21 



The density anomaly of sea water is due to the distribution of both 

 salinity and temperature . Source or sink regions at the ocean surface 

 for salinity coincide with areas in which evaporation exceeds precipitation 

 or vice versa. With exceptions like the equatorial rain belt, the surface 

 of tropical oceans is a source region of both heat and salinity. On the 

 other hand, cooling and an excess of precipitation make the ocean surface 

 in subarctic areas a sink of both heat and salinity. To simplify the 

 formulation of the present study of large-scale heat transfer by ocean 

 currents it will be assumed that the boundary conditions of temperature 

 and salinity have the same dependence on latitude and are independent of 

 longitude . Neglecting second order terms the equation of state of the 

 model is given as, 



P = P^[ 1 - a(T - T ) + o(S - S )] 

 o o o 



where o and o are the respective expansion coefficients for temperature, 

 T, and salinity, S. Since T and S obey the same type of conservation ].aw, 

 and the boundary conditions are proportional, the two variables are no 

 longer independent. A virtual temperature (Pofonoff, 1962) may be defined 

 as 



e = T-T -^S-S) 

 o a o 



The single variable, 6 , then combines the effect of both T and S on the 

 density field. 



EQUATIONS OF THE MODEL 



The basic equations are taken to be the Navier-Stokes equations, 

 written for a Mercator projection in a rotating frame with the following 

 assumptions: a) hydrostatic balance, b) variations in density neglected 

 except where they appear as a coefficient of g (the gravitational accel- 

 leration), c) viscosity and conductivity are replaced by simplified terms 

 representing the diffusion of momentum and heat by smaller scale transient 

 disturbances . 



Let m = sec ^ 



n = sin (j) 



where ^ is the latitude. If ^ is the longitude, end a the radius of the 

 globe, X and y coordinates are defined as follows: 



dx = adX 



dy = amd^ 



A and y are respectively the eddy diffusion coefficients in the horizontal 

 and vertical. 



