ij:; JO . -.- ^ - : ■■■ uvj-Iv^jc- Piacsek - ■'■■ 



1. Forecast new values of the vorticity on interior gridpoints. 



2. Solve the Poisson equation for the stream function, and if there are any 

 rigid boundaries, find the values of the vorticity on them. On the frictionless 

 lid surfaces, both ^ and / vanish. 



3. Forecast new values of T and m, using the newly found stream function 

 in the Jacob ians. Start all over in 1. 



Since the Poisson equation for the stream function must be solved at every 

 time step and is a relatively lengthy procedure compared to the evaluation of 

 the right-hand side of the transport equations, the use of implicit methods and 

 fewer time steps almost always resulted in a large saving of computer time. 



ACKNOW LEDGMENTS 



This work was supported in part by the Office of Naval Research. The 

 generous amount of computer time donated by the computing centers of the Uni- 

 versity of Notre Dame and the National Center for Atmospheric Research is 

 gratefully acknowledged. The author would also like to thank Professors Ray- 

 mond Hide and Norman Phillips of MIT and Paul Roberts of the University of 

 Newcastle-upon-Tyne; also. Dr. Frank Eden of Arthur D. Little, Inc., and Dr. 

 Gar eth Williams of the Geophysical Fluid Dynamics Laboratory of ESSA for 

 many valuable discussions and advice. 



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780 



