非线性海洋波动的研究

IOCAS-IR > 海洋环流与波动重点实验室

	非线性海洋波动的研究
	杨联贵
学位类型	博士
	1998
学位授予单位	中国科学院海洋研究所
学位授予地点	中国科学院海洋研究所
学位专业	物理海洋学
摘要	本文围绕非线性海洋波动理论分别从三个方面作了研究。第一，非线性定形波的研究。采用微分方程的几何理论与动力学相结合的方法，将控制地球流体的运动方程，通过行波变换，作为平面自治系统，利用相图理论，分别分析了非线性惯性重力波、非线性Rossby 波等的定性性质，得到了惯性重力波不存在定形孤波解的结论；通过对平面自治系统在平衡点处作Taylor展开，结合K－B平均法，求得了带有刻划非线性效应小参数的非线性频散关；论证了分式简谐函数为地球流体中有限振幅波解的一般形式。第二，非线性水波时空变化规律的研究，利用水波的变分方程，在行波或空间上进行Galerkin截谱，分离时空变量，并计及非线性效应的二次项，分别导出了水波随时间、空间的变化规律。其中，浅水非笥性波随时、空的变化规律满足用来描述非线性振动现象的Duffing方程，这使得Duffing方程在非线性水波的研究领域也找到了应用背。众所财拓KdV理论是水波的非线性效应和色散效应平衡的产物，在此尺度下，波形随时、空的变化不能被揭示出来。因此，本文所得到的结果是KdV理论和调制波理论的补充和发展。而且，这些结果便于实际应用。第三，非线性随机海浪统计分布的研研。基于动力学原理，研究了非线性波振动和位相的分布规律。利用我们所得到的波形随时间的演化过程，将随机输入看作初值，用渐近方法得到带有随机项的非线性水波的振幅和位相，从而建立了符合动力学原理的非线性波振幅和位相的概率分布，将将其和传统的结论以及测资料作了比较，结果表明，吻合较好。这种尝试性的方法在该领域的应用尚属首次，可望能够成为研究非性线随机波的一种手段。
其他摘要	This dissertation deals mainly with three aspects of nonlinear ocean wave theory.First, the study on nonlinear permanent waves. In this part, the method of combining geometric theory for differential equations and dynamics is used to transform the equations governing geophysical fluids into plane equtonomous systems by travelling wave transforms. Then, phase graph theory was used to analyse the qualitative properties of nonlinear inertia-gravity waves and nonlinear Rossby waves. The results led to the conclusion that there is no permanent solitary wave in inertia-gravity waves. Taylor expansion at the equilibrium points of the plane autonomous systems to the third order, and use of the K-B average method yielded the nonlinear dispersion relationships which contain small parameters to describe nonlinear effects, and at the same time, prove that fractional harmonic functions describe the general form of finite amplitude waves. Second, the study on temporal and spatial variation laws of nonlinear water waves. In this part, utilizing the Galerkin cutting spectrum method on traveling wave or space in the variational equation for fluid, and separating time and space variables, and considering the second power term of nonlinear effect, the equations for the temporal and spatial variations of nonlinear water waves are derived respectively. Among these, the temporal and spatial variation laws for nonlinear shallow water waves satisfy the Duffing equation usually used to describe nonlinear vibration phenomena in nature. As known to all, the KdV theory was established on the basis of the balance of weakly dispersive effect and weakly nonlinear effect, cannot reveal the temporal and spatial variations of nonlinear water waves; This study's resuts cover the generalization and development of the KdV theory and the modulation waves theory, and are convenient in application. Third, the study on statistical distribution of nonlinear random sea waves. In this part, based on the p rinciples of dynamics, the distribution laws for wave nonlinear amplitude and phase are investigated by using one of the nonlinear evolution equation derived above. By taking random inputs for initial values, the nonlinear wave amplitude and phase which contain random terms are obtained asymptotically, the probability distribution for the amplitude and phase of nonlinear random sea waves are established. The results accord with the principles of dynamics, and fit well with traditional and field measurement results, The dynamical method is used for the first time in this area, and is potentially effective for studying theory and application of nonlinear random sea waves.
页数	88
语种	中文
文献类型	学位论文
条目标识符	http://ir.qdio.ac.cn/handle/337002/1415
专题	海洋环流与波动重点实验室
推荐引用方式 GB/T 7714	杨联贵. 非线性海洋波动的研究[D]. 中国科学院海洋研究所. 中国科学院海洋研究所,1998.

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