Gravity Waves and Finite Turbulent Flow Fields 



In applying these diffraction results to the present study, it 

 has been assumed that the refraction phenomenon previously dis- 

 cussed divides the wave crest into several segments which are 

 separately diffracted as they pass through the grid wake. Specifi- 

 cally, the segment of the wave crest just aft of the grid is assumed 

 to behave as though it was a section of the wave which passed through 

 a breakwater gap equal to the grid width. The justification for this 

 analogy follows from the refraction results given on Figs. 25 and 

 26 where it is shown that, for a distance of approximately one-half 

 the grid width on either side of the grid centerllne, the wave height 

 In the wave cannot be maintained at a constant height since just out- 

 board of this segment the refraction analysis yields a small wave 

 height. Thus, It appears reasonable to assume that diffraction 

 effects win be developed and that this centerllne segment of the 

 wave will reduce In amplitude and spread transversely along the 

 crest as It proceeds Into the grid wake. The diffraction coefficients 

 win be taken to be those corresponding to a wave at a breakwater 

 gap as given on pages 188-189 of Wlegel. 



One other portion of the Incident wave which appears to be 

 modified by diffraction is that segment of the incident wave which is 

 located 5 ft outboard of the grid centerllne. From the wave refraction 

 diagrams on Figs. 23 and 24, It Is seen that wave rays and crest 

 lines outboard of 5 ft are not Influenced by the grid wake. Simple 

 refraction considerations then result In a wave of constant amplitude 

 along this length of the wave front. Again, this constant wave height 

 cannot be maintained and a defraction process develops which causes 

 a lateral spreading of the wave crest Into the wake area with an 

 attendant reduction In wave amplitude. This lateral flow of wave 

 energy can be compared to the case of water passage past a seml- 

 Inflnlte breakwater, the solution for which Is plotted on page 183 of 

 Wlegel, Typical diffraction diagrams for the case of breakwater 

 gap and seml-lnflnlte barrier are given In Figs, 27 and 28 of this 

 report. 



The computed results for these two diffraction processes 

 are plotted In Figs, 29 and 30 for the 6 ft and 2 ft wave lengths 

 respectively. Again, the computations are made for transverse 

 section approximately 28 ft Into the grid wake. For the 6 ft wave, 

 the ratio of effective "gap width" to wave length Is 3/6 = 0. 50; for 

 the 2 ft wave, the ratio is 3/2 = 1.50. It Is seen that the Initial 

 constant height wave segment between the grid centerllne and 1 . 5 f t 

 outboard Is diffracted to approximately 0.30 of this height and Is 

 spread laterally to a distance nearly 12 ft from the grid centerllne. 

 Considering the diffraction of the entire wave segment Initially 5 ft 

 outboard of the grid centerllne. It Is seen that this section Is spread 

 Inboard to the grid centerllne with a corresponding reduction In 

 wave height at approximately 0.30 of Its Initial height. It Is seen 

 that, for this wave segment, the attenuation of wave height as it 

 spreads to the centerllne Is much more rapid for the 2 ft wave than 

 for the 6 ft wave. 



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