Hilbert transform and its application to modulation of capillary gravity waves

作     者：Yin Zhongbin, Lu Jun, Tian Jiwei 1. Physical Oceanography Laboratory, Ocean University of Qingdao, Qingdao 266003, China 2. TianJin Polytechnic University, TianJin. China 

作者机构：Physical Oceanography Laboratory Ocean University of Qingdao Qingdao 266003 China Tianjin Polytechnic University Tianjin China 

出 版 物：《Acta Oceanologica Sinica》 (海洋学报（英文版）)

年 卷 期：2001年第20卷第3期

页      面：309-315页

核心收录：

学科分类：0710[理学-生物学] 0908[农学-水产] 0707[理学-海洋科学] 08[工学] 081601[工学-大地测量学与测量工程] 0816[工学-测绘科学与技术] 

主　　题：Hilbert tranform capillary gravity waves 

摘      要：In this paper, the following important problem is answered: Under what condition can the Hilbert transform be put in the simple form. Then, using the Hilbert technique, it is demonstrated that, with some relative weak restrictions, the particle motion at the sea surface and energy transmission may be obtained from a wave record. The analysis show that for the two-dimensional and narrow-band mo- tion (or a physical phenomena, such as capillary waves breaking, which satisfy the narrow-band approx- imation) the local kinetic energy fluctuates in time as the envelope equared multiplied by a constant factor and can be obtained directly from a wave record. It is pointed that the local fluctuatiom of the potential energy as well as the local fluctuations of the total energy can be separated into a slowly varying part and a more rapid oscillating Part. Both Parts can be evaluated by meaas of the Hilbert transform. Finally, a physical interpretation of the envelope of the two-dimensional capillary waves as well as the method for wave group analysis is presented.