Gravity Waves and Finite Turbulent Flow Fields 



mechanism of wave height deformation was due to a redistribution of 

 energy along a crest line rather than to dissipative effects. In this 

 regard, the results of Phillips [ 1959] were examined to determine 

 possible convective distortions of the wave front resulting froni 

 scattering interference between wave and turbulence field. It was 

 found that the observed results could not be accounted for by the 

 turbulent scattering. 



If, in the present studies then, turbulence is assumed to have 

 had a minor effect on wave deformation, it remained to examine the 

 possible interference between the mean flow gradient in the wake 

 and the incident wave. The velocity profiles for the longitudinal 

 mean flow aft of the grids are plotted in Figs. 2 and 4 for the one- 

 and two-dimensional studies, respectively. In both cases there is 

 a relatively sharp velocity gradient between a region of constant 

 wake velocity to zero velocity at the tank wall for the one-dimensional 

 case and to zero velocity in the still water adjacent to the finite grid 

 wake in the two-dimensional case. By application and superposition 

 of elemental theories of wave refraction, defraction and interference, 

 It was found that the observed results could be, at least, qualitatively 

 reproduced and physical mechanisms described to account for the 

 large wave deformations observed. 



A detailed analysis is first made of the two-dimensional tests 

 since these results were free of possible wall reflection effects 

 such as existed in the one-dimensional studies. Further, the 2-D 

 analysis will provide the foundation for explaining the results of the 

 1-D studies which proved to be the more complex case. 



Wave Interaction with Finite Velocity Field 



Two-Dimensional Results . The longitudinal mean flow in the 

 finite wake area aft of the grid is plotted in Fig. 4 and is quantified 

 by an empirical formulation, Eq. (2). 



J 1 )' 



V r nr Vl67 + 0.06ZX/ ^ 



-^ = [ 0.45 - 0.00745x][e ] 



V 



where 



Vw = mean value of longitudinal velocity in wake 

 V = grid velocity 

 X = distance aft of grid, ft 

 y = distance normal to grid centerline, ft 



In the present analysis, regular waves in still deep water en- 

 counter a variable current field V^(x,y) moving in the same direc- 

 tion as the waves. The waves are initially refracted by the current 

 to an extent dependent upon the incident wave length, strength of 

 current, and the velocity gradients in the wake. The orientation 



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