The two functions f..(y) and f 2 (y) can ^ e determined independently 

 and indeed in some cases they were so. However, the device used in the 

 measurement of the velocity amplitude at some distance from the oscillat- 

 ing wall was simultaneously measuring the phase angle of the velocity at 

 this level relative to the wall. In other words the same record could be 

 used to determine both fi(y) and f2<y). This instrument is essentially a 

 modified pitot tube shown diagrammatically in Figure 11. The basic prin- 

 ciple of its operation is that the differential pressure at the two tips 

 causes the diaphragm to deflect; in doing so it modulates a high-frequency 

 signal by altering the capacitance of a Rutishauser pressure pickup. The 

 modulated signal is rectified by a discriminator into a voltage which is 

 proportional to the differential pressure at the tips of the instrument 

 and consequently a function of the incidental velocity. Therefore the 

 excursions of the needle of an oscillograph which is activated by this 

 voltage will give a measure of the local velocity. The instrument was 

 calibrated dynamically by oscillating it with a prescribed simple har- 

 monic motion in water at rest and correlating the amplitude of the needle 

 excursions with the amplitude of the velocity of oscillation. 



The tests were made on a smooth plate of a high-gloss finish as well 

 as on rough plates with two and three-dimensional roughness fixed on them. 

 The vertical distances recorded during the tests were measured from the 

 crest of the roughness elements. These values were subsequently corrected 

 to account for the distance between this level and the theoretical bed. 

 The correction in all cases was equal to 0.2D. The values of the function 

 f^Cy) resulting from the analysis of the experimental records are listed 

 on Tables I, II, and III. The graphical representation of the results is 

 shown in Figures 2, 3 and 4. The exponential dependence of the velocity 

 on the distance seems to describe the data better than any other simple 

 relationship. A small number of points only, obtained in some character- 

 istic runs, were plotted in order to make the graphs readable. However, 

 for the selection of the most representative relationship the complete 

 data was used. 



The experiments with smooth wall indicated that the proper character- 

 istic length for the normalization of the argument of f].(y) should be the 

 amplitude of the oscillation. In a previous report (Kalkanis 1957), it 

 was suggested that the parameter - should be used for this purpose in 

 analogy to the laminar case. The original work on which this suggestion 

 was based consisted of three runs only reported here as runs 111, 112, 

 113, a very inadequate number. As part of the present investigation, 

 which has as its main objective the study of the rough case, four more 

 runs were made with a smooth wall (114, 115, 116, 117) in order to test 

 the reliability of the instrument. The second set of measurements was 

 made more than a year after the first and considering the fact that the 

 equipment in the meantime underwent certain modifications, the agreement 

 of the results between the two sets was remarkable. In any case the 

 adoption of the amplitude as the characteristic length was strongly sup- 

 ported by the experiments with a rough wall performed more recently. 



B-2 



