All-l.Ol 26 



have to be carried out. 



Define p = p [z - T(x,y,t)] in such a way that 



n 



p = p 5 a constant for ^ > ^ > '^ 



p = [l + c(T - z)]pQ for T > z 2 T - d(c,d constants) 



p = p , = (1 + cd)pQ for T - d > z . 



> 



(15) 



With this definition the density is a continuous function of 

 depth and the ocean is divided into three distinct layers. A 

 layer of constant density, p^, lies above a region in which the 

 density increases linearly with depth from p^ to the value p^-^. 

 Finally, at the bottom, there is a layer of constant density, 

 p , . This prescribed distribution agrees well with the observed 

 density distribution. 



If p, as given by (15)? be substituted into equation 

 (1>+), we find that* 



01 = ^ In 9I = -Lo£il (16) 



8x " Ap ax' ay Ap ay 



where Ap = P _]^ - P q' 



If we integrate equations (l6), we obtain 



T = - £o n - C (17) 



Ap 



where z = - C is the constant depth of T when r) = 0. Physically, 

 z = - C is an average depth of the top layer or the depth of T 

 when the ocean surface is undisturbed (i.e., in the absence of 

 winds). These two quantities are, of course, identical. 



* The algebraic manipulation Is given In Appendix ^-(a)* 



