All-101 17 



A final word should be said about the lack of quantita- 

 tive agreement between our computed results and observation. 

 The factor of three is not surprising when one considers the 

 very idealized model which we have assumed, A number of more 

 realistic assumptions may certainly affect our quantitative 

 results by such a factor. The inclusion of the non-linear terms, 

 a better representation of the wind effects on the v/ater, a 

 more natural topography, and a non-constant eddy viscosity may 

 well alter the quantitative results and bring them into closer 

 agreement with reality, 



3, Formu l at ion _of_t he Problem , It is our aim to derive 

 expressions for the velocity and the pressure satisfying the 

 three equations of motion on a rotating sphere 



™ + q • V^ + 2Qxq + Qx(Qxr) = - ^ Vp + F + ^(V ' A,.V)q 



at ~ - _.__.. — p — p -L - 



the continuity equation 



V • q = 



and the boundary condition that q = on a land -water boundary. 



Here, ^ 



q = (UjVjW) denotes the velocity vector relative to a 

 " coordinate system rotating with the sphere, 



Q denotes the angular velocity vector representing the 

 earth's rotation, 



p denotes the pressure, 



p denotes the density, 



F denotes the external forces per unit mass (in our case, 

 gravitation) , 



* u,v,w are spherical components of velocity along the direc- 

 tions of the radius, the meridians, and the parallels of 

 latitude respectively. 



