1. Modification of the Wave by the Structure (Smooth Slopes). 
For a structure with a toe water depth-to-wave height ratio greater than 
five and wave steepness much less than one-seventh, the interaction of the wave 
and structure will have dominant control on the magnitude of the reflection 
coefficient. Miche (1951) proposed that the reflection coefficient for this 
situation is proportional to the ratio of a critical wave steepness to the inci- 
dent wave steepness. The critical steepness is 
(=) -(2)" sin79 (9) 
ib 9 T T 
o/erit 
where Ho is the deepwater wave height, and © the angle the structure slope 
makes with the horizontal, in radians. Miche's equation gives conservative 
results. For example, it overpredicts monochromatic wave reflection from a 1 
on 15 slope by a factor of 2 (Ursell, Dean, and Yu, 1960). 
Battjes (1974) recommends the equation, 
tan@ 
K, = 0-1 E23 — = mates 
Le (10) 
Lo 
which can be written as 
0.1 tan2@ 
Ky = Ho 
i (@aIb) 
its 
Battjes (1974) is assuming an equation similar to the formula proposed by 
Miche (1951) where the critical steepness is 
H: 
(=) = 0.1 tan?6 (12) 
o/crit 
This criterion gives lower and more realistic values of the reflection coeffi- 
cient than Miche (1951) and is especially useful for & < 2.3 where breaking is 
induced by the structure (for plunging breakers). Figure 4 shows the compari- 
son between the equations of Battjes (1974) and Miche (1951). 
The following revised equation, 
Kre=)tanh (Os) 62), (13) 
is recommended to give a conservative prediction of reflection coefficients. 
At small values of the surf similarity parameter (& < 2.3), 
Oniaae= tanh (Ones) (14) 
and equation (13) gives the same results as equation (10). At larger values of 
the surf similarity parameter, £€, equation (13) asymptotically approaches 1.0 
and gives an upper bound closer to the data than equation (10) (see Fig. 4). 
15 
