Internal Field Variables Depending on 6 and S 



The internal field variables are tabulated at equally spaced dimensionless distances above 

 the bottom, i.e., at S/h values of 0, 0.1, 0.2 ... up to and including the free surface, and 

 at d values of 0°, 10°, 20°, 30°, 50°, 75°, 100°, 130°, 180°. Figure 24 shows a sample 

 presentation of the dimensionless horizontal velocity component field. 



A description of the entries in Figure 24 will serve to familiarize the reader with most of 

 the features of the tables. The first row lists the phase angles (theta) in degrees. The second 

 row lists the dimensionless wave profile (7?/H) at the corresponding phase angles. The 

 percent values listed beneath the 17/H values are the differences between the 

 Stream-function and Airy Theories, defined as: 



Stream-function— Airy 



Percent = X 100 percent 



Stream-function 



The main body (remaining portion) of the table Usts the dimensionless horizontal water 

 particle velocities. The row labeled "Surface" represents the dimensionless velocities 

 evaluated at the free surface; the percentage differences for velocities are calculated as 

 defined above for the profile. The remaining part of the table represents the dimensionless 

 velocities and percentage differences evaluated on a grid of (6, S/h). The lack of entries for 

 the higher S/h and higher theta values (right side of page) results from the wave profile in 

 the trough region being lower than in the crest region (left side of page). Two additional 

 comments pertaining to the percentage values will complete the description of the sample 

 table. A percentage difference value of exactly 100 percent implies that the 

 Stream-function profile occured at a (0,S/h) value, however, the Airy profile was lower 

 than the particular S/h at the phase angle, d, i.e., this grid point was not "covered" 

 by the Airy profile. For example, this is the case at = 0°, S/h =1.5 and 1.6 and 6 = 180°, 

 S/h = 0.8 and 0.9. Finally, the asterisks indicate that the percentage differences were not 

 calculated because the Stream -function value was less than 5 percent of the maximum 

 Stream-function value. This avoided the tabulation of very large percentages which would 

 have been the result of division by a small number. 



A brief description of each of the tabulated internal field variables is presented below. 



Horizontal Water Particle Velocity Component, u(6,S) 



The horizontal water particle velocity component, u(d, S), is defined by Equation (21). 

 (The equations for the tabulated functions are presented in Tables D, E, and F.) The values 

 u'(0, S) tabulated, are presented (Table I) in the following dimensionless form: 



u (6, S) (H/T) 



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