will be very closely approximated by each other. Following is a brief 

 description of the apparatus and the procedure used in Li's study. 



A glass walled flume 12 feet long, 1 foot wide and 3 feet high was 

 used. About 4 inches above the bottom of the flume a plate, 78" x 11-1/2" 

 was mounted on a series of rollers so that it was free to move in a plane 

 parallel to the bottom. Through a series of steel cables and levers the 

 plate was connected to a 1/2-HP AC motor which was mounted external of the 

 flume. By means of an eccentric arm the rotating motion of the motor was 

 converted into a reciprocating one which very nearly approximated simple 

 harmonic motion. The motor was equipped with a speed reducer which allowed 

 the period of the oscillation to vary from 1 to 150 cpm. By varying the 

 eccentricity of the arm the amplitude of the linear motion of the plate 

 could be varied from 2 to 18 inches. The amplitude and the frequency of 

 oscillation in the experiments were made to vary within ranges so as to 

 simulate prototype conditions associated with waves of 0.4 to 60 seconds 

 period and 0.5 to 10 feet height in water about 60 feet deep. 



During the testing the water depth was kept at about 2 feet. The 

 shortness of the flume and comparatively shallow depth of water tended to 

 cause the formation of a standing wave. In order to reduce this wave to 

 a minimum a series of vertical baffles together with a set of heavy floats 

 were used. 



Three series. of tests were made in this flume. The first, designated 

 as the smooth series, was carried out with the surface of the plate waxed. 

 The second, designated as the two-dimensional rough series, was carried 

 out with the use of half-round wooden strips or steel rods as roughness. 

 The third, designated as the three-dimensional rough series, was carried 

 out with the use of sand or gravel as a roughness. In all cases each 

 individual run was carried out with a uniform roughness. That is to say, 

 all roughness elements for any one run were of the same size. 



The procedure was to fix a particular roughness to the plate, choose 

 an amplitude of oscillation, and then increase gradually the frequency. 

 The type of the flow regime was determined visually by dropping potassium 

 permanganate crystals from the water surface to the bottom. As the crystals 

 dropped to the bottom they left a trail of dye. Once at the bottom they 

 would oscillate with the motion of the platform. Continuing to dissolve the 

 crystals would leave a clear back and forth trail as long as the flow was 

 stable. The flow was defined as unstable when the trail left by the crystals 

 would break down and mix with layers above. The recorded frequencies and 

 amplitudes at the critical limit together with the size of roughness and the 

 water viscosity were combined to form a critical Reynolds number. The re- 

 sults obtained in these tests as supplemented by Manohar may be summarized 

 as follows: 



According to its performance the boundary can be classified as 

 hydraulically smooth, as rough and as a transition from smooth to rough. 



A-2 



