wave height, B the width of the submerged breakwater, Li the incident wave length, d the water depth above the breakwater, Ls the wave length on the breakwater. The parameter f1 depends on the shape of the submerged breakwater. They obtained f1 = 13.5 for the fan-shaped and triangle submerged breakwaters.
To estimate the wave height on the submerged breakwater, we can substitute the half width of the submerged breakwater crown x for B in Eq.1. But the transmission coefficient estimated by Eq.1 does not agree with that measured in the experiment, because the ratio d/Hi in the present experiment is much smaller than that employed in Suzukis' one. We have proposed the improved formula for wave height estimation.
The ratio Kx of the wave height at the middle of the submerged breakwater crown Hx to the incident wave height Hi is given by
Kx={1-f2･tanh(2.3x/Li)}･tanh(0.61ｄ/Hi) (2)
where, x is the distance from the slope top at the forward side of the submerged breakwater along wave ray, The coefficient f2 should be determined by the comparison with the experimental results. Substituting the half width of the submerged breakwater crown B/2 for the distance x, we employ f2=0.34 for the most approximate estimations. Figure 3(a) shows the comparison of the estimated wave height ratio Kx with the measured one. Good agreements are obtained for the both cases of regular waves and multi-directional irregular waves, therefore, the wave height on the submerged breakwater can be approximately estimated by Equation (2).
The diffracted waves must be considered to estimate the wave height at the backward of the submerged breakwater. The ratio Kb of the wave height at the backward of the submerged breakwater Hb to the incident wave height Hi can be expressed by
Kb=Hb/Hi=(Kt2+Kd2)1/2 (3)
where, Kd is given by the diagram of diffraction coefficient proposed by Goda et al2), Kt is the transmission coefficient given by
Kt={1-f2･tanh(2.3B/Li)}･tanh(0.61d/Hi) (4)
where, Equation (4) is derived by substituting the width of the submerged breakwater crown B for the distance from the slope top of the breakwater x in Eq. (2). Figure 3(b) demonstrates that the estimated wave height ratio Kb agrees with the measured at the backward of the submerged breakwater.
Figure 3 Applicability of experimental formula for wave height (The incident wave height varies from 2 to 6cm and the water depth above the submerged breakwater from 2 to 4cm)
(3) Application of Numerical Model
Figure 4 shows the distribution of the water surface elevation estimated by Boussinesq equation model (Madsen et al.3)). The wave transmission on the submerged breakwater and wave diffraction by the breakwater can be computed in the model.
Figure 5 shows the estimated and measured wave profiles on and at the backward of the submerged breakwater. On the submerged breakwater (from H6 to H8), the both profiles agree with each other, therefore the Boussinesq equation model can be applied to estimate the variation of the water surface elevation on the breakwater. But at the backward of the submerged breakwater (H9), the water surface amplitude given by the model becomes smaller than that measured in the experiment. The reason why the disagreement becomes significant at the back-
