14 C CYCLE AND ITS IMPLICATIONS FOR MIXING RATES 15 



For the circulation models in use in oceanography, the steady-state vertical 

 profiles of dissolved components are calculated by fixing two boundaries. In its 

 one-dimensional form, the theory is only concerned with vertical distribution, 

 and interior horizontal flow is not important. The basic equations take into 

 account the changes in water density as a function of depth. For a component 

 with specific concentration C, the change in concentration with time t is given 21 

 by 



ac a 2 c i a. „. ac ac 



— = K — -r + - r-(pK) T -w t- - AC + B 

 3t 3z poz oz dz 



where K = vertical diffusion coefficient 

 p = density 



w = vertical advection velocity 

 X = decay constant 

 B = biotic production rate 



For a stationary profile the change in concentration with time equals zero; in 

 addition, the product of density and advection velocity has to be constant for a 

 steady-state water-mass transport. With pw constant and if we assume that the 

 mixing parameter K/w is independent of depth, it is clear that (a/3z) (pK) = 0, 

 and the preceding equation becomes 



K^-£+B = w^ + XC (1) 



dz z oz 



This second-order differential equation provides a general solution for C 

 between two boundaries, z = and z = z m , with z m the mixing interval. These 

 boundaries are normally taken in such a manner that they coincide with marked 

 inflection points associated with water-mass boundaries. For our model the 

 boundaries coincide for the Pacific with the obvious geographical limitations of 

 the ocean floor and with (1) the boundary between thermocline layer and deep 

 water at 1 km depth and (2) the boundary between deep water and bottom 

 water at 4 km depth. 



Both the temperature and the salinity of ocean waters are conservative 

 properties (only influenced by mixing, B = 0) and nonradioactive (X = 0). For 

 these components the solution to Eq. 1 becomes C — C = (C m — Co) f(z, z m , 

 K/w). Thus, when salinity is plotted as a function of potential temperature, a 

 linear relation should result because for their ratio the function f cancels. Such a 

 linear relation is found for the 1- to 4-km-deep Pacific water, confirming the 

 applicability of the model over this region. The deep Atlantic is more 

 complicated with regard to this aspect since at least two or three such regions 

 can be identified. 



