ERDC/CHL CHETN-II-45
March 2002
predictive equation should demonstrate a similar trend of decrease. Van der Meer's (1991) reef
equation does not include a crest-width term and is, therefore, independent of B/Lo for all three
modes of transmission. For relative submergence of 1.0 (Figure 4), the van der Meer (1991)
conventional breakwater equation is similar to the Tanaka curve only for values of B/Lo ≤ 0.1.
The Ahrens equation for submerged structures only includes a cross-sectional area term and does
not follow the Tanaka curve form. The equations proposed by Seabrook and Hall (1998) and by
d'Angremond, van der Meer, and De Jong (1996) are similar to the form of the Tanaka curve,
indicating that they may adequately capture the influence of relative crest width.
1.0
vdMc
dA
0.8
SH
A
0.6
0.4
0.2
R/Ho=-1.0
0.0
0.0
0.5
1.0
1.5
2.0
B/Lo
Figure 4. Transmission coefficient versus relative crest width
of submerged structure
Figure 5 shows Kt versus B/Lo for surface-piercing structures with a dominant transmission mode
of overtopping. The Seabrook and Hall (1998) results are not included for this and the
transmission-through modes because their work was intended to be applicable only to submerged
structures. Again, the conventional van der Meer equation does not produce a decaying curve
and is similar to the Tanaka curve for very narrow-crested structures only. The decaying curves
resulting from the d'Angremond and Ahrens equations suggest they have adequately represented
relative crest width. The Ahrens equation also demonstrates a decaying trend for high structures
in which the dominant mode is transmission through the structure. The other equations gave
negative values of Kt for the high structure.
In summary, the Tanaka (1976) curves are referenced here as a qualitative guide for assessing the
validity of predictive equations. Most of the equations investigated follow the Tanaka curve
trends over a narrow range of design conditions. Van der Meer's (1991) equations are best
suited for narrow-crested structures with a crest height near the water surface (i.e., R ≈ 0). Based
on this analysis, general application of van der Meer's equations is not recommended. Seabrook
5
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