Turbulence in the Ocean. 585 



atmosphere may, however, affect the movement of the ocean 

 in another way. If the atmospheric pressure at a place A is 

 greater than that at B, it will create a horizontal force 

 tending to move the water from A towards B. When such 

 a pressure-distribution is steady, the horizontal force steers 

 the water so as to keep it moving along the isobars. Thus 

 a geostrophic distribution of velocity is maintained in the 

 water, and extends to the bottom. This velocity is not,, 

 however, great ; for it is maintained by the same pressure 

 differences as maintain the winds, and therefore, by the 

 geostrophic condition 



2copv = 'dp/'dv, 



the velocities in the air and in the water are inversely pro- 

 portional to the densities. Thus the current velocity is 

 about g, 1 ,,, of the wind velocity, and is of the order of 

 1 cm./sec. These currents are therefore small. Temperature 

 differences, again, produce little effect at great depths ; for 

 the differences in. density produced by them are smalL 

 Salinity currents are probably more important, though they 

 are not usually noticeable except in restricted areas. 



Another type of: current that extends to the bottom of the 

 ocean is the periodic tidal current, and the friction caused 

 by it can be estimated. The two components of horizontal 

 velocity u and r, except near the bottom, satisfy differential 

 equations of the form 



_-2< BW =^(r-r), 



where f is the elevation of the sea-level above its mean 

 position and \ the height of the equilibrium tide. For 

 motions periodic in 12 hours, u and v must therefore be of 

 order gQ<*>a, where a is the radius of the earth. The height 

 of the lunar equilibrium tide is ?ra 2 m/M#, where m is the 

 mass of the moon, n its mean motion, and M the mass of 

 the earth. Thus in all the amplitude of f is 37 cm., and 



m = 0(1 cm./sec). 



The rate of dissipation of energy by skin friction is 

 0*002 u 6 per sq. cm., or 0*002 erg per sq. cm. per sec. Over 

 the whole ocean this gives a dissipation of the order of 

 10 1C ergs per second. 



Phil. Mag. S. 6. Vol. 39. No. 233. May 1920. 2 Q 



