SOME OCEAN MODEL FUNDAMENTALS
4 1
We introduced the expression
W(s) = z,s dsldt,
(52)
which measures the volume of fluid passing through the surface, per
unit area dA = dxdy of the horizontal projection of the surface, per
unit time. That is,
The quantity w(') is called the dia-surface velocity component. It is
directly analogous to the fresh water flux q, defined in equation (27),
which measures the volume of freshwater crossing the ocean surface,
per unit time per horizontal area. To gain some experience with the
dia-surface velocity component, it is useful to write it in the equivalent
forms
w(') = z,, dsldt
= Z,s VS . (v - v(ref))
= ( ; - S) . (v - V b f ) )
where
is the slope of the s surface as projected onto the horizontal directions.
For example, if the slope vanishes, then the dia-surface velocity component measures the flux of fluid moving vertically relative to the motion
of the generalized surface. When the surface is static and flat, then the
dia-surface velocity component is simply the vertical velocity component
w = dzldt.
The expression (52) for w(') allows one to write the material time
derivative in one of the following equivalent manners