23 



Temperature is prescribed at the upper surface as a linear function of 

 latitude . Let A9* be a scale temperature . 



9((|>) = Ae*[ 1 - (<^ - <^^)/ ((|)y - <I>q)], z = 0. 



The boundary conditions on velocity in this preliminary investigation 

 filter out external gravity waves, and eliminate any stresses acting at 

 the bottom or at the upper surface . 



w = ^2 ^ ^z ^ ° z = 0, -D. 



Both the normal and the parallel components of velocity vanish at the 

 lateral boundaries. 



X = 0, X 

 u = V = 



y = 0, Y 



Equations (l) - (5) are solved by finite differencing using a grid of 

 19 X 19 points with 6 levels in the vertical. In some cases a more refined 

 net was used close to the western boundary to obtain a better resolution of 

 the boundary current. The numerical scheme is based on ideas proposed by 

 AreLkawai'and Lilly (1965). Details of the numerical method will be published 

 in a separate paper. 



RESULTS 



In laboratory studies of hydrodynamic models scale analysis is an 

 essential tool. It is also useful in a numerical study to isolate the 

 important variables and eliminate redundant calculations . Following ideas 

 proposed by Robinson (1960), a scale velocity, V*, and a scale depth of the 

 thermocline may be defined in the following way. In terras of a geostrophic 

 balance between the vertical variation of velocity and the horizontal 

 temperature gradient, 



2 n V*/d = g a Ae*/L 



The requirement that the vertical diffusion of heat be of the same order as 

 the horizontal advection of heat may be expressed as, 



V* Ae*/L = <Ae*/d2 



1/ Arakawa, "Computational Design for Long Numerical Integrations of the 

 Equations for Atmospheric Motion," paper presented at the kkfh 'nnual 

 Meeting, A. G. U., Washington, April 1963. 



