refraction patterns as the waves approach the harbor and shoreline, by 

 using the distorted time scale (from eq. 4-24b) described in Section 

 IV,2,b, 



then the resulting wavelengths are longer than those obtained by applica- 

 tion of the horizontal linear scale of the model, and accurate simulation 

 of modes of oscillation and resonance in the harbor basins is not achieved. 

 The use of this method of obtaining similarity of refraction in the ocean 

 and beach areas of the model also results in the loss of similarity of 

 diffraction. Similarity of diffraction requires that the linear scales 

 for horizontal distances on the model be equal to the wavelength scale, 

 or 



(M, = H • ^'-''^ 



Rubble-mound breakwaters and wave absorbers in distorted-scale models 

 have distorted slopes that are steeper than their counterparts in geomet- 

 rically similar models. Therefore, the scale effects in wave reflection 

 are increased in distorted-scale models con^jared with undistorted-scale 

 models. Scale effects in wave transmission are also appreciable in 

 distorted-scale models. The nomograph in Figure 4-5 can be used to 

 determine the size of the model core material required to obtain sim- 

 ilarity of wave transmission if the inverted linear scale, Lp/L^, on 

 the vertical axis is replaced by 



and the relation between Dj„ and Dp, equation (4-32), is replaced by 



^ = K(I^\ . C4-44) 



P ^ 



These changes are reflected in Figure 4-6. 



Keulegan's (1973) equations for wave transmission through rubble- 

 mound structures (eqs. 4*33, 4-34a, 4-35, and 4-36a) can also be used to 

 minimize scale effects of wave transmission in distorted-scale models if 

 equation (4-44) is used to determine the relation between Dj„ and Dp. 

 The use of Keulegan's equations are simplified somewhat for wave periods 

 and depths in which the wave velocity is given with sufficient accuracy 

 by the relation V = (gd)^/^. This is because the term for long waves 



232 



