20 



THEORY OF SEAKEEPING 



0,04 



o o^o 



^^ 



J I I I L 



0.0 2 _ 



m/SGc' 



Fig. 14 Mean-square, wave-slope components and their 

 sum as functions of wind speed. Open circles and solid 

 lines for clean sea surface, solid dots and dotted lines for 

 detergent covered (slick) surface (from Cox and Munk, 

 1954) 



and the wind sea, but such a distinction is missing in the 

 work under consideration. '^ 



A ratio of squared slopes aj/a,- of aloout 2.5, indicat- 

 ing a directional spread of wa\'es of about 130 deg, ap- 

 plies essentially to the small waves bj' which the larger 

 observed wa\''es are overlaid. Spreading of an oil film 

 eliminated these small wa^^es, leaving the larger waves 

 unaffected. It is surprising to find that the ratio 

 (7„-/o-/ in this case is reduced to nearly unity, indicating 

 an increased degree of short-crestedness. A possible 

 explanation is that several swells of different directions 

 (independent of the wind) were present, while the small 

 and steep wa\-es were caused by the local wind. 



Examination of Table 5 and of Fig. 14 shows clearly 

 that steep wave slopes are connected with the small 

 waves by which the larger observed waves are o^'erlaid. 

 The recoi-dcd slopes are drastically reduced when these 

 small wa\'es are eliminated bj' the oil film. The mean 

 square values of slopes a- are seen to have little relation- 

 ship to the observed wa\'e dimensions, since these small 

 waves are neglected in the definition of the "significant 

 wave" as the mean of the l^ highest waves. On the 

 other hand o-- is seen to depend directly on the wind 

 strength. 



The conclusion that a- is proportional to the wind 

 \-elocity, as shown by Fig. 14 and as stated by Cox and 

 ]\Iunk (19o4a) may, however, be misleading. This re- 

 lationship is shown to exist within the scope of observa- 

 tions, but the wave slopes cannot increase indefinitely, 

 and the statistical observations should not be extrap- 

 olated without regard to the physical properties of 

 waves. 



4.4 Horizontal Drag Force Exerted by Wind — 'A'. H. 

 Munk's Hypothesis. The objective of this wcii'k is stated 

 in the folh.nving quotation from Munk (19o5a): "The 

 problem of wind stress on water plays an essential part 

 in studies of ocean circulation and storm tides, and of the 

 momentum balance of atmospheric circulation. The 

 present work is an attempt to connect results from recent 

 experimental determinations of wind stress with the re- 

 sults from measurements of wave statistics . . . ." 



The starting point is the expression by Jeffreys (1925) 

 for the pressure exerted by wind of ^'elocity U nn an ele- 

 ment of the wave surface 



P 



sp'(U - c)- dri/dx 



(37) 



where s is a coefficient called by .Jeffreys "sheltering co- 

 efficient" and assumed to be constant. The horizontal 

 component of this pressure (i.e., drag force or wind 

 stress) is 



sp' < (U - c)- (dv/dxY- > 



(38) 



the fetcli or the wind duration were not large enough to 

 give a fully developed sea. The latter case indicates 

 that the observed significant waves were to a large ex- 

 tent due to the presence of a swell and not due to the 

 local wind. In any study pertaining to waves it is very 

 important to make a clear distinction between the swell 



where the sj-mbol <> indicates that the mean value is 

 taken. 



The foregoing formulas were written for a simple har- 

 monic wave, the celerity c of which is known. When the 



" A more complete description of the environmental conditions 

 of these observations was published by Uarbyshire (1956a). 



