ERDC/CHL CHETN-II-45
March 2002
At present, the Tanaka (1976) curves provide the most comprehensive standard with which to
compare predictive equations empirically derived from a limited set of data. To be considered
reliable, a generalized predictive equation is expected to demonstrate qualitative trends similar to
the Tanaka curves over a wide range of values in representing the physical processes adequately
over a wide range of conditions. However, because Tanaka's experiments were carried out with
monochromatic waves, quantitative agreement cannot be expected for transmission of irregular
waves.
The design curves developed by Tanaka based on monochromatic waves are presented in
Figure 2. The Tanaka curves clearly illustrate the decisive roles of both relative submergence
and relative crest width on wave transmission. Relative submergence has long been recognized
as a primary factor and is incorporated in all design equations. Other researches have also
recognized relative crest width as a pivotal parameter (e.g., van der Meer (1991), d'Angremond,
van der Meer, and De Jong (1996), Seabrook and Hall (1998), and Ahrens (2001)), but have not
always adequately accounted for it in design equations, likely due to limited range in their tests.
Values calculated by the predictive equations proposed by van der Meer (1991), d'Angremond,
van der Meer, and De Jong (1996), Seabrook and Hall (1998), and Ahrens (2001) were compared
to the trends of the Tanaka (1976) design curves to assess their predictive capability. Reference
is given to three fundamental transmission modes as introduced by Ahrens (2001): transmission
through the breakwater for both surface-piercing and submerged structures, transmission by
overtopping of surface-piercing structures, and transmission over the crest of submerged
structures.
1.4
1.0
R/Ho
B/Lo
1.2
-2.1
0.050
0.8
-1.0
0.075
0.2
1.0
0.100
0.6
0.8
0.6
0.4
0.4
0.2
0.2
0.0
0.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
0.0
0.5
1.0
1.5
2.0
R/Ho
B/Lo
(a)
(b)
Figure 2. Wave transmission design curves (redrawn from Tanaka 1976)
The Tanaka transmission curve has an inverted S-shape as a function of relative submergence.
Ahrens (1987) and van der Meer (1991) also found that the transmission coefficient varied as an
S-curve if plotted against relative submergence. With the Tanaka (1976) results accepted as a
guide, a general predictive formula should also describe an S-curve in plotting Kt versus R/Ho.
Figure 3 plots Kt versus relative submergence for relative crest width B/Lo ≈ 0.075. In Figures
3-5 and Figures 7-8, the following abbreviations appear: vdMc = van der Meer-conventional
equation; vdMr = van der Meer-reef equation; dA = d'Angremond equation; SH = Seabrook and
3
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