situations (Table 3), the laboratory Reynolds number is lower than that 

 in the prototype by a factor equal to the length scale raised to the 

 power 1.5. Although this modeling inaccuracy^ is discussed later in 

 Section IV, 2, one effect on the test data is seen in Figure 24. These 

 two [W(a)/W] data sets are for a circular pile in approximately the same 

 flow situation at two different lengtK scales. All the lengths are about 

 2.33 times greater in the 85-foot tank test than in the 96-foot tank, 

 while the Froude number, F^ = (U^/2ga), is nearly the same in the two 

 tests. The two data sets superpose well near the pile's front, but 

 diverge toward the pile's rear. (The noticeable skewness of the 96-foot 

 tank data is probably due to a flow along the wave crest discussed in 

 App. B. ) The smoothly sloping pattern around the sides of the pile breaks 

 near |a| = 130° in the 96-foot tank data and near |a| = 110° in the 85- 

 foot tank data. The depths of the minimums and the peak water level in 

 the wake are markedly different in the two tests. Thus, Figure 24 demon- 

 strates both the limitation and the asset of the scaling by Froude number 

 used for these tests. Modeling of the wake details behind the pile was 

 inaccurate, but modeling of the front stagnation effects was accurate. 



The peak water patterns have definite value because stagnation effects 

 dominate the patterns of most interest, as the following analysis shows. 

 James and Hallermeier (1976) introduced a method for describing the peak 

 water patterns in terms of a symmetric series 



S(a) = X) aj cos [j(cx-Y)] , (2) 



j=0 



where aj is the amplitude of the jth harmonic and y is the angle 

 about which the pattern is symmetric. The amplitudes, aj, and the 

 angle, y> best describing a set of W(a) data can be determined by 

 using a least squares estimation technique. Three harmonics provide a 

 good fit to W(a) patterns produced by both low and high waves. Figure 

 25 superposes W(a) patterns for four wave types with the fitted symme- 

 tric series. Table 6 lists the wave conditions and the percent of pattern 

 variance in each harmonic. For the two low waves, the second harmonic 

 dominates the S(a) pattern, providing the fit to the front and rear 

 maximums. For the two steep waves, the first harmonic dominates the 

 S(a3 pattern, providing the fit to the dominant front maximum. For all 

 four wave types, S(a) fits W(a) fairly well except near the sharp 

 minimums. These data demonstrate that stagnation effects dominate the 

 W(a) pattern when they are significant; this occurs at a circular pile 

 when F has a value greater than about 0.1 (Hallermeier, 1976). 



2. Other Piles . 



The peak water patterns for piles with channels exhibit a somewhat 

 rough variation of measurement with orientation angle. This variability, 

 as mentioned in the discussion of Figure 20, is due to complicated flows 

 caused by the complex obstacle cross section. The variability impedes 

 quantitative analysis of W(6) pattern features. However, comparing 

 patterns for various piles clarifies some general effects of pile channels, 



45 



