Hamiltonian Approach To Intenal Waves

The ocean internal wave has randomness, and this is considered as one of primary causes to the fluctuations of sound field. The ocean internal wave spectrum of shallow water is different from the GM empirical spectrum of the deep ocean. Thorough research of shallow water ocean internal wave dynamics and characteristic stochastic spectrum is of extremely vital significance because it helps clarifying the sound field fluctuation characteristic in shallow water. The shallow water ocean internal wave has a decisive influence regarding the shallow water sea sound field fluctuation because of the ocean dynamics process complexity, but so far there is still no effective theoretical description.Starting from the recent years'development of using theory of weak turbulence (TWT) to describe the deep ocean internal wave spectrum, we attempt to find an effective approach for studying the shallow water internal wave spectrum. First, experimental datum is analyzed and it is found that the shallow water ocean internal wave spectrum is different from that of the deep ocean GM spectrum. Then, the theory of weak turbulence is systematically summarized, and Lvov and Tabak's method of obtaining the deep ocean internal wave spectrum is introduced. They applied the theory of weak turbulence to internal waves of long wave length and found that GM spectrum maybe obtained theoretically. We also introduce the one-dimensional model—Madja-McLaughlin-Tabak model. The MMT model has some interesting property, such as coherent structure. It has been found out that the empirical spectrum of internal waves maybe described theoretically. However, a more effective theory of studying shallow water ocean internal wave spectrum is still in need, and this will be researched in the future.