g is the gravitational force; p , the fluid density; z , the height 

 of the layer considered; U , the velocity of mean, or non-turbulent, 

 flow. The implication of this equation is that a horizontal shearing 



motion, -^ , generates turbulent energy at a rate which must be larger 



oz 



than some critical rate at which energy is lost by mixing at the higher 

 gravitational potential near the top of an eddy. In order to have turbu- 

 lence, R. must not exceed some critical value. Some type of horizontal 

 shearing motion is needed for continuation of the turbulent motion and 

 this may be the result of tidally induced boundary flow over the bottom 

 of the ocean, wind driven surface currents, or even gradients in the 

 large scale horizontal eddy motionSo 



Values of the stability, -^ , were calculated for the North 



p oz 



Atlantic from data obtained on the Crawford cruise 16, 1 Oct. -11 DeCo , 

 1957 (Metcalf, 1957). The averages were 



depth, meters stability,— 



az ' 



l/p ^ . cm"^ 



1000 - 2000 2.5 xlO" 



2000 - 3000 4x10"^^ 



3000 - 4000 2x10"-^^ 



Townsend (1958) showed that turbulence in the developed shear 

 flow of a stably stratified medium will collapse if R. is more than 

 about 0.1. For a stability of 2xl0~ cm" , the gradient required 



■13- 



