text: Horizontal convergences and divergences within the mixed layer due, for example, to Ekman transport convergence imposes a requirement that ocean below the mixed layer must move fluid particles vertically.  But one of the implications of the geostrophic relationship is that the magnitude of horizontal motion must greatly exceed the magnitude of vertical motion.  Thus the weak vertical velocities associated with Ekman transport convergence (measured in meters per day) cause horizontal motion with speeds of 10 centimeters per second or more.  The mathematical relationship between vertical and horizontal velocities can be derived by expressing the idea of conservation of angular momentum for a fluid on a rotating sphere.  This relationship (with a couple of additional approximations) is known to oceanographers as the Sverdrup relation. Among its implications is the result that the horizontal convergence of Ekman transport observed to occur in the subtropical North Atlantic and Pacific forces southward flow throughout the interior of these two oceans.  Western boundary currents (the Gulf Stream and Kuroshio) exist in order to return water to higher latitude.