and Le Mehaute (1955) have shown that this equation is valid within 

 about 5 percent when 



d < 0.2T2 (4-41) 



where d and T are in feet and seconds, respectively. It was also 

 shown that, on distorted-scale models and with prototype quantities d 

 and T, equation (4-41) becomes 



0.2T^ 

 d„ < ^ . (4-42) 



P 



The utility of this equation is in model design. Most distorted-scale, 

 harbor wave action models are conducted to determine the optimum harbor 

 basin and breakwater arrangements to ensure satisfactory mooring and 

 navigation conditions. For such problems, the critical wave periods 

 range from about 20 to 200 seconds. By use of equation (4-42), the maxi- 

 mum depths that can be reproduced in the model areas where wave refrac- 

 tion is important to the problem can be quickly determined. Table 4-4 

 gives the maximum depth for accurate wave refraction for common values 

 of T and DF as determined from this equation. Since the degree of 

 distortion allowable is limited by the reflection error that can be 

 tolerated, after correction to the extent possible by the procedures 

 described earlier, nearly all model studies of this type show that it 

 is infeasible to select model scales such that refraction will be modeled 

 correctly for all wave periods. Determination as to whether the degree 

 of error in the refraction patterns is acceptable is made by comparing 

 computed refraction patterns for the distorted and undistorted conditions 

 (Eagleson, 1960). In the design and operation of distorted-scale models 

 (designed as discussed above), the transference equations for velocity 

 and time are (from eqs. 4-11 and 4-13): 



and 



T, = 



DF 



1/2 



for the special case where the d/X ratio is such that the wave velocity 

 is given by the relation V = (gd)^'^. For the general case, where the 

 relationship (from eq. 4-14) 



= (: 



i '- ¥)'" 



230 



