EM 1110-2-1100 (Part II)
30 Apr 02
so that the pattern of wave propagation can be directly visualized. Wave crests evolve during the shoaling
process to have nonsinusoidal shapes characteristic of shallow-water waves. Currents may be applied
directly. Wave breaking, however, is simulated empirically.
II-3-4. Transformation of Irregular Waves
a. The preceding discussion emphasized
of monochromatic waves. When
this process is applied to an initial significant wave height and period, it is called a significant wave analysis.
For many conditions where propagation is the dominant factor (as opposed to additional wave growth or
bottom dissipation) the significant wave analysis provides a reasonable and generally conservative
approximation. The significant wave analysis may be inadequate when wave conditions have spectra
characterized by wide directional spreads or broad (frequency) spectral widths or multiple spectral peaks.
Cases where the significant wave analysis is adequate primarily involve narrow band swell. This section
outlines differences that may be expected between the application of significant wave analyses and
application of an irregular wave approach.
and shoaling for
monochromatic waves may
to the individual frequency
direction components of the spectrum of an irregular wave system. Two factors become important:
directional spreading and spectral wave mechanics. Directional spreading is important whenever it is present.
Spectral wave dynamics are most important in high-energy, high-steepness wave cases, and negligible for
low-energy, low-steepness cases.
c. Directional spreading is important for two reasons. First, laboratory tests (Berkhoff, Boij, and Radder
1982; Vincent and Briggs 1989) with unidirectional waves indicate that shoals concentrate wave energy
immediately behind the shoal and reduce it on the flanks. The increase behind the shoal can be nearly 250
percent of the initial wave height; the reduction to either side can be about 50 percent. However, laboratory
tests with wave spectra having significant directional spread (Vincent and Briggs 1989) show only a 110- to
140-percent increase behind the shoal and only a 10- to 15-percent reduction on the sides. Numerical models
incorporating directional spread also replicate this (Panchang et al. 1990). In the case with directional spread,
the shoal focusses each frequency-direction component at a different location behind the shoal rather than
at one spot as in the unidirectional case. Consequently some of the high- and low-energy regions overlap and
cancel each other out. Secondly, if the mean angle of wave approach is not directly onshore, one consequence
of directional spreading is that some fraction of the wave energy is heading parallel to shore or offshore. In
the case of a wave system with symmetric directional spread (i.e., 50 percent to the left and right of the mean
direction), if the mean direction were parallel to a straight shoreline (and the measurement were made in deep
water), half of the energy would be moving in directions that could not refract towards shore. So even for
angles up to 30 deg offshore-parallel, significant amounts of energy are not propagating shoreward. In a
significant wave analysis, all the energy would propagate shoreward. If the shoreline, fetch, or bathymetry
is complicated, the fraction of energy that propagates towards shore is more difficult to define.
d. Spectral dynamics arise because waves of different lengths and steepness are propagating through
and with other waves. According to Equation II-3-1, these waves can exchange energy between each other
(nonlinear transfers) and superposition of waves can lead to dissipation due to breaking. Analysis of
thousands of wave records (Bouws et al. 1987; Bouws, Gunther, and Vincent 1985; Miller and Vincent 1990)
indicates that higher energy wind sea spectra achieve a characteristic shape that is different from that obtained
simply by shoaling. As a result, the energy level for shoaling irregular wave tends to be less than that
predicted from linear monochromatic shoaling of the wave components, especially near the surf zone. Smith
and Vincent (1992) also indicate that the shoaling and breaking of irregular waves with two spectral peaks
can substantially differ from the monochromatic (and even single peak spectral) case. Moreover, the wave
spectrum after refraction and shoaling can have a substantially different peak period. Although a satisfactory
Estimation of Nearshore Waves