# Frontiers of Earth Science

 Front. Earth Sci.    2019, Vol. 13 Issue (2) : 336-350     https://doi.org/10.1007/s11707-018-0735-7
 RESEARCH ARTICLE |
Analysis of the relation between ocean internal wave parameters and ocean surface fluctuation
Yufei ZHANG1(), Bing DENG2, Ming ZHANG3
1. National Marine Environmental Forecasting Center, Beijing 100081, China
2. Beijing Applied Meteorology Institute, Beijing 100029, China
3. PLA University of Science and Technology meteorological and Oceanographic Institute, Nanjing 211101, China
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 Abstract The relation between ocean internal waves (IWs) and surface fluctuation is studied using a quasi-incompressible two-dimensional linear ocean wave model. The main conclusions are as follows: the IW parameters can be obtained by solving the boundary value problem of ordinary differential equations with the frequency, wave number, and amplitude of the surface fluctuation. When the ocean surface fluctuation state is given, the ocean IW presents a different structure, i.e., the uncertainty of the solution, which reflects the characteristics of the inverse problem. To obtain a definite solution, this study proposes constraint conditions for the inverse problem, namely, the relationship among background flow, buoyancy frequency, sea surface height, and geostrophic parameters. The necessary and sufficient conditions for the existence of IWs and external waves (surface wave) can be obtained according to the different constraint conditions. The amplitude of the surface fluctuation is positively correlated with IWs, and they share the same frequency and wave number. We also examined the relationship between the vertical structure, the maximum amplitude, and the constraint conditions. For a certain wave number, when the ocean environment is defined, the natural frequency (characteristic frequency) of IWs can be obtained. If the frequency of the surface fluctuation is similar or equal to the natural frequency, the resonance phenomenon will occur and can result in very strong IWs. The presented theory can serve as a basis for the analytical estimation of IWs. Corresponding Authors: Yufei ZHANG Just Accepted Date: 29 November 2018   Online First Date: 20 December 2018    Issue Date: 16 May 2019
 Cite this article: Yufei ZHANG,Bing DENG,Ming ZHANG. Analysis of the relation between ocean internal wave parameters and ocean surface fluctuation[J]. Front. Earth Sci., 2019, 13(2): 336-350. URL: http://journal.hep.com.cn/fesci/EN/10.1007/s11707-018-0735-7 http://journal.hep.com.cn/fesci/EN/Y2019/V13/I2/336
 Tab.1  The settings of the parameters in six typical cases Fig.1  The distribution of IW parameters in the first case. (a) The distribution of stream function; (b)$Ψ(z)$ distribution; (c)$w'$ distribution; (d) $u'$distribution. Fig.2  The distribution of IW parameters in the second case. (a) The distribution of stream function; (b)$Ψ(z)$ distribution; (c)$w'$ distribution; (d) $u'$distribution. Fig.3  The distribution of IW parameters in the third case. (a)The distribution of stream function; (b)$Ψ(z)$ distribution; (c)$w'$ distribution; (d) $u'$distribution. Fig.4  The distribution of IW parameters in the fourth case. (a) The distribution of stream function; (b)$Ψ(z)$ distribution; (c)$w'$ distribution; (d) $u'$distribution. Fig.5  The distribution character of IW in the fifth case. (a)The distribution of stream function; (b)$Ψ(z)$ distribution; (c)$w'$ distribution; (d) $u'$distribution. Fig.6  The distribution character of the surface wave in the sixth case. (a)The distribution of stream function; (b)$Ψ(z)$ distribution; (c)$w '$ distribution; (d) $u'$distribution.
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