Analysis of the relation between ocean internal wave parameters and ocean surface fluctuation

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.