808 BOWDEN [sect. 6 



In a fluid of uniform density, the intensity of turbulence may be maintained 

 at such a level that all the energy supplied from the mean motion is dissipated 

 by viscosity, i.e. 



G = D. 



In the presence of a vertical gradient of density, a portion of the energy supplied 

 is used in increasing potential energy, so that 



G = P + D', 



where D' is the rate of dissipation in this case. Hence, for a given G, D' < D and 

 0' <0. Since depends on the turbulent velocity gradients, a decrease in 

 implies a decrease in the general level of intensity of the turbulence. It also 

 follows that G> P for this case, and hence from (21) and (23) 



NzjKz > Ri, (24) 



where 



Ri is a parameter known as the Richardson number. 



Thus, the effect of a stable density gradient is to reduce the intensity of the 

 turbulence and hence also the coefficients of eddy viscosity Nz and eddy 

 diffusion Kz, but Kz will be decreased more than Nz. 



A parameter Rf, known as the "flux Richardson number", which has been 

 introduced in meteorology, may be defined by 



i^/ = ^ = |iei. (26) 



The condition (24) may then be expressed as 



Rf < 1. (27) 



2. Turbulence in the Sea 



In the sea, the vertical and horizontal components of turbulence usually 

 differ so much in scale and in intensity that their effects are considered sep- 

 arately. These differences arise, firstly, because the horizontal dimensions of the 

 bodies of water concerned are much greater than the vertical dimension, and, 

 secondly, because of the influence of stability. The presence of a stable vertical 

 gradient of density causes a reduction in the intensity of the iv fluctuations but 

 has no direct effect on the fluctuations in u and v. A striking example of the 

 difference in the scale of horizontal and vertical diffusion was given by Revelle 

 et al. (1955). Radioactive material released at a point below the thermocline 

 spread horizontally, or more strictly over an iso-density surface, covering an 

 area of 100 km^, while its vertical extent did not exceed 1 m. In general, the 



