The Sverdrup balance, or Sverdrup relation, is a theoretical relationship between the wind stress exerted on the surface of the open ocean and the vertically integrated meridional (north-south) transport of ocean water.
Aside from the oscillatory motions associated with tidal flow, there are two primary causes of large scale flow in the ocean: (1) thermohaline processes, which induce motion by introducing changes at the surface in temperature and salinity, and therefore in seawater density, and (2) wind forcing.
In the 1940s, when Harald Sverdrup was thinking about calculating the gross features of ocean circulation, he chose to consider exclusively the wind stress component of the forcing.
Looking down on the earth at the north pole, this spin is in a counterclockwise direction, which is defined as positive rotation or vorticity.
The Sverdrup relation can be derived from the linearized barotropic vorticity equation for steady motion: Here
In 1948 Henry Stommel proposed a circulation for the entire ocean depth by starting with the same equations as Sverdrup but adding bottom friction, and showed that the variation in Coriolis parameter with latitude results in a narrow western boundary current in ocean basins.
In 1950, Walter Munk combined the results of Rossby (eddy viscosity), Sverdrup (upper ocean wind driven flow), and Stommel (western boundary current flow), and proposed a complete solution for the ocean circulation.