at half the frequency of the wavemaker." Normally, cross waves occur at 

 the generator and result from critical combinations of generated wave- 

 length and tank width. In movable-bed tests with gradual bottom slopes, 

 cross waves have been observed by the author at isolated sections over 

 the profile where the wavelength, as it decreased in shoaling, passed 

 through a critical value with respect to the tank width and remained at 

 that value for sufficient distance to generate a cross wave. Cross waves 

 are a spatial variation in the lateral direction. Cross waves were 

 observed over a short segment of the movable-bed profile in experiment 

 72B-06; however, the waves lasted only a brief period of time and were 

 not measured. 



Secondary waves (or solitons) result from the breakdown of a finite- 

 amplitude wave of nonpermanent form into a primary and one or more 

 secondary waves traveling at different speeds dependent on depth. 

 Secondary waves can be generated by a sinusoidally moving generator 

 blade or by a wave as it passes a slope onto a shelf of smaller but 

 constant depth (see Madsen and Mei, 1969 and Galvin, 1972) and are a 

 spatial variation in the longitudinal direction. Secondary waves caused 

 by waves passing onto a shelf probably occurred, but were not recorded. 

 Secondary waves caused by sinusoidal generator blade motion occurred, 

 but (as pointed out in Volume VI for the experiments where secondary 

 waves were most pronounced) the wave height variation due to secondary 

 waves was at least an order-of-magnitude less than the variation due to 

 wave reflection from the profile. Because the incident wave height 

 measurement was an average of wave heights all along the tanks, the 

 measured incident wave height was not affected by any spatial variation 

 in height due to secondary waves. 



Transverse waves, generated by a gap at the side of the blade and a 

 critical combination of wavelength and tank width, have an amplitude that 

 varies across the tank, but since the transverse wave has the same period 

 as the plane progressive wave, the combined wave motion causes the wave 

 height at one point to increase from right to left and at another point, 

 farther down the tank, to increase from left to right. (See Madsen, 

 1974.) Transverse waves are spatial variations in both the lateral and 

 longitudinal directions. Transverse waves were observed and recorded 

 in only experiment 72B-10; a complete discussion of the wave height 

 variability resulting from transverse waves is given in Volume VII. 



Re-reflection was the primary source of incident wave height varia- 

 bility in these experiments. The effect of re-reflection on incident 

 wave height variability in an experiment can be determined by comparing 

 the difference in the range of wave heights between the fixed- and movable- 

 bed tanks. The wave height variation in the fixed-bed tank is a measure 

 of the wave height measurement accuracy in the movable-bed tank, and sub- 

 tracting the measurement accuracy from the total variation in the movable- 

 bed tank gives a measure of the incident wave height variation due to 

 re-reflection in the movable-bed tank. 



a. 1.50-Second Wave . The nominal (generated) wave height for the 

 1.50-second wave period was 0.41 foot (12.5 centimeters). In the 



48 



