4.2 Wave Parameters Based on Small Amplitude Wave Theory
129
The diffraction coefficient depends on the distance, r, between a given point
and the tip of the wall (point 0) and angle, !p. For an obstacle of simple shape
such as a long vertical wall, the values of the diffraction coefficient, K d, are
available in graphical form (SPM, 1984). More complicated obstacles require
more advance techniques (Mei, 1983; Massel, 1989). We will again discuss
the diffraction phenomenon while discussing wave behaviour on steep offshore
islands and coral reefs.
4.2.6 Wave Breaking
Waves approaching a shoreline over decreasing water depth gradually change
their height and length. Wavelength decreases because period is constant but
phase speed is smaller, while amplitude increases to ensure constant energy
flux (see Green's law 4.51). Waves approach their limiting slope and eventually
lose their stability and break. Wave breaking on a beach is one of the most
significant physical phenomena in the coastal zone. Its significance arises from
the fact that during breaking, most of the energy transmitted with the waves
is dissipated and partly transmitted to the nearshore currents which may cause
sediment transport both in the on-offshore and along shore directions. Some
wave energy is reflected back out to sea, the amount depending upon the slope
of the beach -- the shallower the angle of the beach slope, the less energy is
reflected. Finally, a small amount of wave energy is dissipated as heat in the
final small-scale mixing of foaming water and sand.
Breaking waves are not limited to the nearshore zone. During storms, waves
break at sea in the form of white-capping, i.e. breaking of the tip of the
wave crest as it is driven forward by the wind faster than the wave itself is
travelling. The initiation of wave breaking in deep water is controlled by wave
slope, s = H / L. Stokes (1847) predicted that limiting wave steepness is:
H
s = - 2 = 0.027.
gT
(4.54)
However, available field and laboratory data, as well as theoretical analysis
(Massel, 1998), indicate that a limiting steepness in deep water is lower than
Stokes' limiting steepness. For the commonly observed probability of breaking
(from 3 to 15%), the limiting wave steepness during a storm is of the order of
0.005.
Breaking on a beach is more complicated than breaking in deep water. Shallow water breakers can be classified into four major types (Massel, 1989):
1. Spilling. White foam and turbulence appears at the wave crest and spills
down the front face of the wave (Fig. 4.17a). Spilling breakers usually
start some distance from shore and dissipate their energy gradually. Such
waves are characteristic of a gently sloping shoreline.
129
The diffraction coefficient depends on the distance, r, between a given point
and the tip of the wall (point 0) and angle, !p. For an obstacle of simple shape
such as a long vertical wall, the values of the diffraction coefficient, K d, are
available in graphical form (SPM, 1984). More complicated obstacles require
more advance techniques (Mei, 1983; Massel, 1989). We will again discuss
the diffraction phenomenon while discussing wave behaviour on steep offshore
islands and coral reefs.
4.2.6 Wave Breaking
Waves approaching a shoreline over decreasing water depth gradually change
their height and length. Wavelength decreases because period is constant but
phase speed is smaller, while amplitude increases to ensure constant energy
flux (see Green's law 4.51). Waves approach their limiting slope and eventually
lose their stability and break. Wave breaking on a beach is one of the most
significant physical phenomena in the coastal zone. Its significance arises from
the fact that during breaking, most of the energy transmitted with the waves
is dissipated and partly transmitted to the nearshore currents which may cause
sediment transport both in the on-offshore and along shore directions. Some
wave energy is reflected back out to sea, the amount depending upon the slope
of the beach -- the shallower the angle of the beach slope, the less energy is
reflected. Finally, a small amount of wave energy is dissipated as heat in the
final small-scale mixing of foaming water and sand.
Breaking waves are not limited to the nearshore zone. During storms, waves
break at sea in the form of white-capping, i.e. breaking of the tip of the
wave crest as it is driven forward by the wind faster than the wave itself is
travelling. The initiation of wave breaking in deep water is controlled by wave
slope, s = H / L. Stokes (1847) predicted that limiting wave steepness is:
H
s = - 2 = 0.027.
gT
(4.54)
However, available field and laboratory data, as well as theoretical analysis
(Massel, 1998), indicate that a limiting steepness in deep water is lower than
Stokes' limiting steepness. For the commonly observed probability of breaking
(from 3 to 15%), the limiting wave steepness during a storm is of the order of
0.005.
Breaking on a beach is more complicated than breaking in deep water. Shallow water breakers can be classified into four major types (Massel, 1989):
1. Spilling. White foam and turbulence appears at the wave crest and spills
down the front face of the wave (Fig. 4.17a). Spilling breakers usually
start some distance from shore and dissipate their energy gradually. Such
waves are characteristic of a gently sloping shoreline.