structures (such as rubble-mound breakwaters, jetties, and wave absorbers) 

 are steeper in distorted-scale models than in the prototype or in geo- 

 metrically similar models; this causes increased wave reflections in 

 distorted models. Scale effects in wave diffraction and refraction may 

 occur in distorted models, depending on the degree of distortion and the 

 ratios of depth to wavelengths that must be reproduced. The total effects 

 of energy loss by friction (including damping due to bottom and internal 

 friction, entrance losses and losses in the voids of rubble-mound break- 

 waters, and wave absorbers around the perimeter of harbor basins) also 

 cause scale effects in the amplification factor and the sharpness, or 

 Q value, of frequency- response curves at resonance. Therefore, special 

 efforts must be made to devise methods of reducing such scale effects as 

 much as possible. Although the effects on test results due to procedures 

 of model operation cannot be strictly classified as scale effects, the 

 maximum peak values of frequency-response curves can be in error if the 

 increment is too large between wave periods used in the tests. 



Bottom friction effects are usually negligible in distorted-scale 

 models; however, in instances where deemed necessary the reduction of 

 wave height with distance of wave travel can be determined from the 

 equations developed by Keulegan (1950b); i.e., equations (4-28) and 

 (4-31). Scale effects due to wave reflection from beach slopes and all 

 types of reflective surfaces can be reduced somewhat by the distortion 

 of wave heights; i.e., the arbitrary increase of wave heights compared 

 with values obtained by application of the vertical scale of the model. 

 This partial reduction of the reflection coefficient is explained by 

 the arbitrary increase in wave heights which results in the increase 

 of values of wave steepness, H/X, and by the reflection coefficient 

 which decreases as the wave steepness increases. For structures that 

 are located where their reflection coefficients are critical to the 

 problem being investigated (especially rubble-mound structures in which 

 the reflection coefficients are exaggerated because of scale effects 

 related to the lack of fully turbulent flow in the voids of the struc- 

 ture), the reflection coefficients can be reduced satisfactorily by 

 wire-mes|i screens placed on the structure slopes, together with a mod- 

 erate increase in the size of the quarrys tones in the outer cover layers 

 of the structure. As in the case described for geometrically similar 

 models, the proper values of reflection coefficients in the model should 

 be determined by the conduct of special, two-dimensional flume tests. 

 Tests would first be made with a large linear scale, in which the 

 Reynolds number is large enough to ensure fully turbulent flow to deter- 

 mine, as nearly as possible, the reflection coefficients of the prototype 

 structures. Tests would then be conducted on the corresponding model 

 structures to determine the optimum combination of wire-mesh screen (or 

 other types of wave filters that have low reflection coefficients) and 

 th.e use of distorted (enlarged) quarrystone sizes in the structures. 



The similitude of refraction can be maintained in distorted-scale 

 models when the waves are long enough relative to depth that the wave 

 velocity is given by the relation V = (gd) ^/^ (see Sec. IV, 2, b). Biesel 



229 



