180 



[chap. 4 



the effect of thermal stratification upon wind-profiles, which depends upon 

 the Richardson number, or the ratio of static stability to wind speed squared. 

 Under unstable conditions (lapse rate about 150% dry adiabatic for normal 

 winds) the squares in Fig. 6 show that CD = rofpUa'^ is considerably larger than 

 in neutral situations ; to use the Cd of the solid line would underestimate to by 

 50% or more. Under extremely stable conditions (lapse rates about one-half 

 adiabatic or less with normal winds), the method breaks down altogether. 

 Sample wind-profiles in Fig. 37, however, suggest that when the stratification 

 approaches isothermal (the stable profile of Fig. 37) use of c^ from the solid 

 line of Fig. 6 in (17) may overestimate to by a factor of two or more. Fortu- 

 nately, extremely stable stratification and high wind speeds are not commonly 

 associated over the open oceans. 



08 9 



Relative Wind Velocity 



Fig. 37. Observed wind-speed profiles as functions of height on logarithmic scale in lowest 

 15 m above the sea. (After Deacon, Sheppard and Webb, 1956, Fig. 4. By courtesy 

 of the Journal.) 



Abscissa is wind speed in fraction of speed at "anemometer level". 



Secondly, the directed nature of t creates additional difficulties. It should 

 be recalled that shearing stress in a fiuid is in general a symmetric tensor. The 

 TQ in (17) denotes a vector which has the value at the air-sea interface of tsz, 

 or the vertical transport of horizontal momentum [s axis along the wind), that 

 is to say the exchange of this component of horizontal momentum across the 

 boundary. Therefore, we would have problems in constructing a mean stress 

 map for the oceans even if (17) were entirely vahd and the dependence of Cd 

 upon wind speed firmly known. Strictly speaking, we would need a dense 

 distribution of oceanic stations reporting accurate winds at least several times 

 daily. For each, two rectangular components of to would be computed from 

 each observation and averaged for the period desired, from which the magnitude 

 and direction of the resultant stress would be obtained vectorially. It would 

 not in general be in the same direction as the resultant wind and could easily 

 be an order of magnitude larger than a to derived from the resultant wind 

 speed, which may in fact be near zero if the directional wind steadiness is low. 

 The climatic wind data over the oceans commonly at our disposal (for example 

 the U.S. Hydrographic Office Pilot Charts) usually consist of wind roses, like 

 those of Fig. 44, showing the average distribution over a given time and 

 region of wind from eight or sixteen compass directions. The length of the 



