the cross wave described by Mahoney (1972). Experiments by Barnard and 

 Pritchard (1972) confirmed that a wavemaker moving at frequency co, 

 exciting a plane progressive wave train with wavelength L, may also 

 generate a standing cross-wave field with frequency a)/2 as a result of 

 nonlinear resonance, if the tank width is greater than L. Madsen (1974) 

 experimentally confirmed the possible occurrence of a standing transverse 

 wave at the frequency of the generator motion if the tank width is greater 

 than L/2. The tank width was never as large as L/2 in the 96-foot tank 

 tests, and the lateral flow was observed with b < (O.l)L. The observed 

 flow may have been due to a slight side motion of the somewhat loose- 

 fitting, generating piston, or to the departures of the tank from a con- 

 stant rectangular cross section. Because a slight leakage around the 

 wavemaker can measurably affect generated wave height (Madsen, 1970), 

 an asymmetric leakage could cause a significant initial variation in H 

 across the tank. This, in turn, could cause an important lateral flow 

 close to the generator. W(a) patterns markedly skewed about a = 0° were 

 often recorded at G = 8.6 feet (see Fig. 24), while measurements at G = 25 

 feet gave patterns that were less skewed, but definitely not symmetric 

 about a = 0° (James and Hallermeier, 1976). 



Figure B-7 shows typical waveforms in the 85-foot tank tests; measured 

 wave dimensions are listed in Table B-6. The short, steep beach in this 

 tank was highly reflective in certain situations, resulting in marked 

 wave variability both along and across the tank. Figure B-8 shows signif- 

 icant wave variability in the 85-foot tank. At T = 3.55 seconds, d = 2.33 

 feet, E = 2.5 inches (6.3 centimeters), and G == 19 feet (5.7 meters), the 

 wave action is distinctly different at the incident gage and the test pile 

 locations, although they are separated by only 4.2 feet (1.3 meters) (Fig. 

 1). With this wave condition, the tank width is about half the wave- 

 length, so this variability might be associated with the standing wave 

 described by Madsen (1974) . Other data obtained in the 85-foot tank was 

 marred by an undesirable test situation. At T = 3.55 seconds, with the 

 test pile at G = 30 feet (9.1 meters), the pile was one wavelength from 

 the generator and from the beach toe, so the incident and reflected waves 

 superposed in phase. However, data of certain value were always obtained 

 with wave pulses in the 85-foot tank. From certain other test data for 

 the same tank, it was established that scale effects do not affect the 

 conclusions about wave transformation from these model tests (see 

 Sec. III). 



In summary, the complicated nonlinear behavior of the test waves in 

 the 96-foot tank should have had little effect on the conclusions present- 

 ed in this report, since the transformation in space is not marked over a 

 distance on the order of the pile cross-sectional dimension. The flow at 

 any wave phase is approximately unidirectional for the thin test piles, 

 and the waves may be regarded as having a permanent form locally. The 

 crest height is the important characteristic of the waveform since it de- 

 fines the peak horizontal flow velocity causing the peak water at the 

 pile. Because the crest height varies as the wave propagates, this 

 normalizing factor must be carefully selected for each test situation. 

 The waveform features are of secondary ■ importance to the present study, 

 although the crest curvature in space must influence the accuracy of the 

 unidirectional flow approximation. 



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