Three Dimensional Internal Waves due to Pulsating Sources and Oscillation of Floating Bodies

Abstract

Different methods have been used to derive Green function in a two‐layer fluid model, which has been treated in different ways. In a two‐layer fluid with the upper layer having a free surface, there exist two modes of waves propagating due to the free surface and the interface. This is because the density does change in the vertical direction of the water in special areas such as lakes, fjords or estuaries, due to variation in salinity and/or temperature where loads on underwater structures are interesting. The fluid in this case is considered to be inviscid, incompressible and the flow is irrotational. In this paper, derived Green functions in three dimensional case of a stationary source oscillating are presented. The source point is located either in the upper or lower part of a two‐layer fluid of finite depths. The method of singularities was used to arrive at the desired Green functions. This method has an advantage because it involves representing the potential as a sum of singularities or multipoles placed within any structures that are present. Further more, experience shows that the systems of equations that result from using a singularity method possess excellent convergence characteristics and only a few equations are needed to obtain accurate numerical results. The presented two‐layer Green function can be validated by showing it reduces to that of a single layer of finite depth, or that the upper Green function coincides with that of the lower, for each case. It is shown how the surface and internal wave amplitudes compare for both the wave modes. We also show the effects of the internal waves on the wave motion.