ERDC/CHL CHETN-II-45
March 2002
Hall equation; and A = Ahrens equation. The van der Meer (1991) and d'Angremond, van der
Meer, and De Jong (1996) equations produce straight lines and are only qualitatively similar to
the Tanaka curve for values of approximately 0.1 < Kt < 0.7 and relative submergence values
between about 1.0 and 0.5. Limited predictability for these equations is expected because they
were developed based upon a restricted range of variables. Transmission values for relatively
high and low structures were deemed to be independent of incident conditions and not included
in the formulation.
The formulation put forth by Seabrook and Hall (1998) is qualitatively similar to the Tanaka
curve for relative submergence values less than zero (i.e., submerged structures), which is
expected because the Seabrook and Hall tests dealt exclusively with submerged structures. The
similarity to the Tanaka curve indicates that this equation may be representing transmission
processes well over a wide range of submerged structures. The Ahrens equations produce an S-
curve that is qualitatively similar to the Tanaka curve, suggesting that the dominant-mode
approach has potential for producing an acceptable general predictive equation. Note that the
equations developed based upon data on reef breakwaters, the Ahrens and van der Meer reef
equations, are shifted to the right in Figure 3. This shift supports an assertion by Daemen (1991)
that reef structures should be considered separate from conventional structures, requiring a
distinct predictive equation.
1.0
vdMc
vdMr
0.8
dA
SH
A
0.6
0.4
B/Lo=0.075
0.2
0.0
-3
-2
-1
0
1
2
3
R/Ho
Figure 3. Transmission coefficient versus relative submergence
Figures 4-5 plot Kt versus B/Lo for submergent (R/Ho < 0) and surface-piercing (0 < R/Ho <2)
structures, respectively. The Tanaka curves in Figure 2(b) are similar, indicating a steep gradient
in Kt versus B/Lo which decreases with increasing B/Lo until there is little change in Kt for B/Lo >
1.5 for submerged structures and B/Lo > 0.6 for surface-piercing structures. An acceptable
4
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