Ocean dynamics

Ocean dynamics define and describe the motion of water within the oceans. Ocean temperature and motion fields can be separated into three distinct layers: mixed (surface) layer, upper ocean (above the thermocline), and deep ocean.Ocean dynamics are governed by Newton's equations of motion expressed as the Navier-Stokes equations for a fluid element located at (x,y,z) on the surface of our rotating planet and moving at velocity (u,v,w) relative to that surface:Mixed layer dynamics are quite complicated; however, in some regions some simplifications are possible. The wind-driven horizontal transport in the mixed layer is approximately described by Ekman Layer dynamics in which vertical diffusion of momentum balances the Coriolis effect and wind stress. This Ekman transport is superimposed on geostrophic flow associated with horizontal gradients of density.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.