where α is the angle the slope forms with the horizontal and *L*0 is the length of the incident wave in deep

water.

(4) Figure II-7-23a is a profile view of the water surface envelope positions for a wave reflecting from

a wall that has a reflection coefficient equal to unity (i.e., *H*i = Hr). The water surface amplitude is given by

2π*x*

2 π*t*

(II-7-7)

cos

where *L *and *T *are the incident and reflected wave length and period respectively, *x *is the horizontal ordinate

and *t *is the time elapsed. The figure also shows the water particle paths at key points. At nodal points, water

particle motions are horizontal and at antinodes, water particle motions are vertical. At *t *= 0, *T*/2, and *T*, the

water is instantaneously still and all of the wave energy is potential energy. At *t *= *T*/4 and 3*T*/4, the water

surface is horizontal and all of the energy is kinetic energy.

(5) When the wall reflection coefficient is less than unity, the water surface envelope positions and

particle paths are as depicted in Figure II-7-23b. As the reflection coefficient decreases toward zero, the

water surface profile and water particle path changes toward the form of a normal progressive wave.

Harbor Hydrodynamics

II-7-27

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