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LV. On Turbulence in the Ocean. By Harold Jeffreys, 

 M.A., D.Sc, Fellow of St. Johns College, Cambridge *. 



I. The Cause of Ocean Currents. 



ff^HE main currents in the ocean were formerly attributed 

 JL to the effects of expansion and contraction caused by 

 differences in temperature between various parts of the 

 water. In a heated area the surface would tend to be 

 raised ; and an outward current would therefore commence 

 at the surface, compensated by an inward return current 

 below. This explanation has, however, ceased to be regarded 

 as adequate. In the first place, the differences in temperature 

 are so small in comparison with their great horizontal extent 

 as to be unable to produce the observed velocity of the 

 surface water, on account of the low coefficient of expansion. 

 In the second place, the heated areas of the sea would corre- 

 spond approximately with those of the air above. Now heat 

 tends to produce an area of high pressure at the top of a 

 medium and one of low pressure at the bottom ; thus, just 

 below the surface of the water and on the same equipotential 

 surface, we should have a high pressure in the heated area. 

 In the air just above the pressure would be low. The hori- 

 zontal forces on the air and the water would therefore 

 always be in opposite directions, and hence the same would 

 be true of the velocities, even when the rotation of the earth 

 is taken into account. Actually this is not even approxi- 

 mately true ; the ocean current and the trade wind agree 

 roughly in direction. 



Accordingly the general circulation of the ocean has come 

 to be regarded as caused directly by the trade w T inds, the 

 surface water being driven along by the wind above it. 

 Here again, however, there is a difficulty with regard to the 

 direction of the current. The ocean currents vary so slowly 

 with time that they can be regarded as phenomena of steady 

 motion, and on a rotating globe a steady velocity is always 

 perpendicular to the controlling force, in this case the skin 

 friction of the wind on the surface of the water. Thus 

 apparently the current driven by a trade wind should be 

 perpendicular to the wind. The problem is however com- 

 plicated by the existence of turbulence in the ocean, and a 

 treatment based on the theory of eddy motion is therefore 

 desirable. 



Let u and v be the components of the horizontal velocity 



* Communicated by the Author. 



