Gravity Waves and Finite Turbulent Flow Fields 



Crest Length Between (|^ and 1 ft. In this region, the current 

 field is essentially constant across any transverse section and in- 

 creases slowly in the longitudinal direction. The effect on this finite 

 wave is to increase the wave length in accordance with Eq, (8). For 

 a mean flow of 0.30 ft/sec, the 2 ft wave length should increase by 

 20% while the 6 ft wave should increase by 10%. This is in reason- 

 able agreement with the results in Figs, 23 and 24. Since the wave 

 length increases, it is expected that the wave heights will decrease 

 in order to maintain wave energy balance, 



Phillips [ 1969] accounts for this wave energy balance in 

 treating the case of long-crested waves running into a current in 

 which the surface velocity varies only longitudinally. His results , 

 plotted on Fig. 3.6 of his work, show that for the present conditions 

 a wave height attenuation of approximately 15% is expected for the 

 2 ft wave and approximately 8% for the 6 ft wave. This is consider- 

 ably less than the experimentally attained values of 80% to 90% 

 attenuation previously discussed. Thus, the refraction procedure 

 alone does not account for the results observed in the vicinity of 

 the wake centerline. It will later be shown that diffraction effects 

 applied to this length of wave crest can indeed result in large local 

 attenuations of wave height. 



Crest Length Between 1 ft and 3.5 ft. The orthogonals for 

 this crest length diverge rapidly in a direction which causes the 

 local wave crest to be redirected out of the wake area into the still 

 water. This finite crest length advances in a constant direction 

 relative to axis system at a speed and wave length equal to the inci- 

 dent wave. It then crosses the undeformed incident crest line at a 

 distance 5 ft from the wake centerline. As a first order effect, it 

 can be assumed that the wave heights decrease as the square root 

 of the ratio of the initial wave ray separation to the separation at 

 any subsequent position of the local crest. For the 2 ft long wave at 

 a position 12 ft aft of the grid (28 ft into the wake), the wave height 

 (Fig. 25) indicates that the average wave height for this local crest 

 is approximately 30% of the incident wave height. 



The deflection of this local wave crest length into the area of 

 the incident wave could account for the irregularity observed in the 

 wave height time histories at fixed points between 7 and 12 ft from 

 the wake centerline. 



Crest Length Between 3. 5 and 5 ft. For this length of wave 

 crest. It was seen that adjacent orthogonals converge and finally 

 cross, resulting in a caustic curve [ Plerson 1951] . On the basis of 

 simple theory, the wave became Infinitely high on the caustic which, 

 of course, is not the case. At present, quantitative analysis of the 

 wave height at and beyond caustics must still be developed for the 

 case where variable currents produce wave distortions. 



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