On the stability of Kelvin waves
On the stability of Kelvin waves
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论开尔文波的稳定性
DOI：
10.1017/s002211208900220x
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发表时间：
1989
影响因子：
3.7
通讯作者：
D. Renouard
中科院分区：
文献类型：
--
作者：
W. Melville;G. Tómasson;D. Renouard
我们考虑旋转通道中弱非线性色散长波的演化。推导了控制方程并获得了对应于开尔文波的初始数据的近似解。由于小的非线性速度校正，表明弱非线性开尔文波对于与通道的线性庞加莱模式的直接非线性谐振是不稳定的。计算了控制方程的数值解，发现其与近似解析解具有良好的一致性。结果表明，波前的曲率和主波振幅沿通道的衰减可归因于共振产生的庞加莱波。这些结果似乎对 Maxworthy (1983) 和 Renouard, Chabert d'Hières & Zhu (1987) 的实验结果给出了定性解释。
We consider the evolution of weakly nonlinear dispersive long waves in a rotating channel. The governing equations are derived and approximate solutions obtained for the initial data corresponding to a Kelvin wave. In consequence of the small nonlinear speed correction it is shown that weakly nonlinear Kelvin waves are unstable to a direct nonlinear resonance with the linear Poincaré modes of the channel. Numerical solutions of the governing equations are computed and found to give good agreement with the approximate analytical solutions. It is shown that the curvature of the wavefront and the decay of the leading wave amplitude along the channel are attributable to the Poincaré waves generated by the resonance. These results appear to give a qualitative explanation of the experimental results of Maxworthy (1983), and Renouard, Chabert d'Hières & Zhang (1987).