therefore 



n(e) = n'O) . h 



The wave profile calculation for Case 4-D is summarized in Table O and is plotted in 

 Figure 37. Note that 77 is an even function of 5. 



Water Particle Kinematics 



The water particle kinematics will be calculated for Case 4-D as presented in the sample 

 output. These kinematics will be calculated for mid-depth (i.e., 20.5 feet above the bottom). 

 The dimensionless forms of these variables are presented in Tables I through IV of the 

 sample output. The dimensionless water particle velocities are defined as: 



and 



w.(6,S)E«fi^ 



and the dimensionless water particle total accelerations are defined as: 



Du 

 - Dt 



and 



(^) 



Dw 

 _ Dt 

 ~ H7T2" 



Note that these are functions of 6 and S, however, for convenience, the dependence has 

 not been indicated in the above expressions. The calculations of the water particle velocities 

 and accelerations over the range 0° <d < 180°, are also summarized in Table and plotted 

 in Figure 37. 



It will be noted that in the tables of wave functions, the variables are only presented for 

 phase angles ranging between 0° and 180°. All of the variables are either symmetrical or 

 antisymmetrical about a phase angle of 0°. The variables tliat are symmetrical include: the 

 water surface profile, the horizontal component of water particle velocity and the vertical 



75 



