Tidal Interaction of the Earth and the Moon and the Lunar Origin

海洋动力学在地月系统研究中是极其重要的。海洋和固体潮汐的相位延迟会产生扭矩，从而扰乱月球的轨道运动和地球的自转。目前，海潮的力矩与固体潮的力矩之比约为10：1。海潮既受海洋摩擦的影响，又受边界形状的影响。海洋动力学似乎与潮汐波的频率有关，还通过科里奥里力受地球自转速度的影响。从早期起，水文学家就进行了许多工作。研究了单层海洋模型水动力方程中涡动粘性项、线性和/或非线性摩擦项的影响，并展示了在海潮数值模拟中的几点经验。将本研究得到的潮汐模型与目前精确的潮汐模型进行了比较，海洋的分布对潮汐隆起有很大的影响。我们使用二叠纪和寒武纪大陆模型研究了这些影响。与更早的时代相对应，我们使用了更简单和理想化的大陆模型。潮汐扭矩的影响由拉格朗日行星方程计算。在估计轨道演化时，使用Rigry公式来考虑轨道的偏心率和倾角以及专业运动。这些过程后的结果将限制过去月球轨道和地球自转的变化。给出了地月系统演化的模拟研究。

Ocean dynamics is extremely important in the study of the Earth-Moon system.Phase delays in oceanic and solid tides generate torques to perturb the orbital motion of the Moon and the Earth's rotation. At the present day, the ratio between the torques of the oceanic and the solid tide is about 10:1.The oceanic tide is affected by friction in the oceans and also by the shapes of boundaries. Ocean dynamics seems to be functional to the frequencies of the tidal waves and also is affected by the Earth's spin velocity through the Coriori force.Many works have been performed by hydrologists since earlier time. We investigated effects of the eddy viscosity and the linear and/or non-linear friction terms in the hydrodynamic equations of one-layered ocean models and showed several experiences in the numerical simulation of ocean tide. Tidal models obtained by the present study were compared with current accurate models.The distribution of the oceans affects the tidal bulge to remarkable extents. We investigated these effects using a Permian and a Canbrian continental model. Corresponding to the much earlier era, we used more simple and idealized continent models.The effects of the tidal torques were computed by Lagrangian Planetary equations.Rigorous formulas were used to take account the eccentricity and the inclination of the orbit and also the prefessional motions in the estimation of the orbital evolution.Obtained results after these procedures would set bounds to the past variations of the lunar orbit and the Earth's rotation. Simulation studies of the evolution of the Earth-Moon system were presented.