14.6 Wave reflection
A wall in a wave field interacts with a progressive wave by reflecting it; the
reflected wave moves in a direction depending on the angle of the incident
wave. If the crests of the incident wave are parallel to the wall, the crests
of the reflected wave will also be parallel to it. The coefficient of reflection,
which is the ratio of the amplitude of the reflected wave to the amplitude
of the incident wave, depends on the angle of the incident wave and the
energy absorption capability of the wall which, in turn, depends on its
geometry, porosity, and roughness.
In linear theory, linear superposition of the surface profiles due to
the incident and reflected waves is permissible. The surface profile of the
incoming wave is given by equation (14.11b) as
iasin(kx t)and that due to the reflected wave is given by
rasin(kxt). (14.43)(Note that the direction of the reflected wave is in the negative x-direction
and that total reflection is assumed.)
The resulting wave surface is described by
ir 2 asinkxcost. (14.44)Equation (14.44) represents a standing wave, as shown in Fig. 14.10. The
positions of no vertical motion are called nodes, and those of maximum
amplitudes are called antinodes.
Standing waves forming adjacent to a vertical wall can cause deep
erosion because the particle velocity increases near the bed owing to the
increase in wave height.
WAVE REFLECTION 591
Fig. 14.10 Standing wave formed by reflection at a vertical wall