THEORY OF SEAKEEPING 



0.4 



0.3 



o 0.2 

 to 



0.1 



• Soap 

 o No Soap 

 + Raining 



° o ^°'^ 



OO O rrpn 



_J I L 



10 

 V 10 000 m/s 



12 



Fig. 9 Original data for setup as a function of wind speed at 10 m elevation. Smooth curves were drawn by 

 inspection. Each point is a 20-min time average for both wind and setup (from Van Dorn, 1953) 



Table 3 Results of Wind-Flume Measurements of Johnson 

 and Rice (1952) 



c* = c, + c. 



0.0282 

 0330 

 0.0372 

 0202 

 0.0190 



° .\t the end of the fetch. 



Only the mean drag coefficients C^* = Cj + C\ over the 

 flume length were determined. These and the X //- 

 value.s of the waves at about 73 of the a\'ailable fetch 

 are listed in Table 3. 



The drag coefficients are exceptionally high and cor- 

 respond to the extreme mean steepness of the waves. 

 It should be noted that while the included angle of 120 

 deg at wa\'e crests, used in Motzf eld's wave model Xo. 4 

 (with C'i* = 0.0222) is the minimum for a stable wave, in 

 the breaking of a wind-driven wa\'e sharper angles and, 

 more significantly, steeper slopes of the lee faces may 

 occur instantaneously causing a further increase of air 

 drag. Much sharper crests with the included angle down 

 to 90 deg may also occur (Taylor, 1953) if a standing 

 waxc system is present. 



2.5 Observations of Keuligan and Van Dorn. The 

 observations of Keuligan (1951) and Van Dorn (1953) on 

 the water surface inclination in a wind recjuire special 

 discussion in view of (i) the form of analysis u.sed, and (ii) 

 the alternate use of natural water surface and surface 

 covered with a detergent. The Keuligan experiments 



were made in a wind flume, and Van Dorn's observations 

 in a large outdoor pool. In both cases the primary ob- 

 jecti\es were to determine the water-surface drag and 

 the surface current generated by it. The wave proper- 

 ties were not measured ; ne\'ertheless the type of analysis 

 used permits certain intere.sting deductions to be made in 

 regard to waves. The method of analysis originated 

 with Keuligan, but it will be used here in connection with 

 the data of \i\\\ Dorn. 



A'an Dorn measured the difference of water level at 

 two points spaced 220 m (722 ft) apart in a pool about 

 790 ft long. The depth of the pool over most of its 

 length was from 2 to 2.4 m, but owing to the sloping 

 bottom at the ends the mean effective depth was 1.85 m 

 (6.07 ft). The wind velocity was measured at heights of 

 25 cm, 1 m and 10 m (0.8, 2.3 and 33 ft) above the water 

 surface. Wind \-elocit\' always decreases with decreasing 

 height above the surface becau.se of the loss of momen- 

 tum caused by the drag force. The setup, i.e., the dif- 

 ference in the mean water le\'el at the two ends of the 

 measured stretch of 722 ft, is shown in Fig. 9 plotted 

 against the square of the wind \'elocity measured at the 

 height of 10 m. Fig. 10 .shows similar plots for the wind 

 A-elocity measured at the heights of 1 m and 25 cm. 

 It was found that by spreading a detergent on the water 

 surface the formation of waves is prevented, and the 

 setup can then be taken as caused entirely by the smooth 

 siu'face skin friction. This is essentially proportional to 

 the square of the wind velocity, and the plot is a straight 

 line. Using the symbol JJ for the wind velocity meas- 

 ured at a certain small elevation, the setup >S' is expressed 

 therefore as 



