Gravity Waves and Finite Turbulent Flow Fields 



Superposition of Elemental Results 



The results of the refraction and diffraction results have been 

 superposed in order to provide an analytical estimate of the wave 

 height distribution along a crest line as it progresses through the 

 grid -wake. The computations were carried out for a transverse 

 section 12 ft aft of the grid for a grid wake 40 ft long. These are 

 identical to the refraction calculations previously described. The 

 following procedure is used in this superposition of elemental results: 



a) The initial crest length between the grid centerline and 

 1.5 ft outboard is diffracted by the breakwater gap technique as 

 plotted on Figs. 29 and 30. 



b) The initial crest length 5 ft outboard of the grid centerline 

 is diffracted by the technique of wave passage past a semi- infinite 

 barrier as plotted on Figs. 29 and 30. 



c) The segnnent of wave length initially between 1 . 5 f t and 

 3.5 ft is refracted by the orthogonal method and the wave heights 

 are obtained by Eq, (17). The orientation (or phase) of this wave 

 crest segment to the transverse section 12 ft aft of the grid is ob- 

 tained from the computed refraction diagrams such as given in 

 Figs. 23 and 24, The resultant wave heights for this segment are 

 plotted on Figs. 29 and 30. 



d) The segment of the wave crest between 3.5 ft and 5.0 ft 

 outboard has been neglected in this simiplified procedure since it 

 develops into a caustic line. 



e) The results of (a), (b) , (c) and (d) are superposed to ob- 

 tain the final wave height distribution. 



The results of the above procedure are presented in Figs. 29 

 and 30 for the 6 ft and 2 ft wave respectively and compared with the 

 experimental data. It is seen that agreement between computed and 

 measured results is qualitatively acceptable for the 2 ft wave length 

 and is good for the 6 ft wave length. It appears then that the physical 

 processes responsible for the observed deformation of waves pro- 

 gressing into a finite current field have been established. It is 

 strongly recommended that further studies of this problem be di- 

 rected towards the development of a unified, rigorous theory which 

 can be used to quantify this interesting wave-current interaction 

 phenomenon. 



One -Dimensional Results 



No similar detailed analysis has been made of the one-dimen- 

 sional results previously described. It does appear, however, that 

 the transverse gradient in the longitudinal wake velocity existing 

 at the outer edges produces a local wave refraction. This refracted 

 wave segment must then be reflected from the tank walls and prog- 

 ress across the wake, running into similarly refracted wave seg- 

 ments from the opposite wall. These continuously crossing wave 



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