Turbulence in tlie Ocean. 581 



over the sea. Accidental error in the determination of the 

 wind or the current must also be a very important factor; 

 for in the calculation of k the wind velocity is raised to the 

 fourth power and the current velocity to the second, so that 

 any such error, even if itself small, becomes greatly magnified 

 in importance. Local conditions, such as cyclonic dis- 

 turbance and the temperature lapse-rate, affect the turbulence 

 in the air and perhaps indirectly that in the water. Vari- 

 ations in the vertical distribution of salinity in the water 

 near the surface may also affect the stability of the mass- 

 distribution, and hence the turbulence ; though in mid- 

 ocean mixing is probably sufficiently thorough in the upper 

 layers for such variations to be insignificant. It is on the 

 whole, therefore, not surprising that considerable variations 

 in the calculated turbulence occur. 



The relation of the surface current to the wind has 

 previously been considered by Waltrid Ekman *, who ob- 

 tained the result here given that they are mutually inclined 

 at 45°, and showed that in the main Atlantic current in 

 latitude 10° N". the velocity is reversed at a depth corre- 

 sponding to a turbulence coefficient of 29'5 Grti. 2 /sec, about 

 i 1 ^ of the value here found for a similar place, though w r ell 

 within the limits of real variation. He did not apparently 

 determine k for comparison from the observed velocities 

 of the wind and current, as has been done here; the possi- 

 bility of this comparison is largely due to G. I. Taylor's 

 recent w 7 ork on the skin friction of the wind on the surface 

 of the earth. 



It remains to be seen whether any other evidence indicates 

 that such turbulence as is here calculated is possible. 

 Direct observations of eddy currents in mid-©cean are 

 lacking, but indirect evidence may be obtained from two 

 other sources. Taylor showed that the value of k at any 

 point is the average of the product of the vertical velocity 

 in the eddies and the range through which they move 

 vertically. Now near the surface the vertical range is 

 presumably not very different from the wave-height Ji ; while 

 the vertical eddy velocity will not be greater than the 

 maximum vertical velocity of the water in a w T ave, and is 

 probably very much less, since wave-motion in mid ocean 

 is fairly regular in character, and the eddy motion corre- 

 sponds only to the irregular part. Now D. W. Johnson 

 mentions as a typical mid-Atlantic wave")", one with wave- 

 length 400 feet, height 15 feet, wave-velocity 45 ft. /sec., 



* Arkivfor Matematik, #c, Akad. Stockholm, Bd. 2, m\ 11 (1905). 



f • Shore Processes and Shore-line Development,' pp. 25 & .32 (1919). 



