Analysis of nonlinear water waves due to Coupled Vibration Equations and Application to wave breaking

耦合振动方程引起的非线性水波分析及其在破波中的应用

• 批准号: 08650616
• 负责人: NOCHINO Masao
• 金额: $ 1.41万
• 依托单位: Osaka Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1996
• 资助国家: 日本
• 起止时间: 1996 至 1997
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08650616/
• 关键词: water waves; nolinear waves; coupled vibration; numerical calculation; water breaking; 非線型波動; 破波

In recent reserches, it is pointed out that the coupled vibration equation (CVE) by Nochino is appicable for nonlinear water waves such as Solitary wave and for wave breaking. The goal of the project is to investigate the capability of CVE for nonlinear water waves on arbitarary configuration of depth, espesially the wave deformation on slope pf bottom and wave braking by the numerical calculation.On first year of project (1996), the CVE for the orbitirary config ation of depth is derived by applying the Legendre polyniominals with both the even and odd oder series, in order to satisfy the baoundary condition at bottom. The numerical calculation are excuted with the new CVE.The results of the calculation show unstable at the wave bottom, which is clearly different from the unstablity of wave breaking.On the second year (1997), the unstability of numerical calculation for nolinear water waves by the new CVE investigated by trying varius algorism of calculation. The problems of CFL number and the numerical instability of differenrial equations was carefully tested and ovewhlemed. the alculation results, however, sill show unstable. After careful research, it is found that the log wave at wave front stimulate the problem of CFL number. The numerical calculation is started from the water at still, and waves incident through the incident baoundary on the first year developed. The waves in the calculation region make up the wave front at the tip of waves progressing. Consiquently, waves in the region of its relative depth less than 1/20 are stable in the present calculation method. This region implies the shallow water waves and also is the same as one of the Boussinesq Equation is applicable.

近年来的研究指出，Nochino的耦合振动方程（CVE）适用于孤立波等非线性水波和波浪破碎问题。本项目的目的是通过数值计算研究在任意水深条件下的非线性波浪的计算能力，特别是波浪在底坡上的变形和波浪的制动，在项目的第一年（1996年），应用勒让德多项式的奇偶级数，推导了轨道水深条件下的计算能力。以满足底部的Baouncement条件。用该方法进行了数值计算，计算结果表明，波浪在波底处是不稳定的，这与波浪破碎时的不稳定性有明显的区别，第二年（1997年），通过对各种计算算法的尝试，研究了该方法在非线性水波数值计算中的不稳定性。对CFL数和微分方程的数值不稳定性问题进行了仔细的检验和讨论。但计算结果仍不稳定。经过仔细研究，发现波前处的对数波激发了CFL数的问题。数值计算从静止的水面开始，第一年发展的波浪通过入射池入射。计算区域内的波在波前进的过程中构成波尖的波前。因此，在相对水深小于1/20的区域内，波浪是稳定的。该区域包含浅水波，也与Boussinesq方程的适用范围相同。