The water level in the channel is not visible when the bow wave is present 

 (Fig. 16, c, d, and e) but the main flow clearly curves past and does not 

 penetrate the channel . 



4, Conclusions . 



The photo sequences show free- surface effects at a pile are most 

 marked as the high crest passes. Crest stagnation is significant at 

 circular and channeled piles in the photographed situations. The surface 

 configurations at peak crest flow in Figures 14, 15, and 16 resemble the 

 free surfaces for steady unidirectional flow past a circular surface- 

 piercing pile (see Figs. 21, 22, and 23 in Petryk, 1969). 



Dagan and Tulin (1972) analyzed steady two-dimensional, free-surface 

 flow past an obstacle of shallow draft, D. Stagnation effects were found 

 to depend critically on the Froude number based on draft, Fp = u^/gD, 

 where u is incident flow velocity. Figure 17 shows the three stagnation 

 regimes occurring with increasing F^: (a) a smooth elevation equal to 

 (u^/2g) in the free surface at the obstacle; (b) a stable breaking wave 

 with a surface elevation somewhat less than (u^/2g), when V^ rises above 

 1.4; and (c) at larger F^, a vertical jet. The photo sequences of wave 

 flows show these three stagnation regimes at the test pile. However, the 

 flow obstacle is thin, rather than of shallow draft, and the important 

 Froude number is based on obstacle diameter. (Dagan, 1975 analyzed 

 the influence of obstacle slenderness on free-surface nonlinear effects.) 



Petryk (1969) noted that, in steady unidirectional flow, the free- 

 surface features near a vertical circular pile depend on the Froude 

 number based on pile diameter. For wave flow, Hallermeier (1976) docu- 

 mented effects of the Froude number, F^ = U^/2ga, on the free-surface 

 geometry during peak water. One effect of F^ is directly visible in 

 Figure 14(d): the finned pile is twice the diameter of the circular pile 

 and, at peak flow, the water slope at the side of the finned pile is about 

 half that at the smooth pile, because Fq is halved. 



F^ also determines the stagnation regime in a way analogous to Vd 

 in the situation considered by Dagan and Tulin (1972) . When F^ increas- 

 es above unity,- the front runup and side slope at a circular pile cease 

 their linear increase with the velocity head, U^/2g, possibly indicating 

 a transition from smooth to breaking runup (Figs. 4 and 5 in Hallermeier, 

 1976). Smooth runup occurred in most of the present test series. The 

 photos showing breaking and jetting runup are of situations with maximum 

 values of U and F^. 



The stagnation regime occurring in the photo sequences and the 

 calculated value of F^ = U^/gt, where t is obstacle cross-sectional 

 thickness normal to wave direction, are listed in Table 4. Velocity was 

 calculated using McCowan solitary wave theory, since measurements by 

 Le Mehaute, Divoky, and Lin (1968) show this theory accurately gives U 

 for high waves near d/L = 0.08, the condition for all the photos. Table 4 

 indicates the stagnation regime can be roughly categorized by the value 



35 



