^/ 



Figure 30. (a) Definition of angle 6 describing channel geometry 

 of pile; (b) hypothetical flow streamlines for yaw angle 

 3 < e and g > e (assuming no circulation). 

 As the yaw angle of the pile increases beyond 6=6, the flow no longer 

 penetrates the channel to stagnate in the corner; it bypasses the chan- 

 nel. These hypothetical streamlines are applicable only if the water 

 particle excursion is large compared to the channel dimension, so the 

 crest flow approximates steady unidirectional flow. Linear wave theory 

 gives the horizontal semiaxis of the elliptical surface particle orbit as 



h = W[cosh (kW+kd)]/sinh kd = (U T/27r) 



(3) 



Although the test waves were nonlinear, equation (3) gives the order of 

 magnitude of the fluid excursion, showing it is much larger than X for 

 H-piles with high waves at the medium period (T = 2.32 seconds for 

 d = 1.00 foot; T = 3.55 seconds for d = 2.33 feet). Figure 31 shows 

 peak water patterns measured at five H-piles with maximum fluid excursion, 

 (The 3x3 H-pile is excluded because no data are available for the medium 

 period and pile confinement effects also may be significant for this 

 pile; see Sec. IV.) 



Table 7 compares the angle e for these piles with the angular half- 

 width, X, of the front runup region in_Figure 31; x is defined as 

 the angle at which W(6) drops below %[W(B = 0°) + W] . For the rela- 

 tively ideal situations represented in Figure 31, Table 7 shows a 

 clear relationship between 9 and x- The five (e , x) pairs have a 

 correlation coefficient of 0.732, so the hypothesis that there is no 

 linear relationship between 6 and x can be rejected with about 

 81.3-percent confidence (Sec. 13.4.1 in Freund, 1962). 



54 



