To investigate the JES circulation as a whole, we integrate the velocity
vertically from the surface (z=0) to the bottom (z=-h)
Due to the continuity the volume transport stream function (
) is defined
by
and satisfies the Poisson equation
For each time instance, we solve the two-dimensional Poisson equation (10)
with the given boundary conditions, that is, zero transport at the rigid
boundaries and known transport at the open boundaries (see Table 1).