'bm 



= angle of bottom slope seaward of the structure, measured 

 from the horizontal 



= wavelength measured in depth d + Ad corresponding to the 

 breaking depth 



= dynamic viscosity of the water 



= mass density of the breakwater material 



p = mass density of the water in which the structure is 

 situated 



a = surface tension of the water 

 Thus , in accordance with the tt theorem 



f(d, g, H, T,9,^, M, a, p^, E^, E^^, p^^, p, p^,, k) - 



P-P.t .,.. .r ^ . . ^ r.- - ,.^ _ « 



Pat 





' ^w w bm' '^bm' ^ 



and 





P - Pat _ f„ 

 Pat 



H (gH)l/2T 

 d'^'^' d 



dH oT^ y /^w' 



1/2^ /e: V/2 



bm 



d'Pbr 



(6-6a) 

 (6-6b) 



(6-6c) 



With geometrical similarity and similar test conditions, model-to-prototype, 

 and considering that viscous shear forces are negligible with respect to 

 gravity, inertia, pressure, and elastic forces, the functional relation 

 for use in guiding the testing program and correlating test data is 



P - P. 



= f" 



H (gH)^/2T pT^ 



d' 



,Hd^ 



1/2 



EUV'^ 



Phv 



Pv, 

 d'Pbr 



C6-6d) 



The above discussion and functional relations show that the extremely 

 complex interactions of the water, compressed air, and capillary forces 

 cause difficulty in determining approximate equations for correcting 

 model results to minimize errors in transferring the results to proto- 

 type quantities. However, it is believed that the model should be de- 

 signed and operated based on Froude's law and the test data transferred 

 to prototype terms using approximate methods of reducing the resulting 

 scale effects to a minimiom. The method suggested by Lundgren (1969) is 

 adopted. According to Lundgren the three breaking waveforms that cause 

 shock-type pressures with intensities greater than those of the clapotis 

 are generally similar to the ventilated, compression, and hammer types of 

 shock pressures shown in Figure 6-1. 



(1) Ventilated Shock . If the wave front approaches the vertical 

 wall so that the air between the wave front and the wall is able to escape 



322 



