14.4 Waves approaching a shore
Waves generated in the deep water of the ocean travel without change of
form for a considerable distance. As they approach the shore, the decreas-
ing depth begins to have an effect. The waves undergo a decrease in wave-
length and increase in height, and hence become steeper as they travel
towards the shore. Waves at an oblique angle of approach are refracted
(so that the crests are turned to become nearly parallel to the shoreline)
before they break. As the waves break (Section 14.5), with the attendant
air entrainment, virtually all of the energy is lost and a swash (the onrush
of water towards the beach followed by the downrush away from the
beach) is established. When the line of breaking is at an angle to the
beach, currents parallel to the beach, known as longshore currents, are
established. The swash and the longshore currents are important causes of
sediment motion that shapes the coastline.
Apart from refraction, waves at the shore will be affected by reflec-
tion (Section 14.6), and diffraction (Section 14.8) depending on the bed
features. For a gently sloping beach, the wave behaviour is mainly deter-
mined by refraction. The analysis of refraction is usually carried out using
linear theory, even though its basic assumptions are violated in the
shallow-water region where the wave breaks. In fact, steep waves assume a
non-linear form in the same way as do cnoidal waves, changing almost to
solitary waves before they break on the beach.
The refraction diagram showing wave crests and rays, drawn ortho-
gonal to the crests, is extremely useful in coastal engineering practice.
Generally, a ridge in the bed topography causes the rays to converge
while a valley makes them diverge. Conservation of radiated energy
within adjacent rays means that for converging rays the wave height
will increase, and a structure in the region of converging rays may be sub-
jected to potentially damaging wave forces. A study of wave refraction is
also useful in the design of sea outfalls and the location of a harbour
entrance.
The continuity principle requires that the period of the wave approach-
ing the shore should be the same everywhere, and in refraction analysis
it is assumed that the radiated energy is conserved between two adjacent
rays.
For a constant wave period, T,
TL 0 /c 0 L/cconstant
or
c/c 0 L/L 0 (14.29)
where the subscript ‘0’ denotes deep-water conditions.
586 WAVES AND OFFSHORE ENGINEERING
