48
STEPHEN GRIFFIES
3.5
Cells adjacent to the ocean surface
%
Grid cell k=1
Figure 9. Schematic of an ocean grid cell next to the ocean surface labeled by k = 1.
Its top face is at z = r], and the bottom is a surface of constant generalized vertical
coordinate s = s k = l .
For a grid cell adjacent to the ocean surface (Figure 9), we assume
that just the upper face of this cell abuts the boundary between the
ocean and the atmosphere or sea ice. The ocean surface is a time dependent boundary with z = q(x, y, t). The outward normal ng is given
by equation (25), and its area element dAg is given by equation (26).
As the surface can move, we must measure the advective transport
with respect to the moving surface. Just as in the dbsurface transport
discussed in Section 2.5, we consider the velocity of a reference point on
the surface
Vref - Uref
-
+gwref
Since z = q represents the vertical position of the reference point, the
vertical component of the velocity for this point is given by
which then leads to
vref . V (z - q) = q,t.
(82)
Hence, the advective transport leaving the ocean surface is