60 DEACON AND WEBB [CHAP. 3 



A large number of double-theodolite pilot-balloon results enabled them to 

 compute the air flow across the isobars in the lowest few hundred metres. This, 

 together with the pressure gradient, indicated a drag coefficient of around 

 0.0015 for wind speeds averaging 5 m/sec. 



C. Surface-Tilt Observations 



The wind-induced surface tilt of lakes and arms of the sea provides another 

 method of assessing the stress of the wind on the water. With the water in 

 equilibrium under the action of a uniform and steady wind, the relationship 

 found by Ekman for a body of water of uniform depth d and density p^ is 



T + Tb = ipwgd, (21) 



where t^ is the stress between water and lake bottom caused by the return 

 current and i the slope of the water surface. Measurements of t^ by Van Dorn 

 (1953) for a pond and of return current velocities in small-scale experiments by 

 Francis (1951) show that t^ may be neglected in comparison with the surfaee 

 stress. Difficulties with this method arise from tidal and seiche movements of 

 the whole body of water tending to mask the slope caused by the drag, the 

 rarity of a steady state of equilibrium between wind and waves and surface 

 slope, and departures from homogeneity of the water. ^ The last consideration 

 will be most important in light winds when the stirring action of the wind is 

 small. For a surface stress of 0.5 dyne cm~2^ as would be expected for a wind 

 speed of 5 m/sec, the surface slope on a body of water 20 m deep is only 1 cm in 

 40 km. An equal effect on the slope would be produced by the density dif- 

 ferences associated with a horizontal temperature gradient of 6°C per 40 km 

 (for sea temperature around 10°C). Temperature differences amounting to an 

 appreciable fraction of this magnitude are to be expected in light winds and, 

 as no allowance has been made for them hitherto in applications of the slope 

 method, only the results for the stronger winds are likely to have an acceptable 

 accuracy. 



For these reasons only sea-slope results at wind speeds of 10 m/sec or more 

 are shown in Fig. 7. The results for the Gulf of Bothnia are those of Palmen 

 (1932) and Palmen and Laurila (1938) for mean water depths of from 50 to 

 70 m. The results of Keulegan (1952) and Hellstrom (1953) for Lake Erie and 

 for Ringkobing Fiord respectively have been corrected to agree with the 

 assumption of Tft = in equation (21), as was also done by Francis (1954) in a 

 review of the wind-stress problem. 



Darbyshire and Darbyshire (1955), in an analysis of results for Lough Neagh, 

 have found some evidence for a rising drag coefficient with fetch. For neutral 

 stability and 30 km fetch their value of cio = 0.0021 is much the same as those 

 shown in Fig. 7. 



In all the work by the tilt method, the wind observations have been rather 

 unsatisfactory, as anemometers over the water have not been available. Re- 



1 Other sources of error have been pointed out by Stewart (1961a). 



