EM 1110-2-1100 (Part II)
31 July 2003
Figure II-4-6. Shallow-water transformation of wave spectra (solid line - incident, d = 3.0m; dotted
line - incident breaking zone, d = 1.7m; dashed line - surf zone, d = 1.4m)
(e) In shallow water, the shape of the wave spectrum is influenced by nonlinear transfers of wave energy
from the peak frequency to higher frequencies and lower frequencies (Freilich and Guza 1984; Freilich, Guza,
and Elgar 1990). Near incipient breaking higher harmonics (energy peaks at integer multiples of the peak
frequency) appear in the spectrum as well as a general increase in the energy level above the peak frequency
as illustrated in Figure II-4-6. Low-frequency energy peaks (subharmonics) are also generated in the surf
(Figure II-4-6, also see Part II-4-5). Figure II-4-6 shows three wave spectra measured in a large wave flume
with a sloping sand beach. The solid curve is the incident spectrum (d = 3.0 m), the dotted curve is the
spectrum at the zone of incipient breaking (d = 1.7 m), and the dashed curve is within the surf zone (d =
1.4 m). Presently, no formulation is available for the dissipation rate based on spectral parameters for use
in Equation II-4-13. Therefore, the energy in the spectrum is often limited using the similarity method. Smith
and Vincent (2002) found that in the inner surf zone, wave spectra evolve to a similar, single-peaked shape
regardless of the complexity of the shape outside the surf zone (e.g., multipeaked spectra evolve to a single
peak). It is postulated that the spectral shape evolves from the strong nonlinear interactions in the surf zone.
(4) Waves over reefs. Many tropical coastal regions are fronted by coral reefs. These reefs offer
protection to the coast because waves break on the reefs, so the waves reaching the shore are less energetic.
Reefs typically have steep seaward slopes with broad, flat reef tops and a deeper lagoon shoreward of the reef.
Transformation of waves across steep reef faces and nearly flat reef tops cannot be modeled by simple wave
breaking relationships such as Equation II-4-12. Generally, waves refract and shoal on the steep reef face,
Surf Zone Hydrodynamics
II-4-11
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