the energy imparted to the waves by U^ , with a minimiim duration t^^ + Z/2 

 for a minimum fetch F^^ + F/2, does not change, U2 will be assumed to 

 impart energy to waves which already contain energy due to Uj^. 



Plotted on Figures 3-15 and 3-16 are dotted lines of constant H^T'^ which 

 are considered lines of constant wave energy. To a first approximation, 



deepwater wave energy is given by 



E - ^^ = M2pg(m: . 

 "88 



If energy had been imparted to the waves by U2 acting alone, these waves 

 would be of length and height given in Figures 3-15 or 3-16 by the inter- 

 section of the U2 ordinate with the constant energy line (plotted or 

 interpolated) corresponding to energy imparted by Ui with a minimum 

 duration of t^-^ + Z/2 or a minimum fetch F^^ + F/2. By increasing 

 the minimum duration at this point by an amount Z/2 or by changing the 

 minimum fetch by an amount AF/2, wave conditions under U2 at the 

 time of the second chart may be approximated. 



For example, if the wind speed increases so that U2 = 40 knots, and 

 with Ui = 35 knots, t^-^ = 10 hours, F^^ = 92 nautical miles, t^^ + Z/2 = 

 13 hours; an interpolated (by eye) dotted line of constant H^T^ would be 

 followed up to the LI2 = 40-knot line where the duration = 6.5 hours. To 

 this value Z/2 or 3 hours is added and then moving horizontally along 

 the line U2 = 40 knots to t = 6.5 + 3.0 = 9.5 hours, it is found that 



H^2 - 15.6 feet, T^2 ~ ^-^ seconds, t^2 ~ ^-^ hours, and F^2 - ^^ nautical 

 miles. If the measured fetch F2 had been less than 95 nautical miles, 

 this length of fetch would limit the growth of waves. Although the pre- 

 ceding discussion would indicate that AF should be calculated, in practice 

 this need not be done; the results obtained through calculation of AF 

 would be found by reading off wave heights at the intersection of U2 and 

 F2 if F2 is limiting. Therefore, if F2 had equalled 85 nautical miles, 

 in this case less than 95 miles and therefore limiting, at the intersection 

 of U2 = 40 knots, then Hp2 = 15.0 feet, T^2 =8.5 seconds, T^2 = 8. 8 hours, 

 and F^2 - 85 nautical miles. Note this important distinction: t;^, F^ and Fj 

 are calculated by use of Figure 3-15. Some of the measured and calculated 

 values will be the same, but not all of them. 



If the wind velocity U2 is less than Ui , the procedures followed 

 are nearly the same. From the intersection of U-^ and t^-^ + Z/2 a 

 constant energy line is followed to its intersection, if there is one. 



3-39 



