All-101 6 



the simplifications Involved in the formulation of the problem 

 might be welcomed by workers in this field and that it might 

 help to clear up any existing misconceptions concerning the 

 validity of some of the assumptions. 



2. Di_s..cu ssion of R esu lts* At this point we shall discussj 

 without resorting to mathematical detail, the basic assumptions, 

 the results, and the conclusions of the present investigation. 

 In this manner we hope to convey a more integrated picture of 

 the physics of the problem* 



Mathematically 5 the motion which we want to study can 

 be defined by the Navier-Stokes equations of motion with the 

 viscous terms replaced by terms arising from a macroscopic vis- 

 cosity, vizo , an eddy viscosity. The complete non-linear equa- 

 tions are too difficult to solve, however, so that \ie are forced 

 to make a number of simplifying assumptions which we shall list 

 below, 



1, The fluid is assumed to be incompressible, but it may 

 be inhomogeneous. 



2, The equations on a rotating sphere are approximated by 

 equations in a rectangular Cartesian system. The effect of the 

 sphericity of the earth is retained by allowing the Coriolis 

 parameter to depend on the latitude. Since we shall consider a 

 rectangular ocean in the Cartesian system, a fev/ remarks must 

 be made concerning the region of the sphere onto which the rec- 

 tangle is mapped. The constant east-west distance of the rec- 

 tangle is preserved in the mapping of the rectangle onto the 



