Solution of Laplace’s equations for the M 2 tide in the world oceans
Solution of Laplace’s equations for the M 2 tide in the world oceans
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DOI：
10.1098/rsta.1969.0062
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发表时间：
1969-12
期刊：
影响因子：
--
通讯作者：
C. Pekeris;Y. Accad
中科院分区：
文献类型：
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作者：
C. Pekeris;Y. Accad
根据观测到的海底地形，在现实的世界海洋模型中求解了 M2 潮汐的拉普拉斯潮汐方程。当忽略摩擦力时，理论上的潮汐会很高，但数量级是正确的。事实证明，潮汐高度对海岸线形态的变化很敏感，表明处于接近共振的状态。然而，双性中心的位置保持稳定，并且位于靠近经验推导的双性中心的位置。需要精细的计算网格来确保解的数值收敛。假设底部摩擦力与速度的一次幂成正比，还提出了包含摩擦力的解决方案。对于适合浅水中潮流的摩擦系数，理论潮汐高度与观测值相当一致。考虑到摩擦力，该解决方案对海岸线结构的变化不敏感，并且数值收敛性也得到了改善。由此产生的潮汐消散率高于观测推导值，但超出部分在后者的不确定性范围内。我们对潮汐的解如图 10 所示，相应的潮流图如图 12 所示。图 11 给出了从理论推导的中南大西洋环形流场与岛屿站潮汐观测的比较。
Laplace’s tidal equations were solved for the M2 tide in a realistic model of the world oceans based on the observed topography of the ocean bottom. When friction was neglected, the theoretical tides came out high, but of the right order of magnitude. The tidal heights proved to be sensitive to changes in the configuration of the coastline, indicating a state of near resonance. However, the positions of the amphidromic centres remained stable and were located close to the empirically deduced amphidromes. A fine computational grid was required to assure numerical convergence of the solution. A solution was also carried out with friction included, on the assumption of a bottom frictional force proportional to the first power of the velocity. For a coefficient of friction appropriate to tidal currents in shallow waters, the theoretical tidal heights came out in fair agreement with the observed values. With friction included, the solution proved insensitive to changes in the configuration of the coastline, and the numerical convergence was also improved. The resulting rate of tidal dissipation was higher than the observationally deduced values, but the excess is within the uncertainty of the latter. Our solution for the tide is given in figure 10, and the corresponding tidal current chart in figure 12. Figure 11 gives a comparison of the Middle South Atlantic amphidrome, which was derived from theory, with tidal observations in island stations.