The most important result is that the quantity, (wave energy) /(wave 

 frequency), is "conserved," i.e., obeys a conservation equation, where 

 both energy and frequency are measured relative to the moving medium. 

 This quantity is called "wave action." 



Hamilton's principle is one example which is considered at length. 

 It is derived for water waves and the results demonstrated. 



Coastal Engineering Significance . This rather mathematical and very 

 general paper is of fundamental importance to wave-current interaction. 

 Building on the remarkable advances in the methods of solving problems 

 for nonlinear waves by Whitham (1965, 1967), the authors show that in 

 conservative systems considerable simplification can be made by intro- 

 ducing the concept of wave action. Instead of the relatively compli- 

 cated energy equation with the physically important radiation stress 

 term, many practical examples can be solved directly by conservation of 

 wave action. This allows for the flow of energy between waves and 

 currents without explicitly calculating the energy exchange. 



6. BREVIK, I., and AAS, B., "Flume Experiment On Waves and Currents I. 

 Rippled Bed," Coastal Engineering, Amsterdam, The Netherlands, Vol. 

 3, No. 3, 1980, pp. 149-177. 



Keywords. Bottom Friction; Comparison of Theory and Measurement; 

 Current Velocity Profile; Currents, Unidirectional; Experiment; Wave 

 Dissipation; Wave Effect on Current. 



Discussion. Properties of mean current and waves were measured in a 

 flume along which regular periodic waves and a current could be sent. 



The flume, of length 30 meters and width 1.0 meter, had a piston- 

 type wave generator at one end and a beach which gave reflection co- 

 efficients between 5 percent and 10 percent at the other end. The still- 

 water depth was 30 centimeters for the experiments, and the bottom of 

 the flume was covered by corrugated iron plates with transverse ridges 

 of height 1.4 centimeters and wavelength 8 centimeters. A current was 

 generated in the wave direction by a pump which supplied water through 

 an inlet about 2 meters in front of the wave generator. The current 

 outlet was under the beach. At full flume width, the maximum current 

 was about 20 centimeters per second. This was increased to 40 centi- 

 meters per second by halving the width of the flume for some runs. 



Wave heights and lengths were measured using resistance gages. 

 Horizontal fluid velocities were measured with a 10-millimeter-diameter 

 propeller meter. This meter is unsuitable for measuring reversing 

 flows, so the fluid velocity measurements were performed for the case of 

 strong following currents in the half-width section. Most of the wave 

 measurements were with absolute wave periods of 1.8 and 2.0 seconds, and 

 with mean current velocities of 9.1 and 16.7 centimeters per second. 



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