SOME OCEAN MODEL FUNDAMENTALS
55
sea ice. Following the discussion of the tracer budget at the ocean surface
in Section 3.5 leads to the expression for the transport of momentum into
the ocean due to mass transport at the surface
The force arising from the contact stresses at the surface is written
Bringing these results together leads to the force acting at the ocean
surface
Details of the various terms in this force are generally unknown. Therefore, just as for the tracer at z = q in Section 3.5, we assume that a
boundary layer model provides information about the total force, and
that this force is written
where v, is the velocity of the fresh water. This velocity is typically
taken to be equal to the velocity of the ocean currents in the top cells
of the ocean model, but such is not necessarily the case when considering the different velocities of, say, river water and precipitation. The
stress T~"P is that arising from the wind, as well as interactions between
the ocean and sea ice. Letting the horizontal area vanish leads to the
thickness weighted budget for a grid cell next to the ocean surface
dt (dz p v ) = - Vs [ dz u (p v)] + (w(') p v),=,,=,
+a, [dz (2. T - fip)]
+ a g [ d x ( 9 . ~ - 9 ~ ) 1
- [z,s (Vs 7 - P V ~ ) ] s = s ~ = ~
+ [T~"' - ~ a V ( z - q ) +~wqwvw]
- p d z [ g P + ( f + M ) P A v].
55
sea ice. Following the discussion of the tracer budget at the ocean surface
in Section 3.5 leads to the expression for the transport of momentum into
the ocean due to mass transport at the surface
The force arising from the contact stresses at the surface is written
Bringing these results together leads to the force acting at the ocean
surface
Details of the various terms in this force are generally unknown. Therefore, just as for the tracer at z = q in Section 3.5, we assume that a
boundary layer model provides information about the total force, and
that this force is written
where v, is the velocity of the fresh water. This velocity is typically
taken to be equal to the velocity of the ocean currents in the top cells
of the ocean model, but such is not necessarily the case when considering the different velocities of, say, river water and precipitation. The
stress T~"P is that arising from the wind, as well as interactions between
the ocean and sea ice. Letting the horizontal area vanish leads to the
thickness weighted budget for a grid cell next to the ocean surface
dt (dz p v ) = - Vs [ dz u (p v)] + (w(') p v),=,,=,
+a, [dz (2. T - fip)]
+ a g [ d x ( 9 . ~ - 9 ~ ) 1
- [z,s (Vs 7 - P V ~ ) ] s = s ~ = ~
+ [T~"' - ~ a V ( z - q ) +~wqwvw]
- p d z [ g P + ( f + M ) P A v].