涌潮；当落潮流减弱并开始转向时，首先在涌潮前锋裂变出孤立子，当潮流转向和涨潮流加强时，更多的孤立子裂变出来。在吕宋海脊东侧，无论是涨潮还是落潮均存在一个上升型波，但未发现有孤立子从东侧的上升型波裂变出来。对于全日潮和半日潮，吕宋海峡两个海脊都是超临界地形，潮程参数小于1，处于内潮生成区，因此潮流与地形相互作用促使内潮生成，内潮波束向上和向下辐射逐渐演变成内潮涌，再由于非线性加陡和频散效应裂变成孤立子波。
This paper investigates phinomina of internal tide and nonlinear internal wave inthe Northern South China Sea (NSCS) based on hydrographic field observation andnumerical simulation. Including: the analysis of direct-obervation current data in theLuzon Strait (LS), and comparition between observation and polarization relations forlinear internal wave; the geostriphical distribution and seasonal characteristic of thebackground environment and mechanism parameters of nonlinear internal wave in theNSCS, the influence of mesoscale eddy on internal solitary wave propagation, thenumerical simulation for depression to elevation conversation of large-amplitudeinternal solitary wave in the shelf of the NSCS, and the numeicial simulation of thegeneration for internal wave on the double ridges in the LS.
1. The analysis of observational current in the LS
Due to rare observation for current in the LS, the moring observation was carriedout. The characteristics of current are investigated by using statistic analysis andEmpirical Orthogonal Function. Spectral analysis and energy estimation show that thediurnals and semidiurnals carry most of the energy of internal tides. Near-inertialpeaks are only present in the baroclinic component. The behavior of typical tidalfrequencies and the near-inertial frequency is basically consistent with linear internalwave theory, which predicts E+(ω)/E-(ω)=(ω-f)~2/(ω+f)~2at depths above66m, whilenot all prominent tidal components coincide well with the relation of the linearinternal wave field at other depths. The surface tides and internal tides are both ofmixed type. The K1and O1tides have comparable cross-and along-shelf components,while the M2and S2tides propagate toward the shelf in the northern South China Seaas wave beams. The M2and S2tides appear to have structures dominated by the firstmode, while the K1and O1tides resemble second-mode structures. The minor tomajor axis ratios are close to expected values of f/ω in the thermocline.
2. Geostriphical distribution and seasonal characteristic of the backgroundenvironment and mechanism parameters of nonlinear internal wave in theNSCS
The phenomena of internal waves in the SCS show remarkable seasonal andinterannual variance from satellite image. On the basis reanalysis data, the stratification characteristics, and the geographical and monthly variability of theeKdV equation coefficients, are analyzed. Seasonal pycnocline with maximalbuoyancy frequency at about20m depth, begins to appear in February, is strongest inJun and Jul., weakens in Aug., starts to dissipate in Oct. Another deeper pycnoclineappears with maximal buoyancy frequency at about80m depth during Aug. and Nov.,and maximal buoyancy frequency moves to120m depth in winter. The seasonalpycnocline is very distinct from Apr. to Sep.. The double pycnocline is obvious fromAugust to Oct.. In winter, only the second pycnocline exists. Maxima buoyancyfrequency in deeper basin is higher than that in shallow shelf area from Jan. to Mar.and from Oct. to Dec., but the configuration is opposite during May and Sep.. Thedepth of maxima buoyancy frequency varies with season. It is deepest in winter, andis shallowest in June and July. It is shown that the variations of the long wave phasespeed, the dispersion parameter and amplitude factor are mainly related to topographycharacteristics without obvious seasonal variation. The quadratic nonlinear parameteris very sensitive to variations of the vertical stratification, and the cubic nonlinearparameter depends on water depth and stratification condition. Holding higheroccurrence in summer in the NSCS and the scarce existence of nonlinear internalwave on east of the LS is interpreted by using theses coefficient characteristic.
3. Mesoscale eddy effects on the internal solitary wave propagation
The mesoscale eddy and internal wave both are phenomena commonly observedin oceans. This paper aims to investigate how the presence of a mesoscale eddy in theocean affects waveform deformation of the internal solitary wave propagation. Anocean eddy is produced by a quasi-geostrophic model in f-plane, and theone-dimensional nonlinear eKdV equation is used to simulate an internal solitarywave passing through the mesoscale eddy field. The results suggest that the modestructures of the linear internal wave are modified due to the presence of themesoscale eddy field. A cyclonic eddy and an anticyclonic eddy do differentinfluences on background environment of internal solitary wave propagation. Theexistence of a mesoscale eddy field has almost no prominent impact on thepropagation of a small-amplitude internal solitary wave only based on the first modevertical structure, but the mesoscale eddy background field exerts a considerableinfluence on solitary wave propagation if considering high-mode vertical structures.Furthermore, whether an internal solitary wave first passes through anticyclonic eddyor cyclonic eddy, the deformation of wave profiles is different. Many observations of solitary internal waves in the real oceans suggest formation of the waves, excepttopography effect, this study shows that the mesoscale eddy background field is alsoan considerable factor which influences the internal solitary wave propagation anddeformation.
4. The numerical simulation for polarity covertion of interal solitary wave in theself of the NSCS
The phenomia of polarity covertion of internal solitary wave oftern are capturedby satellite images in the shelf of the NSCS. The physical process that internal wavetransfers their polrity is investigated by the numerical simulation. When the depressssolitary wave propates from deeper water area to shallower water area, the rear of thewave begin to speepen owing to effect of shallower topography, some soliton split outfrom the rear of the wave, the elevation solitary wave appears slowly, with theshallower water depth, the amplitude of the elevation solitary wave is growing, andthe distance between the front wave and behind wave is also increasing, showing thepersperion property of internal wave.
5. The numerical simulation for generation of internal wave on the doubleridges in the LS
The satellite images show the LS is an important original area for internal wavein the NSCS. It is difficult to trace the internal wave siginal in the sea surface of theLS from the results of the numerical simulation, this consists with observations fromsatellite images, which also demonstrated that the internal signals mainly present westof120.5°E. The tidal bore is firstly built up to west of the Luzon ridge in the ebbyphase. When the ebby tide current weaks and becomes flood, the soliton splits outfrom the front of the tidal bore. More and more solitons split out with the enhancedflood. An elevation wave is observed to east of the Luzon ridge during both ebby andflood phases, howere, there is no any solion fission from the evevation wave. Thedouble ridges is supercritical with respect to both diurnal and semidiurnal tides, andthe tide excursion parameter is less than1, so the LS is suitable for the generation ofinternal tides. The tidal beam radiates upward and downward and evolutes the internaltidal born, and the solitary waves split out on the premise of nonlinear and dispersioneffects.
1.吕宋海峡内潮的观测分析
鉴于吕宋海峡观测流的稀少，开展了该海域的海流锚定观测。运用统计和经验正交函数分析方法研究了观测流特征。谱分析和能量计算均显示全日潮和半日潮为主要的能量频带，近惯性频率峰值仅出现在斜压分量。在66m以浅，显著分潮和近惯性频率分量都基本符合线性内波能量一致性关系式E+(ω)/E-(ω)=(ω-f)~2/(ω+f)~2；在其它观测深度，并非所有的主要分潮都满足上述关系。正压潮和内潮均为混合潮，潮日不等现象明显。全日分潮平行与垂直于陆架方向的分量几乎相等；而半日分潮垂直于陆架方向分量远大于平行于陆架方向分量；M2和S2潮垂向结构主要表现为第一模态，而K1和O1潮则接近于第二模态；在主温跃层附近，它们的短轴与长轴之比与比值f/ω接近。
2.南海北部非线性内波背景环境及运动学参数的地理特征及其季节变化
从遥感图像的统计分析表明，南海北部内波呈现显著的季节变化。基于海洋再分析资料研究了南海北部的层化特征和非线性内波运动学参数的地理分布特征和季节变化。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20m；它在6-7月达到最强，自8月开始减弱，在10月消退。在8-11月出现另一较深的密度跃层，最大浮力频率约在80m，冬季大致在120m。季节性密度跃层在4-9月十分明显，在8-10月出现双跃层现象，而在冬季仅出现较弱的第二密度跃层。在1-3月和10-12月深水区最大浮力频率值要大于浅水区，而在5-9月情况则相反。浮力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。线性内波相速度、频散系数和幅度放大因子的空间分布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，随季节变化较大，它们主要取决于局地海洋环境特征。分析了变系数扩展KdV方程中出现的系数特征，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。
3.中尺度涡旋对内孤立波传播影响的数值模拟
内波和中尺度涡都是海洋中出现的普遍现象，中尺度涡对内波的传播具有怎样的影响呢？应用准地转模型假定得到中尺度涡旋场，变系数扩展KdV方程用于模拟内孤立波通过中尺度涡的形变。计算结果表明，中尺度涡旋修改了线性内波的垂直模态结构，而且气旋涡和反气旋涡对内波传播的背景环境具有不同的影响。仅考虑第一模态垂直结构背景场，则中尺度涡对小振幅内孤立波的传播几乎不存在影响。但是，对高模态的垂直结构背景场，对内孤立波的传播的影响十分明显。在观测中，通常在不同位置观测到的内孤立波波形各异,研究结果表明除了地形影响因素外，中尺度涡背景场对内孤立波的传播和形变也是一个重要的影响因素，且不同的中尺度涡对内孤立波具有不同的影响。
4.南海北部陆坡区内孤立波极性转换的数值模拟
卫星图像经常观测到南海北部陆坡区内波的极性转换现象，采用数值模拟研究了南海北部陆坡区内孤立波极性转换的物理过程。深水区的下降型内孤立波在向陆坡传播过程中，受地形变浅的影响，波形尾部加陡，并在尾部分裂出孤立子列，逐渐出现上凸型的内孤立波；随着水深越来越浅，上凸型内孤立波幅度也逐渐增大，且头波与后面波列的距离也逐渐增大，体现了内波的频散特性。
5.吕宋海峡双屋脊上内波产生的数值模拟
卫星图像观测表明吕宋海峡是南海北部内波产生的重要源区，数值模拟吕宋海峡双屋脊上内波的产生，表明在表层难以追踪到内波信号，这与从卫星图像观测到的内波信号也主要出现在120.5°E以西海域相一致。落潮阶段在吕宋海脊的西侧形成涌潮；当落潮流减弱并开始转向时，首先在涌潮前锋裂变出孤立子，当潮流转向和涨潮流加强时，更多的孤立子裂变出来。在吕宋海脊东侧，无论是涨潮还是落潮均存在一个上升型波，但未发现有孤立子从东侧的上升型波裂变出来。对于全日潮和半日潮，吕宋海峡两个海脊都是超临界地形，潮程参数小于1，处于内潮生成区，因此潮流与地形相互作用促使内潮生成，内潮波束向上和向下辐射逐渐演变成内潮涌，再由于非线性加陡和频散效应裂变成孤立子波。
This paper investigates phinomina of internal tide and nonlinear internal wave inthe Northern South China Sea (NSCS) based on hydrographic field observation andnumerical simulation. Including: the analysis of direct-obervation current data in theLuzon Strait (LS), and comparition between observation and polarization relations forlinear internal wave; the geostriphical distribution and seasonal characteristic of thebackground environment and mechanism parameters of nonlinear internal wave in theNSCS, the influence of mesoscale eddy on internal solitary wave propagation, thenumerical simulation for depression to elevation conversation of large-amplitudeinternal solitary wave in the shelf of the NSCS, and the numeicial simulation of thegeneration for internal wave on the double ridges in the LS.
1. The analysis of observational current in the LS
Due to rare observation for current in the LS, the moring observation was carriedout. The characteristics of current are investigated by using statistic analysis andEmpirical Orthogonal Function. Spectral analysis and energy estimation show that thediurnals and semidiurnals carry most of the energy of internal tides. Near-inertialpeaks are only present in the baroclinic component. The behavior of typical tidalfrequencies and the near-inertial frequency is basically consistent with linear internalwave theory, which predicts E+(ω)/E-(ω)=(ω-f)~2/(ω+f)~2at depths above66m, whilenot all prominent tidal components coincide well with the relation of the linearinternal wave field at other depths. The surface tides and internal tides are both ofmixed type. The K1and O1tides have comparable cross-and along-shelf components,while the M2and S2tides propagate toward the shelf in the northern South China Seaas wave beams. The M2and S2tides appear to have structures dominated by the firstmode, while the K1and O1tides resemble second-mode structures. The minor tomajor axis ratios are close to expected values of f/ω in the thermocline.
2. Geostriphical distribution and seasonal characteristic of the backgroundenvironment and mechanism parameters of nonlinear internal wave in theNSCS
The phenomena of internal waves in the SCS show remarkable seasonal andinterannual variance from satellite image. On the basis reanalysis data, the stratification characteristics, and the geographical and monthly variability of theeKdV equation coefficients, are analyzed. Seasonal pycnocline with maximalbuoyancy frequency at about20m depth, begins to appear in February, is strongest inJun and Jul., weakens in Aug., starts to dissipate in Oct. Another deeper pycnoclineappears with maximal buoyancy frequency at about80m depth during Aug. and Nov.,and maximal buoyancy frequency moves to120m depth in winter. The seasonalpycnocline is very distinct from Apr. to Sep.. The double pycnocline is obvious fromAugust to Oct.. In winter, only the second pycnocline exists. Maxima buoyancyfrequency in deeper basin is higher than that in shallow shelf area from Jan. to Mar.and from Oct. to Dec., but the configuration is opposite during May and Sep.. Thedepth of maxima buoyancy frequency varies with season. It is deepest in winter, andis shallowest in June and July. It is shown that the variations of the long wave phasespeed, the dispersion parameter and amplitude factor are mainly related to topographycharacteristics without obvious seasonal variation. The quadratic nonlinear parameteris very sensitive to variations of the vertical stratification, and the cubic nonlinearparameter depends on water depth and stratification condition. Holding higheroccurrence in summer in the NSCS and the scarce existence of nonlinear internalwave on east of the LS is interpreted by using theses coefficient characteristic.
3. Mesoscale eddy effects on the internal solitary wave propagation
The mesoscale eddy and internal wave both are phenomena commonly observedin oceans. This paper aims to investigate how the presence of a mesoscale eddy in theocean affects waveform deformation of the internal solitary wave propagation. Anocean eddy is produced by a quasi-geostrophic model in f-plane, and theone-dimensional nonlinear eKdV equation is used to simulate an internal solitarywave passing through the mesoscale eddy field. The results suggest that the modestructures of the linear internal wave are modified due to the presence of themesoscale eddy field. A cyclonic eddy and an anticyclonic eddy do differentinfluences on background environment of internal solitary wave propagation. Theexistence of a mesoscale eddy field has almost no prominent impact on thepropagation of a small-amplitude internal solitary wave only based on the first modevertical structure, but the mesoscale eddy background field exerts a considerableinfluence on solitary wave propagation if considering high-mode vertical structures.Furthermore, whether an internal solitary wave first passes through anticyclonic eddyor cyclonic eddy, the deformation of wave profiles is different. Many observations of solitary internal waves in the real oceans suggest formation of the waves, excepttopography effect, this study shows that the mesoscale eddy background field is alsoan considerable factor which influences the internal solitary wave propagation anddeformation.
4. The numerical simulation for polarity covertion of interal solitary wave in theself of the NSCS
The phenomia of polarity covertion of internal solitary wave oftern are capturedby satellite images in the shelf of the NSCS. The physical process that internal wavetransfers their polrity is investigated by the numerical simulation. When the depressssolitary wave propates from deeper water area to shallower water area, the rear of thewave begin to speepen owing to effect of shallower topography, some soliton split outfrom the rear of the wave, the elevation solitary wave appears slowly, with theshallower water depth, the amplitude of the elevation solitary wave is growing, andthe distance between the front wave and behind wave is also increasing, showing thepersperion property of internal wave.
5. The numerical simulation for generation of internal wave on the doubleridges in the LS
The satellite images show the LS is an important original area for internal wavein the NSCS. It is difficult to trace the internal wave siginal in the sea surface of theLS from the results of the numerical simulation, this consists with observations fromsatellite images, which also demonstrated that the internal signals mainly present westof120.5°E. The tidal bore is firstly built up to west of the Luzon ridge in the ebbyphase. When the ebby tide current weaks and becomes flood, the soliton splits outfrom the front of the tidal bore. More and more solitons split out with the enhancedflood. An elevation wave is observed to east of the Luzon ridge during both ebby andflood phases, howere, there is no any solion fission from the evevation wave. Thedouble ridges is supercritical with respect to both diurnal and semidiurnal tides, andthe tide excursion parameter is less than1, so the LS is suitable for the generation ofinternal tides. The tidal beam radiates upward and downward and evolutes the internaltidal born, and the solitary waves split out on the premise of nonlinear and dispersioneffects.
引文
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