occurs when 9 = 0, 2tt, etc., while the maximum horizontal velocity in the 

 negative direction occurs when 9 = tt. Sit, etc. On the other hand the 

 maximum positive vertical velocity occurs when 9 = tt/2, 5tt/2, etc., and 

 the maximum vertical velocity in the negative direction occurs when 

 e = 377/2, 777/2, etc. (See Figure 2-3.) 



The local fluid particle accelerations are obtained from Equations 

 2-13 and 2-14 by differentiating each equation with respect to t. Thus, 



gTTH cosh[27r(z + d)/L] . , _..^ „„. , ._ ^_. 

 "- = "" IT cosh (277d/L) "" '-^ - ^^- ^'"''^ 



gTTH sinh[277(z + d)/L] , -,_ .„., ,_ _, 

 '^^ = " IT cosh (2.d/L) '''' [-^ - ^'- ^'"''^ 



Positive and negative values of the horizontal and vertical fluid 

 accelerations for various values of 9 = 277x/L - 277t/T are shown in 

 Figure 2-3. 



The following problem will illustrate the computations required to 

 determine local fluid velocities and accelerations resulting from wave 

 motions. 



************** EXAMPLE PROBLEM 



************** 



GIVEN : A wave with a period of T = 8 seconds, in a water depth of 

 d = 50 feet, and a height of H = 18 feet. 



FIND : The local horizontal and vertical velocities, u and w, and 

 accelerations a^ and a.^ at a depth d = 15 feet below the SWL 

 when 9 = 277x/L -277t/T = 7t/3 (60 degrees). 



SOLUTION : Calculate 



L^ = 5.12 T^ = 5.12(8)^ = 328 feet , 



50 



= 0.1526 . 



L, 328 



From Table C-1 in Appendix C for a value of 



d 



— = 0.1526 , 

 L 



d , 27rd 



- « 0.1854; cosh = 1.759 , 



L L 



2-13 



