the decay area is thus given by the graph, the height obtained by multiply- 

 ing the height at the end of the fetch by the height ratio (in the above 

 case the decay height would be 0.37 x 25 = 9.25 feet), and the arrival time 

 by adding the travel time to the time of the map used. 



Plates 16 - 20, inclusive were developed at tha Scripps Institution 

 of Oceanography- These plates are revisions*- of curves which originally 

 appeared in the Navy Hydrographic Office publication, "Wind Waves and Swell, 

 Principles of Forecasting," H.Q. Miscellaneous Publication 11-275 • 



Tables of Functions of d/L and d/L Q 



In many of the basic equations describing gravity waves various 

 functions of d/L and d/Lo occur. Some of these wave equations were dis- 

 cussed above and summarized in graphical form in Plates 1 to 20= In 

 evaluating these equations in certain instances it is often just as con- 

 venient and certainly more accurate to utilize tabulated values of various 

 functions of d/L and d/L > Those functions that are presented below in 

 tabular form are summarized in Plate 21 „ The theory involved in calculating 

 the various terms in the tables is discussed as follows ; 



Values of tanh 277 d/L, b ^/a ^ lA. Q . and C/C Q ; The basic equation for 

 wave velocity (where the wave jtoepness is small; is 



C = -|^r- tanh 2 77" d/L 



In deep water, that is, where d > 1.0 L Q , tanh 27fd/L approaches unity 

 and since L = CT and Lq - o T (Note that deep water ordinarily is defined 

 as d i 0.5 L Q . However in these tables it is noted that the values of 

 tanh 2 tt d/L departs appreciably from unity for the range d/l^ = 0<>5 to 

 d/Lo - 1) 



2 



thus 



and 



2 tt L6iG ° "277 



_2tt L tanh 2 7T d/L = L_ tenh 2 w d / L 



S— L, L ° 



27T ^ 



M% =-£ — tanh 2 7Td/L, C/C = tanh 277 d/L 



L o/ T h> 



Wave Report No. 73, Scripps Institution of Oceanography, March 194-8 



