(2000) performed experiments of refraction-diffraction on a flat bottom, a
sloping bottom, and a third configuration with a flat bottom with a channel
incised through two semi-infinite breakwaters. Such studies have measured or
examined wave height, but not wave direction. The present study was designed
to measure both wave height and direction.
Refraction and Diffraction Processes
Some of the following material is taken from Hales (1980), who presents
background material describing the refraction and diffraction of water waves.
Except in deep water, the wave phase speed depends on water depth. Because
wave celerity decreases as depth decreases, the wavelength must also decrease
for the period to remain constant. Phase velocity varies along the crest of a wave
propagating at an angle to underwater contours because that part of the wave in
deeper water moves faster than that part in shallower water. This variation
causes the wave crest to bend toward alignment with the contours. The bending
of wave crests in response to changes in bottom topography, called refraction,
depends on the relation of water depth to wavelength and is analogous to
refraction of other types of waves such as light, where, in the case of water
waves, water depth determines the refractive index. A basic assumption in wave
refraction theory is the conservation of energy between orthogonals (i.e., no
diffraction of energy along wave crests).
Diffraction of water waves is the phenomenon where wave energy
propagates into the sheltered lee of structures apart from bathymetric refraction.
Here, wave crests bend (even in constant water depth) and gradients of wave
height exist along the wave crest. The theory of water wave diffraction can be
explained by Huygen's principle. Each point of an advancing wave crest may be
considered as the center of a secondary circular wave that advances in all
directions. The resultant shape of the crest is the sum of all these secondary
waves. In a straight-crested wave, the envelope of the secondary waves is a
straight line also. As the wave passes an obstruction, the energy at a certain point
is a vector combination of all the circular waves emitted by every point of the
passing wave train.
The bathymetry in the vicinity of coastal structures can be irregular, and the
phenomenon of refraction can occur in conjunction with diffraction. The
historical procedure to determine the wave-height variation behind the coastal
structure was to construct refraction diagrams from the sea toward the structure,
then construct diffraction diagrams for three or four wavelengths shoreward of
the structure and then refract the last wave crest on toward the shoreline (Hales
1980). Mobarek (1962) experimentally investigated refraction-diffraction and
found that this "rule of thumb" was reasonable for medium-period waves, but for
longer periods, transformation by refraction over a shoaling bottom should be
taken into consideration.
Various numerical approaches for numerical work examining diffraction-
refraction include those of Liu and Mei (1976), Liu and Lozano (1979), Houston
(1980), and Goda (1985).
Chapter 1 Introduction