422 General Theory of Ocean Currents in a Homogeneous Sea 



A summary of all values of the resistance coefficient shows that the stress can be 

 represented by a formula of the form 



where n may differ somewhat from 2 or /c itself is a function of u-. For wind speeds of 

 up to 10 m/sec the values of k are very scattered and it is not easy to decide whether 

 this scattering is due to errors in measurement or due to effects which have not been 

 taken into account (such as the vertical stability of the air mass over the water or 

 deviations from the steady state or stratification of the water and others). The dis- 

 continuity imagined by Munk at 6-8 m/sec has not yet been confirmed and no definitive 

 relationship between the stress and the wind can be obtained at the present time, 



Frictional depth and frictional coefficient. According to equations (XIII.26) the 

 frictional depth depends on the wind stress T and on the surface velocity V^. For 

 T a dependence of the form (XIII.48) can be taken with an average coefficient of 

 2-9 X 10-3 p' ^ 3.5 X io-« ; Fo is related to the wind speed w by (XIII.42) (A approx. 

 0-0114). Tand Vq can be eliminated in this way from the formula 



7tT 



\/2' Vq pco sinrf) 



giving 



7-6hr 

 D = ,, ■ ,, , (XIir,50) 



V(sm <^) ' 



where \v is given in m/sec and D in m. If Vq is retained, a very simple formula results 

 which was already derived by Ekman 



D = 670 Fo (XIII.51) 



which is very useful for the estimation of D. This states that the frictional depth is 

 approximately equal to the distance travelled by the surface water in a pure drift 

 current in about 600 sec or 10 min. It should be noted that equation (XIII.51) does not 

 involve the latitude. Thorade (1914) derived the equation 



\/(sm 4>) 

 for wind speeds less than Beaufort 3 (about 6 m/sec). All these formulae are of course 

 only approximations, since at the present time systematic current measurements 

 from which accurate values could be derived are not available. 



Observations on the thickness of drift currents are usually in general agreement 

 concerning magnitude with the values given by formula (XIII. 50). The oceanic struc- 

 ture in the region of the North and South Equatorial Currents in the Atlantic Ocean 

 indicates that the wind current here has a depth of about 150 to, at the most, 200 m and 

 and thus that the frictional depth in these latitudes only barely reaches these values. 

 Towards higher latitudes it decreases. Brennecke (1921) found a frictional depth of 

 about 50 m during the ice drift of the "Deutschland" in the Weddell Sea and Sverdrup 

 (1928) has shown from Brcnnecke's values that there is an increase with increasing 

 wind speed as is shown by the following values : 



Drift velocity (cm/sec) : 5.52 9.81 14.85 24.60 



Frictional depth £> (m) : 45.6 56.2 (39.1) 69.1. 



