In the movable-bed tank in experiment 72A-06 the range of values was 

 0.10 foot (3.0 centimeters), 0.03 foot due to varying reflectivity, and 

 in experiment 72-10 the range was 0.12 foot (3.7 centimeters), 0.08 foot 

 (2.4 centimeters) due to varying reflectivity. The average incident 

 heights in the movable-bed tanks were 0.07 foot and 0.04 foot, both 

 greater than the nominal (generated) height. 



e. Comparison of the Ten Experiments . Varying profile reflectivity 

 caused no measurable change in the incident height in experiment 72B-10 

 (2.35 seconds), a moderate change (0.01 to 0.03 foot) in experiments 

 70X-06, 70X-10 (1.90 seconds), 71Y-06, 72D-06, 72A-06, and 72B-06, and 

 a significant change (0.06 to 0.08 foot) in experiments 71Y-10 (1.90 

 seconds), 72C-10 (1.50 seconds), and 72A-10 (3.75 seconds). The effect 

 in the 6-foot-wide tank was in the moderate range for all five experi- 

 ments and in the 10-foot-wide tank ranged from no change to 0.08 foot, 

 and the effect was not a function of wave period. It appears then that 

 the wider tank may have amplified this effect. 



III. EQUILIBRIUM PROFILES 



1. Definitions and Importance of Equilibrium Profiles . 



The term "equilibrium profile" implies a profile whose mean position 

 is fixed in space for the given wave and sediment conditions, with the 

 expectation that the actual profile at any given time will deviate some- 

 what from the mean profile. It has been assumed that equilibrium is a 

 state which can be reached on a model profile with a constant wave action 

 impinging on it for a sufficiently long time. 



Laboratory studies of longshore transport often depend on having an 

 equilibrium profile to determine the longshore transport rate without 

 having an onshore-offshore transport component (Savage, 1959, 1962; 

 Fairchild, 1970a). Coastal engineering models are frequently based on 

 simulating the equilibrium profile. However, Savage (1962) and Fairchild 

 (1970a) found that equilibrium profiles are not always easily attained. 

 Collins and Chesnutt (1975, 1976) showed that the final unchanging pro- 

 file for the same wave and sediment conditions was not always repeatable 

 and that the initial slope could affect the final profile shape. 



Swart (1974) found that for a single periodic wave impinging on a 

 profile, 1,500 hours of wave action was required to reach equilibrium 

 for some wave and sediment conditions. However, 1,500 hours is not a 

 practical test duration for most models or experiments. 



J.W. Kamphuis (Professor of Civil Engineering, Queen's University, 

 Kingston, Ontario, personal communication, 1978) used a series of wave 

 conditions replicating a year's seasonal variations and found that 

 when using a wave in the transition region in place of either the winter 

 or summer waves the profile reached equilibrium much less readily than 

 when using only winter and summer waves. Kamphuis further compared two- 

 dimensional tests with three-dimensional tests, and found that 9 to 11 

 yearly cycles were required to reach equilibrium with the two-dimensional 

 setup and only 1 to 2 cycles with the three-dimensional setup. 



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