TABLE OF CONTENTS Fluid motions are characterized by two different elements, i.e. vortices and waves. In this chapter, we consider water waves and sound waves. There exists a fundamental difference in character between the two waves from a physical point of view. The vortices will be considered in the next chapter.
A liquid at rest in a gravitational field is in general bounded above by a free surface. Once this free surface experiences some disturbance, it is deformed from its equilibrium state, generating fluid motion. Then, the deformation propagates over the surface as a wave. Waves are observed on water almost at any time and are called water waves which are sometimes called a surface wave. The surface wave is a kind of dispersive waves whose phase velocity depends on its wave length.
On the other hand, a sound wave is nondispersive and the phase velocity of different wave lengths take the same value. This results in a remarkable consequence, i.e. invariance of wave form during propagation.
Suppose that water of uniform density ? is at rest in a uniform field of gravity. Then, setting v = 0 and f = g = (0 , 0 , ? g) in (5.2), with respect to the ( x, y, z)-cartesian frame, the z axis taken vertically upward (where g is a constant of gravitational acceleration), the Euler equation of motion reduces to
Horizontal x and
