Basic Principles of the General Oceanic Circulation 591 



oceanic circulation is constant (see p. 336); that is, dldt{t, -'rf)/dc, — 0, where ^ is 

 here the relative vorticity. Since generally ^ < /, this equation reduces to 



dy \ d I 







for stationary predominantly zonal currents. From this it follows, since C <^ /, that 



/ \8d I 8f p 



^~ const, or -^ =--/=-„ (XVIII.28) 



d ddy fdy f 



which is equation (XVI1I,26). However, the assumption of constant potential vorticity 

 is valid only for horizontal geostrophic currents, but does not hold when vertical 

 velocity components are also present. Stommel's objection seems then to be justified 

 and Neumann's equations are valid as a first approximation only when the vertical 

 velocities are small compared with the horizontal ones. 



