TABLE OF CONTENTS It is a fundamental scientific principle to start with the simplest possible formulation that contains the principal features of the problem.
So we first restrict the analysis to the following situation
Constant depth, h.
Periodic waves with period T.
2 dimensional motion in the vertical x, z-plane (2DV), i.e. one dimensional motion in the horizontal direction (1DH).
These assumptions merely restrict the physical situation considered and do not represent approximations about the wave motion.
However, as a necessary approximation, we neglect the effect of the boundary layer that develops at the bottom. This includes neglecting the viscous or turbulent stresses that develop in the boundary layer and also neglecting the disturbances the boundary layer causes in the flow above. There are two major reasons for this: one is that the shear stresses inside the boundary layer are small in comparison to the inertia and pressure forces that are the primary forces in the wave motion outside the boundary layer; the other that under waves with wave periods like wind waves the boundary layer is usually very thin in comparison to the water depth h. Both reasons imply that the local disturbances from the bottom boundary layer are really small. This will be discussed further in Chapter 10. [2]
The internal viscous stresses in the motion are also extremely small. [3] Notice, however, that away from boundary layers these stresses do not create vorticity so the flow remains irrotational inspite...
