differ from those measured by less than 10 percent. In view of this, Harms 

 (1979b) concluded that equation (52) describes the wave transmission charac- 

 teristics of these structures adequately, at least until more comprehensive 

 models become available. The value of C^ was found to be fairly constant at 

 around 0.6; however, it must be realized that C^ incorporates, among other 

 things, the integrated effect of nontire structural components and binding 

 materials. Hence, for other types of floating tire breakwaters, C. may 

 differ from 0.6. For the Goodyear concept, Harms and Bender (1978) found the 

 porosity to be approximately 0.87. The porosity of the Wave-Guard approaches 

 0.53, which partially accounts for the better wave attenuation capacity of the 

 Wave-Guard concept. 



b. Mooring Force Estimate Based on Radiation Stress . Galvin and Giles 

 (1978) developed a method of predicting mooring forces for scrap-tire floating 

 breakwaters, based on the radiation stress concept of Longuet-Higgins and 

 Stewart (1964). Wave forces in a floating tire breakwater differ from the 

 more studied cases of wave forces on fixed cylinders and in a ship mooring 

 line. The forces on a fixed cylinder alternate with time; those in a ship 

 single mooring line vary from slack to taut in a rather irregular manner, 

 being essentially zero for a significant fraction of the wave period, and then 

 rising abruptly to a peak; the floating tire breakwater is wide enough that 

 parts of the structure tend to move in one direction while parts are being 

 stressed in the opposite direction. The result is that the mooring lines are 

 subjected to continual forces which alternate in magnitude but always remain 

 positive (the force in the oceanside mooring is opposite to the wave travel 

 direction throughout the wave cycle). The fact that the force in the cable on 

 the oceanside remains positive and greatly exceeds the force in the mooring 

 line on the landside is assumed to be due to the wave-induced radiation 

 stress. Although radiation stress is normally small relative to wave-induced 

 drag and inertia forces on fixed cylinders, drag and inertia forces on a 

 floating tire breakwater tend to cancel out internally since the breakwater 

 usually extends more than one-quarter of a wavelength (the distance between 

 maximum of drag and inertia forces). (This is not precise at the mooring line 

 point of attachment, but is approximately correct at a finite distance from 

 the mooring point. ) 



The radiation stress, S , is the excess flux of momentum, due to the 

 presence of waves, in the direction of wave travel. It is obtained by 

 integrating the flux of momentum, from bottom to surface, then taking the mean 

 value with respect to time, and finally subtracting the hydrostatic 

 pressure. S* is defined as the net radiation stress due to incident and 

 transmitted waves only (the case of zero reflection) 



S* = —„ — -z (53) 



xx 8H?(1 - c£) n 



where 



f+ 



(kd) 



(sinh 2kd) 



(54) 



and k is the wave number, d the Stillwater depth, and y the unit weight 

 of fluid. If F is defined as the maximum instantaneous mooring force, then 

 a balance of forces on the breakwater indicates that 



141 



