Chinese Journal of Theoretical and Applied Mechanics ›› 2019, Vol. 51 ›› Issue (6): 1589-1604.DOI: 10.6052/0459-1879-19-326

Special Issue: 海洋工程专题(2019年第6期)

• Articles on“Ocean Engineering” • Previous Articles     Next Articles

THEORY, MODELLING AND COMPUTATION OF NONLINEAR OCEAN INTERNAL WAVES1)

Wang Zhan*2)(),Zhu Yuke**   

  1. *Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
    School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
    **School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China
  • Received:2019-10-25 Accepted:2019-11-10 Online:2019-11-18 Published:2019-12-26
  • Contact: Wang Zhan

Abstract:

Salinity and temperature variations in the vertical direction lead to density stratification in oceans, and the fluctuation of isopycnal surfaces resulting from internal perturbations (such as stratified shear flow over a bottom topography) or external disturbances (such as the dead water phenomenon) is called the internal wave. Internal waves are ubiquitous in the ocean and usually arise in the situation when the density stratification is obvious and stable such as at the mouth of strait. Oceans are usually characterized by a sandwich-like structure: a mixing layer and a deep-water layer featuring an almost uniform density, and a transition layer in the middle with continuous density variation. Fluctuations of the transition layer have great impact on ocean engineering and ocean ecology, while waves inside the transition layer has potential applications in the non-acoustic detection of submarines (conversely, in the stealth operation of submarines). The main reason for these important influences lies in the ability of internal waves to propagate in both horizontal and vertical directions, which is the essential difference from that of ocean surface waves. In the current paper, two types of ocean density models, continuously stratified models and discontinuous layered models, are thoroughly discussed. Various nonlinear models used to study ocean internal waves (including celebrated weakly nonlinear models, such as the Korteweg-de Vries equation, the Benjamin-Ono equation, and the Kadomtsev-Petviashvili equation, and strongly nonlinear models, such as the Miyata-Choi-Camassa equation, the fully nonlinear potential theory, and the incompressible Navier-Stokes equation with density variations), as well as their respective scope of application, are reviewed from the aspects of theoretical analyses, numerical simulations, and laboratory experiments. Particular attention is paid to the important role of internal waves in transferring mass, momentum and energy in oceans.

Key words: internal ocean wave, layered model, continuously stratified model, nonlinear wave, boundary integral method, Boussinesq equations, high-order numerical scheme

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