4.2 Wave Parameters Based on Small Amplitude Wave Theory
131
2. Plunging. The whole front face of the wave steepens until vertical; the
crest curls over the front face and falls into the base of the wave (Fig. 4.17b).
The classic form of plunging breakers, much beloved by surf-riders, is
arched, with a convex back and a concave front. This type of breaker
appears on beaches of relatively gentle slope where long swells, generated
by distant storms, are present.
3. Collapsing. The lower part of the wave's front face steepens until vertical,
and this front face curls over as an abbreviated plunging wave (Fig. 4.17c).
Minimal air pocket and usually no splash-up are observed. Such breakers
occur on beaches with moderately steep slopes.
4. Surging. The wave slides up the beach with little or no bubble production.
The water surface remains almost plane, except where ripples may be
produced on the beach face (Fig. 4.17d). Surging breakers are found on
very steep beaches.
Laboratory experiments have shown that breaker types can be distinguished
depending on the so called 'surf similarity parameter' ~ (Massel, 1989):
(3
~ = ffli.'
VTo
( 4.55)
where (3 is the beach slope, Hb is the wave height at breaking point, and La is
the deep water wavelength. The following values of parameter ~ are associated
with particular breakers types:
surging or collapsing:
plunging:
spilling:
~ > 2.0 }
0.4 < ~ < 2.0 .
~ < 0.4
( 4.56)
The breaking wave height, H b , in Eq. (4.55) can be found from the formula
developed by Goda (1985):
Hb = 0.18Lo {1- exp [-1.5~~ (1 + 15(34 / 3)]}.
( 4.57)
Formula (4.57) is presented in graphical form in Fig. 4.18.
In Fig. 4.18, a limiting wave height for waves propagating over a horizontal
bottom is added. Horizontal sea bottoms usually occur at sea banks or at
the top of coral reefs. In current oceanographic and engineering practice, it is
assumed that for a horizontal bottom the H /h ratio is equal to 0.78, what is
consistent with the value predicted from solitary waves theory. However, Tucker
et al. (1983) measured waves using two waverider buoys, seaward and landward
of a relatively fiat offshore bank of the east coast of England. Minimum water
depth over the bank was approximately 4.5 m at mid-tide level. The measured
131
2. Plunging. The whole front face of the wave steepens until vertical; the
crest curls over the front face and falls into the base of the wave (Fig. 4.17b).
The classic form of plunging breakers, much beloved by surf-riders, is
arched, with a convex back and a concave front. This type of breaker
appears on beaches of relatively gentle slope where long swells, generated
by distant storms, are present.
3. Collapsing. The lower part of the wave's front face steepens until vertical,
and this front face curls over as an abbreviated plunging wave (Fig. 4.17c).
Minimal air pocket and usually no splash-up are observed. Such breakers
occur on beaches with moderately steep slopes.
4. Surging. The wave slides up the beach with little or no bubble production.
The water surface remains almost plane, except where ripples may be
produced on the beach face (Fig. 4.17d). Surging breakers are found on
very steep beaches.
Laboratory experiments have shown that breaker types can be distinguished
depending on the so called 'surf similarity parameter' ~ (Massel, 1989):
(3
~ = ffli.'
VTo
( 4.55)
where (3 is the beach slope, Hb is the wave height at breaking point, and La is
the deep water wavelength. The following values of parameter ~ are associated
with particular breakers types:
surging or collapsing:
plunging:
spilling:
~ > 2.0 }
0.4 < ~ < 2.0 .
~ < 0.4
( 4.56)
The breaking wave height, H b , in Eq. (4.55) can be found from the formula
developed by Goda (1985):
Hb = 0.18Lo {1- exp [-1.5~~ (1 + 15(34 / 3)]}.
( 4.57)
Formula (4.57) is presented in graphical form in Fig. 4.18.
In Fig. 4.18, a limiting wave height for waves propagating over a horizontal
bottom is added. Horizontal sea bottoms usually occur at sea banks or at
the top of coral reefs. In current oceanographic and engineering practice, it is
assumed that for a horizontal bottom the H /h ratio is equal to 0.78, what is
consistent with the value predicted from solitary waves theory. However, Tucker
et al. (1983) measured waves using two waverider buoys, seaward and landward
of a relatively fiat offshore bank of the east coast of England. Minimum water
depth over the bank was approximately 4.5 m at mid-tide level. The measured