Theory of Free Surface Waves

Abstract

Various phenomena related to waves on the sea surface present several interesting research themes in the fields of physical oceanography and ocean engineering. The term “waves” includes not only surface waves generated at the boundary between the atmosphere and ocean but also internal waves generated within different densities of stratified fluid. The frequencies (or wavelengths) of ocean waves are highly diverse, ranging from high-frequency ripples to ultra-low-frequency waves associated with the Coriolis force of the Earth’s rotation . In this chapter, we restrict ourselves to wavelengths on the order of several tens of centimeters to several tens of meters, which typify free surface waves observed on the general sea surface. In such free surface waves , the effect of viscosity is negligibly small; thus, we can regard typical ocean fluids as incompressible perfect fluids, as discussed in the previous chapter. Moreover, if the fluid motion is considered to start from a static or irrotational (non-vortex) state, then the subsequent fluid motion is irrotational by Lagrange’s vortex theorem. In other words, as flow fields can be described by their velocity potential, how to find the velocity potential is explained in this chapter.