Turbulent Diffusion of Temperature and Salinity 



III. THERMAL DIFFUSION 



The model assumed Is shown schematically in Fig. 3, At 

 zero tinne to and depth z©, a semi- Infinite region of water at the 

 temperature T2 is assumed to be brought together with a semi- 

 Infinite region of water at temperature T| . Further, It Is assumed 



that Zq and Tq are essentially constant for t, , t2] 



Eventucilly 



as t becomes large, the semi- infinite model breaks down in prac- 

 tice because the effective value of Tq decreases. 



© 



H. 



® 



Tr 



i- 



Fig. 3. Schematic presentation of temperature diffusion as a 



function of water depth z cuid time t. Semi- infinite depth 

 is presented vertically with Zq a reference. At time t© 

 a sharp temperature discontinuity Is assumed, and T^ 



At t. diffusion has started and 



defined as (Tg - T,)/2. 

 To remains constant. For long times t„, t the seml- 

 Infinite model breaks down because the effective value of 

 T- does not remain constant In practice. 



The heat flow for this model Is governed by the one-dlmienslonal 

 diffusion equation 



9T 



at 



= D 



9^T 



(1) 



where D Is the dlffusivity, usually expressed In cmVsec. 



Due to vertical symmetry the problem can be formulated 

 using the T. part of Fig. 3, where Tr = (T + T )/2 is the 



= 0, to 



= the initial 



reference temperature. Taking T^ =0, z^ 



and the boundary conditions for z > and t = Is T(z,0) = T^ = 



(T, 



T,)/2. 



For z = and t > 0; T(0,t) = T^ 



315 



