(MOORING DYNAMICS) 



T„Ct> 



INCIDENT 



WAVE 



(RIGID BODY 

 DYNAMICS) 



Ha; 



(w) 



gj(t) 



'T K 



MOORING LINE TENSION 



IN CALM WAT 



BREAKWATER 

 MOTIONS 



w.» 



GENERATED 

 WAVES 



♦vyfRi 



♦ WA\ 



(FIXED BODY AND 

 INCIDENT WAVE) 



Vf 



(x,t) 



'TRANSMITTED 

 WAVE 



WAVE TRANSMITTED 

 BY FIXED BODY 



i • I SWAY 



I .2HEAVE 



i »3R0LL 



Figure 9. Linear system describing floating breakwater performance 

 (after Adee, Richey, and Christensen, 1976). 



The effectiveness of the theoretical linear model by Adee, Richey, and 

 Christensen (1976) in evaluating the performance of floating breakwaters was 

 determined by comparing the theoretical predictions with the physical model 

 experiments of Davidson (1971) who carried out model tests of a proposed 

 breakwater at Oak Harbor, Washington. The comparison between the theoreti- 

 cally predicted and experimentally measured transmission coefficient is shown 

 in Figure 10. The results compare reasonably well (Adee, Richey, and 

 Christensen, 1976), except for the predicted dip in transmission just above 

 a W/L value of 0.20, where W is the structure width normal to the direc- 

 tion of wave propagation, and L is the wavelength. There is also some 

 difference at the higher W/L ratios. The theory predicts that the trans- 

 mitted wave which would result when the body is rigidly fixed is almost 100 

 percent for a W/L value less than 0.10, but drops rapidly at higher W/L 

 ratios to the point where the transmitted wave is of little consequence above 

 0.15. Waves generated by the breakwater motions play an increasing role in 

 W/L ratios above 0.15. Heave motion is the major contributor to the trans- 

 mitted wave in the very narrow band of W/L between 0.15 and 0.18, with a 

 predicted heave resonance at a W/L value of approximately 0.18. The dip in 

 the curve occurs because the waves generated by heave and sway motions are 

 almost 180° out of phase and, hence, cancel each other. At W/L ratios above 

 0.25, sway motion assumes an increasingly dominant role. According to Adee, 

 Richey, and Christensen (1976), roll motions are small throughout and generate 

 only very small waves. 



b. Model by Stiassnie . Although a large volume of published work dealing 

 with floating breakwaters exists, there does not appear to be an analytical 

 expression that describes the influence of various breakwater characteristics 

 (such as mass, draft, mooring stiffness, etc.) on performance (displacement 

 and anchor forces) and on the transmission coefficient. Stiassnie (1980) 

 developed a simple mathematical model, based on the solution of the two- 

 dimensional problem of a vertical floating plate and on rigid body dynamics, 

 to investigate the influence of these different characteristics on the break- 

 water performance. The results include information on the transmission 

 coefficient, the plate displacement, and anchoring forces as functions of the 

 plate geometry and incident wave parameters. This floating breakwater model 

 has the advantage of having a closed mathematical solution, which permits 

 focusing on the influence of each parameter separately. 



40 



