内潮生成机制以及吕宋海峡周边海域内潮的季节变化研究
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摘要
正压潮在地形上传播生成内潮以及内潮的演变过程与地形、层化和潮流息息相关。为此，本文对地形、层化和正压潮对内潮的影响进行了分析。在此基础上，还研究了吕宋海峡和南海陆架陆坡的内潮的季节变化和海水混合的关系。
首先解析结果表明弱地形（本文中只研究了正弦地形）下，当地形波数和某一斜压模态的水平波数相同时，会发生潮地共振，地形上产生的共振内潮的振幅的最小值从地形中间一直增长到地形两侧，而最大值在地形上保持不变。在地形左侧的共振斜压模态的振幅随着地形长度的增加而增加，而非共振模态的振幅非常微弱，随着地形长度的增加有周期的变化，即当地形长度是第一模态波长的整数倍时，振幅为零。数值模拟结果表明，共振模态的内潮随着地形长度的增加，扰动压强的位相与正弦地形的位相逐渐吻合，地形上的转化率一直为正值，从而共振模态一直从正压潮和地形的相互作用中获取能量，因而转化率会随着地形长度的增加而增加；非共振模态随着地形的增加，扰动压强的位相逐渐变得不规则，地形中部的转化率接近零，在某些位置转化率还出现负值，因而内潮不能从潮地作用中获取能量。
内潮的模态结构不仅取决于生成过程，还受传播过程中内潮和地形的相互作用的影响。数值实验的结果表明正压潮和正弦地形作用产生的内潮模态的形成一方面来自共振（正压能转化为斜压能），另一方面来自散射（斜压模态之间的转化）。研究还表明，内潮和地形作用，不仅会产生散射，而且还会产生共振，这两者都可以导致内潮能量的模态转化。另外，当地形和层化条件不满足散射和共振条件时,内潮和地形相互作用就不会产生模态的转换。
其次，在高斯地形中，随着地形高度增加和地形变窄，地形周围的斜压流场从低模态结构变为波射线结构。在低矮的高斯地形中，随着正压潮流的增大，斜压流场结构基本不变，在高窄的地形中，随着正压流速的增大，非线性增强，斜压流场变得混乱。当存在东西两个高斯地形且正压潮流较强时，西侧的地形有利于加强向西传播的内孤立波。
实际地形的二维数值模拟实验研究了南海北部21°N断面的K1和M2内潮生成、传播和相互作用的季节变化特征。结果表明吕宋海峡和南海北部陆架、陆坡区生成的M2和K1内潮夏季大于冬季。对于K1内潮来说，南海北部陆坡区和吕宋海峡西部海山大部分为超临界地形，因此，生成的部分K1内潮会在这些地形处反射回南海深水海盆，它们被捕陷在海盆内，形成驻波或者部分驻波。与K1内潮不同，对于M2内潮来说，南海北部陆架、陆坡区大部分为亚临界地形，因此，从吕宋海峡传来的绝大部分的M2内潮一直沿陆坡传向陆架；南海北部陆架、陆坡生成的少量M2内潮也有一部分会向东传播，并可能会与吕宋海峡传来的内潮在海盆中辐聚，形成少量的部分驻波。夏季，被捕陷在海盆内的K1内潮的部分驻波以第二、三模态为主，高模态（第五模态以上）的K1内潮的能量密度在海盆中占15％～20％，而冬季部分驻波以第一、三模态为主，高模态的K1内潮的能量密度在海盆中占20％～40％。K1内潮的驻波分布情况和K1内潮在陆坡处的反射有关，而内潮反射与各模态的位相有关，夏季第一、二模态的K1内潮的位相差比冬季接近同相，故冬季K1内潮的反射率大。K1内潮的辐聚和高模态K1内潮都将导致垂向形成高剪切，而冬季海盆中的高模态能量所占比例远大于夏季，这意味着冬季内潮引起的南海深层混合强于夏季。
三维数值模拟结果表明吕宋海峡是南海内潮的主要生成源地，90％以上的K1和M2内潮都生成于吕宋海峡。其中，西侧海脊是M2内潮最大的生成源地，而东侧海脊中部则是K1内潮最大的生成源地。K1和M2内潮的生成的季节变化是海水层化的季节变化和地形作用共同影响的结果。在发生内潮共振的地形处，当层化的改变有利于共振的发生时，内潮转化率就会比较大，反之，若层化的变化削弱共振，即使层化是增强的，内潮转化率也不一定增加。
吕宋海峡还是内潮的主要耗散区，33％左右的生成的K1内潮和50％以上的生成的M2内潮在吕宋海峡局地耗散。M2正压潮传入南海后其中一个分支向东北传播与台湾西南的陆架陆坡发生作用，故台湾西南部的陆架陆坡处也有比较明显的M2内潮的生成和耗散。总体说来，在研究海区中，冬季K1和M2内潮的生成和耗散都强于夏季。
吕宋海峡的双海脊地形的特点，有利于K1和M2内潮在吕宋海峡传播时形成显著的驻波和半驻波。在整个研究海区，冬季的驻波和半驻波比夏季范围广泛。在南海海盆中，K1内潮第一模态驻波和半驻波主要分布在海盆周围，而第二模态的驻波和半驻波主要分布在海盆中间；M2内潮第二模态驻波和半驻波比第一模态分布广泛。
The generation and evolution of internal tides over the topography is closelyrelated to topography, stratification and barotropic tide, which have been studied byusing analytical and numerical calculations. Furthermore, seasonal variations ofinternal tides around the Luzon Stait and their relation with mixing in the basin ofSCS have been discussed.
Firstly, internal tide generated over weak topographies was studied. Resultsobtained from the analytical solution show that tide-topography resonance takes placewhen the topography wavenumber is equal to that of one baroclinic mode (theresonant mode). For resonant modes, the amplitudes increase with topography length.For non-resonant modes, the amplitudes are weak and vary periodically with theextending of the topography. The numerical results show that phase of theperturbation pressure gradually agrees with the phase of topography with the increaseof topography length for resonant modes, and the conversion rate is always positiveover the topography, thus the resonant mode persists in absorbing energy from thebarotropic tide, and the conversion rate is increased. Otherwise, phase of theperturbation pressure gradually becomes more and more irregular with the increase oftopography length for non-resonant modes, the conversion rate in the middle of thetopography is approaching zero, negative conversion rates appear on some sites, sointernal tides can not absorb energy from tide topography interaction.
As the baroclinic modes propagate, they continue to interact with the bottom topography, scattering might take place to convert one baroclinic mode to otherbaroclinic modes. Furthermore, it is shown that the interaction between internal tideand bottom topography can lead to not only scattering but also resonance, transferringenergy into other baroclinic modes. When none of the conditions for resonance andscattering are satisfied, the modes of incident internal tides will not be changed by theinteraction with the topography.
Over the high single gaussian topography, baroclinic velocity field change fromlow mode structure to ray-like structure as the topography becomes higher andnarrower. Over the low and wide topography, the structure of baroclinic velocity fielddoes not change obviously with the strengthen of barotropic tides; while over high andnarrow topography, with the strengthen of barotropic tides, nonlinear effects areenhanced, and the structure of baroclinic velocity field becomes disordered. Whenboth of the western and eastern guassian topographies are present and the barotropictides are strong, the generation of westward propogating internal solitary waves willbe enhanced due to interactions with the western topography.
Seasonal variations of baroclinic tides for K1and M2constituents wereseparately studied using two-dimensional numerical simulations along the21°Nsection of the northern South China Sea (SCS). Results show that the continentalslope of the northern SCS and the west ridge of the Luzon Strait are supercritical toK1internal tides, which may be trapped in the deep basin of the SCS and formstanding or partial standing waves. Meanwhile, these areas are sub-critical to M2internal tides, which can transmit onto the shelf and are seldom reflected back into thebasin. The trapped K1internal tides are dominated by mode-2and mode-3in summer and by mode-1and mode-3in winter. Moreover, high mode K1internal tides accountfor nearly20%to40%of the total energy density in winter and15%to20%insummer. The pattern of K1internal tides in the basin is mainly determined by thepercentage of reflected energy from the continental slope. The phase differencebetween the incoming mode-1and mode-2K1internal tides near the continental slopeare nearly out of phase in winter, which means the percentage of reflection of the K1internal tide is larger than that in summer. Both the convergence and high mode K1internal tides can enhance the vertical shear. The above results indicate that, in thedeep basin of the SCS, water mixing potentially induced by internal tides in winter isstronger than in summer.
The3-D model simulation for the internal tides in the northern South China Seashows that Luzon strait is the most important source site for internal tides with90%generation of total K1and M2internal tides. The major source site for M2internaltide is the west ridge in the LS, for K1internal tides, it is in the middle of the eastridge. The seasonal variation of the generation of K1and M2internal tides is relatedwith the joint action of the stratification and topography. If the stratification isfavarable for the resonance, the barotropic to baroclinic tide conversion rate will beincreased. Otherwise, if the stratification weakens the resonance, the barotropic tobaroclinic tide conversion rate may be decreased, even if the stratification isenhanced.
Luzon Strait is also the main dissipation area for the internal tides. It is estimatedthat about33%of K1intenral tides and50%of M2intenral tide are dissipated locallythere. One branch of the M2barotropic tide propagating into the South China Sea spreads toward the eastnorth direction and interacts with the continental shelf at thewestsouth of Taiwan. Hence, the generation and dissipation of M2internal tides isvery obvious over the continental shelf of the westsouth of Taiwan. As a whole, in thestudy area, the generation and dissipation of K1and M2internal tides is stronger inwinter than that in summer.
The topography with double ridges in the Luzon Strait is favorable for theformation of standing and partial standing waves during the propogation of K1andM2internal tides there. For the entire study area, the standing and partial standingwaves in winter spreads more widely than in summer. In the basin of SCS, thestanding and partial standing waves for the first mode of K1internal tide mainlydistributes around the basin, while the second and the third modes of K1internal tidesis mainly in the middle of the basin. The standing and partial standing waves for thesecond mode of M2internal tide distributes more widely than that for the first modeof M2internal tide.
首先解析结果表明弱地形（本文中只研究了正弦地形）下，当地形波数和某一斜压模态的水平波数相同时，会发生潮地共振，地形上产生的共振内潮的振幅的最小值从地形中间一直增长到地形两侧，而最大值在地形上保持不变。在地形左侧的共振斜压模态的振幅随着地形长度的增加而增加，而非共振模态的振幅非常微弱，随着地形长度的增加有周期的变化，即当地形长度是第一模态波长的整数倍时，振幅为零。数值模拟结果表明，共振模态的内潮随着地形长度的增加，扰动压强的位相与正弦地形的位相逐渐吻合，地形上的转化率一直为正值，从而共振模态一直从正压潮和地形的相互作用中获取能量，因而转化率会随着地形长度的增加而增加；非共振模态随着地形的增加，扰动压强的位相逐渐变得不规则，地形中部的转化率接近零，在某些位置转化率还出现负值，因而内潮不能从潮地作用中获取能量。
内潮的模态结构不仅取决于生成过程，还受传播过程中内潮和地形的相互作用的影响。数值实验的结果表明正压潮和正弦地形作用产生的内潮模态的形成一方面来自共振（正压能转化为斜压能），另一方面来自散射（斜压模态之间的转化）。研究还表明，内潮和地形作用，不仅会产生散射，而且还会产生共振，这两者都可以导致内潮能量的模态转化。另外，当地形和层化条件不满足散射和共振条件时,内潮和地形相互作用就不会产生模态的转换。
其次，在高斯地形中，随着地形高度增加和地形变窄，地形周围的斜压流场从低模态结构变为波射线结构。在低矮的高斯地形中，随着正压潮流的增大，斜压流场结构基本不变，在高窄的地形中，随着正压流速的增大，非线性增强，斜压流场变得混乱。当存在东西两个高斯地形且正压潮流较强时，西侧的地形有利于加强向西传播的内孤立波。
实际地形的二维数值模拟实验研究了南海北部21°N断面的K1和M2内潮生成、传播和相互作用的季节变化特征。结果表明吕宋海峡和南海北部陆架、陆坡区生成的M2和K1内潮夏季大于冬季。对于K1内潮来说，南海北部陆坡区和吕宋海峡西部海山大部分为超临界地形，因此，生成的部分K1内潮会在这些地形处反射回南海深水海盆，它们被捕陷在海盆内，形成驻波或者部分驻波。与K1内潮不同，对于M2内潮来说，南海北部陆架、陆坡区大部分为亚临界地形，因此，从吕宋海峡传来的绝大部分的M2内潮一直沿陆坡传向陆架；南海北部陆架、陆坡生成的少量M2内潮也有一部分会向东传播，并可能会与吕宋海峡传来的内潮在海盆中辐聚，形成少量的部分驻波。夏季，被捕陷在海盆内的K1内潮的部分驻波以第二、三模态为主，高模态（第五模态以上）的K1内潮的能量密度在海盆中占15％～20％，而冬季部分驻波以第一、三模态为主，高模态的K1内潮的能量密度在海盆中占20％～40％。K1内潮的驻波分布情况和K1内潮在陆坡处的反射有关，而内潮反射与各模态的位相有关，夏季第一、二模态的K1内潮的位相差比冬季接近同相，故冬季K1内潮的反射率大。K1内潮的辐聚和高模态K1内潮都将导致垂向形成高剪切，而冬季海盆中的高模态能量所占比例远大于夏季，这意味着冬季内潮引起的南海深层混合强于夏季。
三维数值模拟结果表明吕宋海峡是南海内潮的主要生成源地，90％以上的K1和M2内潮都生成于吕宋海峡。其中，西侧海脊是M2内潮最大的生成源地，而东侧海脊中部则是K1内潮最大的生成源地。K1和M2内潮的生成的季节变化是海水层化的季节变化和地形作用共同影响的结果。在发生内潮共振的地形处，当层化的改变有利于共振的发生时，内潮转化率就会比较大，反之，若层化的变化削弱共振，即使层化是增强的，内潮转化率也不一定增加。
吕宋海峡还是内潮的主要耗散区，33％左右的生成的K1内潮和50％以上的生成的M2内潮在吕宋海峡局地耗散。M2正压潮传入南海后其中一个分支向东北传播与台湾西南的陆架陆坡发生作用，故台湾西南部的陆架陆坡处也有比较明显的M2内潮的生成和耗散。总体说来，在研究海区中，冬季K1和M2内潮的生成和耗散都强于夏季。
吕宋海峡的双海脊地形的特点，有利于K1和M2内潮在吕宋海峡传播时形成显著的驻波和半驻波。在整个研究海区，冬季的驻波和半驻波比夏季范围广泛。在南海海盆中，K1内潮第一模态驻波和半驻波主要分布在海盆周围，而第二模态的驻波和半驻波主要分布在海盆中间；M2内潮第二模态驻波和半驻波比第一模态分布广泛。
The generation and evolution of internal tides over the topography is closelyrelated to topography, stratification and barotropic tide, which have been studied byusing analytical and numerical calculations. Furthermore, seasonal variations ofinternal tides around the Luzon Stait and their relation with mixing in the basin ofSCS have been discussed.
Firstly, internal tide generated over weak topographies was studied. Resultsobtained from the analytical solution show that tide-topography resonance takes placewhen the topography wavenumber is equal to that of one baroclinic mode (theresonant mode). For resonant modes, the amplitudes increase with topography length.For non-resonant modes, the amplitudes are weak and vary periodically with theextending of the topography. The numerical results show that phase of theperturbation pressure gradually agrees with the phase of topography with the increaseof topography length for resonant modes, and the conversion rate is always positiveover the topography, thus the resonant mode persists in absorbing energy from thebarotropic tide, and the conversion rate is increased. Otherwise, phase of theperturbation pressure gradually becomes more and more irregular with the increase oftopography length for non-resonant modes, the conversion rate in the middle of thetopography is approaching zero, negative conversion rates appear on some sites, sointernal tides can not absorb energy from tide topography interaction.
As the baroclinic modes propagate, they continue to interact with the bottom topography, scattering might take place to convert one baroclinic mode to otherbaroclinic modes. Furthermore, it is shown that the interaction between internal tideand bottom topography can lead to not only scattering but also resonance, transferringenergy into other baroclinic modes. When none of the conditions for resonance andscattering are satisfied, the modes of incident internal tides will not be changed by theinteraction with the topography.
Over the high single gaussian topography, baroclinic velocity field change fromlow mode structure to ray-like structure as the topography becomes higher andnarrower. Over the low and wide topography, the structure of baroclinic velocity fielddoes not change obviously with the strengthen of barotropic tides; while over high andnarrow topography, with the strengthen of barotropic tides, nonlinear effects areenhanced, and the structure of baroclinic velocity field becomes disordered. Whenboth of the western and eastern guassian topographies are present and the barotropictides are strong, the generation of westward propogating internal solitary waves willbe enhanced due to interactions with the western topography.
Seasonal variations of baroclinic tides for K1and M2constituents wereseparately studied using two-dimensional numerical simulations along the21°Nsection of the northern South China Sea (SCS). Results show that the continentalslope of the northern SCS and the west ridge of the Luzon Strait are supercritical toK1internal tides, which may be trapped in the deep basin of the SCS and formstanding or partial standing waves. Meanwhile, these areas are sub-critical to M2internal tides, which can transmit onto the shelf and are seldom reflected back into thebasin. The trapped K1internal tides are dominated by mode-2and mode-3in summer and by mode-1and mode-3in winter. Moreover, high mode K1internal tides accountfor nearly20%to40%of the total energy density in winter and15%to20%insummer. The pattern of K1internal tides in the basin is mainly determined by thepercentage of reflected energy from the continental slope. The phase differencebetween the incoming mode-1and mode-2K1internal tides near the continental slopeare nearly out of phase in winter, which means the percentage of reflection of the K1internal tide is larger than that in summer. Both the convergence and high mode K1internal tides can enhance the vertical shear. The above results indicate that, in thedeep basin of the SCS, water mixing potentially induced by internal tides in winter isstronger than in summer.
The3-D model simulation for the internal tides in the northern South China Seashows that Luzon strait is the most important source site for internal tides with90%generation of total K1and M2internal tides. The major source site for M2internaltide is the west ridge in the LS, for K1internal tides, it is in the middle of the eastridge. The seasonal variation of the generation of K1and M2internal tides is relatedwith the joint action of the stratification and topography. If the stratification isfavarable for the resonance, the barotropic to baroclinic tide conversion rate will beincreased. Otherwise, if the stratification weakens the resonance, the barotropic tobaroclinic tide conversion rate may be decreased, even if the stratification isenhanced.
Luzon Strait is also the main dissipation area for the internal tides. It is estimatedthat about33%of K1intenral tides and50%of M2intenral tide are dissipated locallythere. One branch of the M2barotropic tide propagating into the South China Sea spreads toward the eastnorth direction and interacts with the continental shelf at thewestsouth of Taiwan. Hence, the generation and dissipation of M2internal tides isvery obvious over the continental shelf of the westsouth of Taiwan. As a whole, in thestudy area, the generation and dissipation of K1and M2internal tides is stronger inwinter than that in summer.
The topography with double ridges in the Luzon Strait is favorable for theformation of standing and partial standing waves during the propogation of K1andM2internal tides there. For the entire study area, the standing and partial standingwaves in winter spreads more widely than in summer. In the basin of SCS, thestanding and partial standing waves for the first mode of K1internal tide mainlydistributes around the basin, while the second and the third modes of K1internal tidesis mainly in the middle of the basin. The standing and partial standing waves for thesecond mode of M2internal tide distributes more widely than that for the first modeof M2internal tide.
引文
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[43] Adcroft A, Hill C and Marshall J. Representation of Topography by Shaved Cells in aHeight Coordinate Ocean Model. Monthly Weather Review,1997,125.(9):2293~2315
[44] Zhang Z, Fringer O B and Ramp S R. Three-dimensional, nonhydrostatic numericalsimulation of nonlinear internal wave generation and propagation in the South ChinaSea. J. Geophys. Res.,2011,116.(C5): C5022
[45] Buijsman M C, Kanarska Y and McWilliams J C. On the generation and evolution ofnonlinear internal waves in the South China Sea. J. Geophys. Res.,2010,115.(C2):C2012
[46] Holloway P E and Merrifield M A. Internal tide generation by seamounts, ridges, andislands. J. Geophys. Res.,1999,104.(C11):25937~25951
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