Gravity Waves and Finite Turbulent Flow Fields 



aft of the grid. Similar sets of plots are given In Figs. 8 and 9 for 

 the 4 ft long wave and In Figs. 10 and 11 for the 8 ft long wave. 



The Irregular, oscillatory behavior of the wave height envelope 

 Is apparent In all plots and decreases as the wave length Increases. 

 Further, the average wave heights at 13.25 and 16.5 ft aft of the 

 grid continuously decreases with Increasing time of grid travel 

 (which corresponds to an Increasing length of turbulent wake through 

 which the wave travels). 



Repeat runs for otherwise Identical test conditions did not 

 produce Identical time histories of wave height envelopes. This can 

 be seen by comparing the time histories for a point 13.25 ft aft of 

 the grid as shown In Figs. 6 and 7; 8 and 9; and 10 and 11. The time 

 histories are much more nearly alike for the 8 ft long wave than for 

 the 3 ft long wave. 



Crest Line Deformation: An examination of the phase relation 

 (9) between the wave crest at a point 13.5 ft aft of and on the grid 

 centerllne and the wave crest at a point 4 ft transverse to this point 

 Indicates the first clear regularity to these one-dlmenslonal test 

 results. For the case of the 4 ft long wave (Fig. 6), it Is seen that 

 phase angle Is zero, Implying a crest line parallel to the grid for 

 the first 20 seconds (20 ft of wake development) of grid travel. As 

 time Increases, the phase angle Increases so that crest at the center- 

 llne precedes the wave crest 4 ft off the centerllne. The phase angle 

 Increases nearly linearly with increasing time. For the 4 ft long 

 wave (Fig. 8), a similar linear phase shift occurs except that the 

 rate of phase shift is now somewhat slower. The phase shift for the 

 8 ft long test wave (Fig. 10) has a maximum value of only 45°. For 

 this long wave, the centerllne crest lags the outboard crest. A com- 

 parison of the wave amplitude shows nearly similar values at both 

 wave probes when the phase Is 0° or 360° and maximum differences 

 when the phase angle Is 180°. 



Apparent Wave Length : The apparent wave length along the 

 wake centerllne was determined from an analysis of the time histories 

 of the wave amplitudes at the two wave probes which were 3. 25 ft 

 apart (probes at distances of 13.25 ft and 16.50 ft aft of the grid). 

 The apparent wave length generally Increases with Increasing time 

 of grid travel. The 3 ft long wave (Fig. 7) attains a value of approxi- 

 mately 4 ft eifter 50 seconds of grid travel and then decreases to a 

 value of 3. 5 ft. The 4 ft test wave (Fig. 9) attains a value of nearly 

 6.5 ft after 100 seconds of grid travel while the 8 ft wave (Fig. 11) 

 attains a value of approximately 1 1 f t after 90 seconds of travel. 

 The wave lengthening is expected because of the longitudinal mean 

 wake flow in the direction of wave celerity. 



Effect of Grid Velocity: Figures 12 and 13 present the wave 

 height envelopes for the 3 ft and 4 ft long waves when the grid speed 



409 



