584 Basic Principles of the General Oceanic Circulation 



(c) the consideration of the variability of Coriolis parameter with latitude 



(Stommel, 1948) which makes it possible to explain the westward intensification 



of a wind-generated ocean circulation. 



This theory accounts for many of the major features and some of the details of the 



general ocean circulation on the basis of known mean annual winds. Briefly the 



fundaments of this new theory are: 



The vorticity equation (XVII. 5) can be put into a practical form by the introduction 

 of expressions for the lateral frictional forces. According to (XL 13 and 14) these 

 frictional forces have the form 



(d^u dhi\ , IdH cH\ 



^- = '^ (a? + 8/) ^°^ "' = ^ (a? + if) ■ (^^"") 



A is the lateral eddy viscosity pertaining to horizontal shear v*'hich is presumed to be 

 constant and horizontally isotropic, neglecting variations due to differences between 

 zonal and meridional motion of large horizontal vortices on a rotating earth. Intro- 

 duction of these expressions into (XVII. 5) with the stream function according to 

 (XVI. 25), gives the differential equation for mass transport 



AV^ - iS ^\^ = - curL T, (XVIII.8) 



where V^ is the biharmonic operator (see XVI.26) and curl, Tis the vertical vorticity 

 component of the wind stress. It can be shown, in accordance with the relationship 



lateral stress curl + planetary vorticity + 



western solution + wind stress curl = 



^r 



(XVIII.9) 



central solution J 



that in the central and eastern oceanic areas the planetary vorticity and the wind- 

 stress curl have opposite signs, resulting in balance in which the lateral stress plays a 

 negligible part. Along the western boundary the planetary and the wind-stress curl 

 have the same sign, and the lateral-stress curl balances both, planetary vorticity and 

 wind-stress curl. It can be verified that in this region the wind-stress curl is numerically 

 unimportant although it is, of course, the primary cause of the circulation. 

 To equation (XVIII. 7) must be added the boundary conditions 



^- = 0; (yj-O, (XVIII.IO) 



boundary \ / boundary 



where v is normal to the boundary. The first equation states that the boundary itself 

 is a stream line, the second that no slippage occurs against the boundary. 



Munk assumed : 



(1) a rectangular ocean extending from x = to .v = r and from y = —s to y = -\-s. 

 The boundary conditions will then be 



= dijjjdx = for ;c = and x — r "\ rxVTlT 1 H 



= dxltjdy — for_y = —s and y = A^s j 



