Although the tethered-float breakwater is a tuned oscillator, its perform- 

 ance was found to be remarkably insensitive to tether length. For example, a 

 spectrum with energy peaked at a period of 8 seconds produces Lp = 330 feet 

 and df/Lp = 0.035, or a float diameter of 11.5 feet. For a 90-foot water 

 depth, it was determined that the number of rows (and the cost of the break- 

 water, to a first approximation) varied by only 15 percent over depths which 

 varied from 50 to 180 feet. Performance improves with increasing diameter, 

 but at a decreasing rate. This is the result of the decay of the pressure 

 gradient force as the center of the float is lowered farther below the water 

 surface with increasing diameter. In the Pierson-Moskowitz spectrum model, 

 the significant wave height, H , can be shown as 



H g = 0.026 L p (70) 



so that reasonable diameters for the breakwater floats will be of the same 

 order as the significant wave height, and reasonable water depths will be 5 to 

 20 times H (Seymour and Isaacs, 1974). However, the optimum depth per- 

 formance can be achieved at all greater depths by using the floating anchor 

 concept. Other application and performance estimations have been discussed by 

 Essoglou, Seymour, and Berkley (1975) and Seymour (1975, 1976a, 1976b, 1977). 



3. Potential Open-Ocean Applications. 



Jones (1978) referred to a 7-second breakwater as one which produces 50- 

 percent reduction of the significant wave height in a storm sea represented by 

 the Pierson-Moskowitz wave spectrum with a 7-second peak period. Since the 

 significant wave height for this spectrum is 6.4 feet, the significant wave 

 height in the lee of the breakwater would be 3.2 feet (within the sea-state 3 

 range). It is characteristic of partial wave barriers that the reduction of 

 wave height is somewhat less than 50 percent if the incident wave spectrum is 

 more sharply peaked than the Pierson-Moskowitz spectrum. It is also charac- 

 teristic that the degree of wave height reduction decreases as the dominant 

 period of the incident wave increases. Under fetch-limited conditions, spec- 

 tra that are more peaked than the Pierson-Moskowitz spectrum are observed. 

 The Joint North Sea Wave Project (JONSWAP) spectra were derived from measure- 

 ments taken on the open ocean in the North Sea. An example of the JONSWAP 

 spectra is compared to the Pierson-Moskowitz spectra in Figure 118. The 

 modified spectrum in this figure is an artificial case devised to represent, 

 by means of a spectrum which is readily expressible mathematically, certain 

 bimodal sea-plus-swell spectra which are often observed in nature. Jones 

 (1978) applied the performance estimation procedure of Seymour (1976a) for a 

 float diameter of 5 feet and the Pierson-Moskowitz spectrum. Moffatt and 

 Nichol Engineers, Ogden Beeman, and International Maritime Associates (1977), 

 utilizing a newer mathematical model, indicate that the number of rows of 

 floats predicted by Seymour (1976a) should be increased by about 45 percent. 

 Jones (1978) incorporates this adjustment into Figure 119. 



The number of rows of floats required for a given degree of reduction in 

 wave height is a fairly strong function of the size of the floats (Jones, 

 1978). When the size of the floats is some reasonable value, the system is 

 most efficient when the length of the tethers is equal to a specific fraction 

 of the dominant wavelength. For deepwater floating systems, the optimum 

 arrangement consists of spherical lightweight floats positioned with tops 

 submerged one-fourth diameter, and spaced horizontally two diameters apart. 



172 



