814 BOWDEN [sect. 6 



transport. In the main current of the Kuroshio, where the momentum flux 

 could rehably be related to the gradient of mean velocity, dU jdy, the corre- 

 sponding eddy viscosity Ny was of the order 10^ to 10'^ cm^/sec. 



4. Vertical Turbulence 



A . Eddy Coefficients and the Influence of Stability 



Turbulence is generated in the surface layer of the sea by the stress of the 

 wind. The rate of generation depends on the shearing stress and the velocity 

 gradient, while the latter is itself dependent on the effective eddy viscosity. In 

 its simplest form, Ekman's theory of wind-driven currents is based on a con- 

 stant eddy viscosity Nz within the surface layer, and it then follows from 

 observational data (Sverdrup et al., 1942, p. 494) that Nz is related to the wind 

 velocity W by the equation 



pNz = 4.3 If 2 for W > 6 m/sec, 



where W is measured in m/sec. 



In fact it is more probable that the intensity of wind-induced turbulence, 

 and hence also the magnitude of Nz, will have a maximum value a small 

 distance below the surface and will then decrease with increasing depth. 

 Theories have been developed by Rossby and Montgomery (1935) and others 

 which treat Nz as a function of z. However, it is still true, as stated by Sverdrup 

 et al. (1942), that "no observations are as yet available by means of which the 

 results of a refined theory can be tested". 



When the density of the water increases with depth, due, for example, to a 

 downward flux of heat, the effect of stability is to reduce the values of Nz and 

 Kz. In the wind-mixed layer, the diffusing effect of the turbulence is sufficient 

 to keep the density gradient small, but at some depth the rate of generation of 

 turbulent energy may no longer be great enough to overcome the stability 

 effect and a transition region, known as the thermocline, will be formed. This 

 region is characterized by a steep density gradient, with a low intensity of 

 turbulence and, hence, low values of Nz and Kz. 



Munk and Anderson (1948) developed a theory of the thermocline in which 

 they considered the shearing stress and heat flux as functions of depth, with 

 the coefficients Nz and Kz as functions of the Richardson number Ri. In the 

 present notation, they took 



Nz = Ao{l+^vRi)-y^, Kz = ^o(l +i8Ti^^)-'/^ 

 where 



Nz = Kz = Ao for Ri = 0. 



The forms of these functions and the numerical values of the constants ^v and 

 ^T were chosen to be consistent with the data of Jacobsen (1913) and Taylor 

 (1931). The appropriate values of the constants were ^v= 10, ^r = 3.33. Thus a 

 value Ri = 0.1 would correspond to iV^2 = 0.71^o, ir2 = 0.65^0 and a value 

 Ri=l to iV2 = 0.30^o, Kz = 0.11Aq. In spite of the great simplification of the 



