Turbulent Diffusion of Temperature and Salinity 



There is heat energy liberated due to viscous friction. Also, apart 

 of the turbulent energy is dissipated in changing the potential gravi- 

 tational energy of the pycnocline by changing its thickness. 



The power density associated with a change in potential energy 

 can be shown for water to be approximately 



sfSt] ergs/cm sec (6) 



where g is acceleration of gravity in cm/sec , (^p) is either (Ap)- 

 or (Ap)s symbolizing the change in density due to temperature or 

 salinity differences across the pycnocline in gm/cm', (Ah) the change in 

 thickness of the pycnocline in cm, and (At) =(t2- t,) in s£c. For tur- 

 bulence #1, P,' = 0.0074 ergs/cm^ sec. For turbulence #2, P^= 0.055. 



The power density due to viscous friction P was estimated by 

 measuring the temperature rise in the water due to turbulence #1 

 and #2 being maintained for measured lengths of time. For turbulence 

 #1 this was about P, = 0.014(10"^) ergs/cm^ sec. For turbulence #2, 

 Pg = 0.082(107). 



The ratio of P,/P| = 1.9 (10^), and Pg/^g = 1.5(10^). Thus, 

 it appears that the power density due to viscous friction is on the 

 order of 10^ greater than the power density associated with a change 

 in the pycnocline thickness. 



However, the ratios for the two conditions of turbulence are 

 different only by about 25%. This is interesting, for if it should 

 turn out that P/P' is relatively constant over a practical range of 

 turbulence, temperature and salinity diffusivities could be estimated 

 directly from the time rate of change of pycnocline thickness (after 

 internal waves are filtered out). Possible application to the ocean 

 is intriguing. 



For physical and dimensional reasons, let us divide P' by 

 the dynamic viscosity of water x] = 0,01 gm/cm sec, and take the 

 square root. Equation (6) then becomes 



(P'/n)'^^ = 110(Ap/At)'''^(Ah) 1/sec (7) 



This equation contains variables that are relatively easy to measure 

 and has the dimension of vorticity. It is plotted in Fig. 6 for the 

 average values of the variables used in the small scale laboratory 



experiments . 



319 



