Influence of Sea Surface Fluctuation on Internal Waves' Vertical Structures in a Two-Layer Model

Using a two-layer linear ocean wave model that is quasi-incompressible and two-dimensional, we studied the relationships between surface fluctuation and ocean internal waves (IWs). The main conclusions were as follows. In a two-layer ocean, the analytical solution of IW was obtained by solving a homogeneous ordinary differential equation with constant coefficients according to the frequency, wave number (wavelength), and vertical velocity amplitude of the ocean surface fluctuation. The vertical structure and characteristics of IW in the ocean were analyzed under the conditions of different stratification parameters and background currents. Once the surface fluctuations were determined, the features of IW showed different shapes, which indicated the indeterminacy of the solution. Such indeterminacy reflects the characteristics of the inverse problem. To obtain a definite solution, the constraint conditions of the inverse problem should be provided-that is, the environmental parameters of the two layers, such as the background flow, stratification parameters, thickness of the two layers, and geostrophic parameters. If the environmental parameters are fixed, four situations of solutions can be determined. The first three solutions have IWs, and the fourth solution only has an external wave. For certain environmental parameters, the wave number and natural frequency (characteristic frequency) of the first three situations of IWs were determined in this study. We showed that a resonance phenomenon will occur and cause very severe ocean internal waves when the wave number and frequency of the surface fluctuation are analogous or equivalent to the natural wave number and natural frequency.