338
Equatorial Dynamics of the Thermocline: The Equatorial Undercurrent
locity, W, and the frictional forces which are scaled by the estimate of the
pressure force in each equation.
Scales for the Undercurrent
At the equator the Coriolis acceleration vanishes, and by hypothesis the relative acceleration must enter to balance the pressure gradient. The largest
relative acceleration (by a factor(£/ L ) 2 ) is the acceleration of the zonal velocity
in (6.3.lla). For it to balance the pressure gradient we must choose the relationship between U and £ such that:
(6.3.12)
This is precisely the relation obtained from the Fofonoff and Montgomery
solution, and it arises here for the same reason, i.e., the need to balance relative
acceleration with the Coriolis acceleration or, equivalently, to balance the relative vorticity against the planetary vorticity in the equatorial zone. Of course,
right at the equator the Coriolis acceleration vanishes, but in the equatorial
zone it is still present, although with reduced effect, and is of the same order as
the relative accleration.
It is difficult to give a clear estimate of the size of the dissipative terms in
the momentum equations. If, however, we regard F,xl as due to horizontal
mixing of the zonal momentum we might estimate F,xl by:
(x) -
[8 2 u 8 2 u]
Fn -AH 8y2 + 8x2
(6.3.13)
which would lead to an estimate of the last term in (6.3.11a) as:
(6.3.14)
We recognize the first ratio in (6.3.14) as ratio of the Munk boundary layer
thickness to the EUC meridional scale, all to the third power. Unless the
horizontal mixing is very large, the mixing term is negligible. Using the scales
for£ and L previously noted, AH would have to be larger than 1.6 x 10 8 cm 2 js
for horizontal mixing to enter the x momentum equation. We can comfortably
assume that AH is not this unrealistically large and therefore assume that
horizontal mixing can be neglected at least to the lowest order. A similar
analysis can be applied to the frictional term with regard to vertical mixing. If
the contribution of vertical mixing to the frictional force in the zonal direction
can be represented by:
F(x) =A 82u = 0 (A .!!_)
n
v 8z2
v H2
(6.3.15)
Equatorial Dynamics of the Thermocline: The Equatorial Undercurrent
locity, W, and the frictional forces which are scaled by the estimate of the
pressure force in each equation.
Scales for the Undercurrent
At the equator the Coriolis acceleration vanishes, and by hypothesis the relative acceleration must enter to balance the pressure gradient. The largest
relative acceleration (by a factor(£/ L ) 2 ) is the acceleration of the zonal velocity
in (6.3.lla). For it to balance the pressure gradient we must choose the relationship between U and £ such that:
(6.3.12)
This is precisely the relation obtained from the Fofonoff and Montgomery
solution, and it arises here for the same reason, i.e., the need to balance relative
acceleration with the Coriolis acceleration or, equivalently, to balance the relative vorticity against the planetary vorticity in the equatorial zone. Of course,
right at the equator the Coriolis acceleration vanishes, but in the equatorial
zone it is still present, although with reduced effect, and is of the same order as
the relative accleration.
It is difficult to give a clear estimate of the size of the dissipative terms in
the momentum equations. If, however, we regard F,xl as due to horizontal
mixing of the zonal momentum we might estimate F,xl by:
(x) -
[8 2 u 8 2 u]
Fn -AH 8y2 + 8x2
(6.3.13)
which would lead to an estimate of the last term in (6.3.11a) as:
(6.3.14)
We recognize the first ratio in (6.3.14) as ratio of the Munk boundary layer
thickness to the EUC meridional scale, all to the third power. Unless the
horizontal mixing is very large, the mixing term is negligible. Using the scales
for£ and L previously noted, AH would have to be larger than 1.6 x 10 8 cm 2 js
for horizontal mixing to enter the x momentum equation. We can comfortably
assume that AH is not this unrealistically large and therefore assume that
horizontal mixing can be neglected at least to the lowest order. A similar
analysis can be applied to the frictional term with regard to vertical mixing. If
the contribution of vertical mixing to the frictional force in the zonal direction
can be represented by:
F(x) =A 82u = 0 (A .!!_)
n
v 8z2
v H2
(6.3.15)