a diagnostic of the vertical velocity for the equatorial atlantic a diagnostic of the vertical...
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A Diagnostic of the Vertical Velocity for the Equatorial AtlanticA Diagnostic of the Vertical Velocity for the Equatorial Atlantic Hervé Giordani and Guy Caniaux (CNRM/GAME (Météo-France/CNRS) 42, Av. G. Coriolis 31057 Toulouse Cedex)
Corresponding author: [email protected] Tel: 33(5)-61-07-93-81. Fax: 33(5)-61-07-96-10
Estimating the vertical velocity (w) in the upper-layers of the ocean is a key issue for understanding the cold tongue development in the eastern equatorial Atlantic. For that, we developed a general formulation of the
vertical velocity based on the primitive equation (PE) system, in order to gain new insight into the physical processes responsible for the
development of the equatorial and Angola upwellings. This approach is more accurate for describing the real ocean than simple considerations based on just the wind-driven patterns of surface layer divergence (i.e., the Ekman theory). The w-sources are diagnosed from a realistic ocean
simulation of the equatorial Atlantic.
Conclusions Sources of w are numerous in the eastern equatorial Atlantic and express the complexity of processes related to the turbulent momentum flux, to the circulation and to the mass fields. The equatorial upwelling is found to be mainly induced by: (1) the zonal wind-stress, (2) the stress-curl and (3) the imbalance between the circulation and the pressure fields. The Angola upwelling in the eastern part of the basin is mainly controlled by the stress-curl. A strong cross-regulation is evidenced between the forcing terms dependent on w and those independent of w. This cross-regulation suggests the existence of an equatorial balanced-dynamics (Giordani and Caniaux, 2011).
ReferencesGiordani, H., G. Caniaux, and L. Prieur, 2005: A simplified oceanic model assimilating geostrophic currents: application to the POMME experiment. J. Phys. Oceanogr., 35, 628-644. Giordani, H., and G. Caniaux, 2011: diagnosing vertical motion in the equatorial Atlantic. Submitted to Ocean Dynamics.Holton, J., 1992: An introduction to dynamic meteorology. Third Edition, Academic Press, Sao Diego, 511pp.
WMay-August 2006 averaged w at 20
m depth provided by a realistic open boundary PE
model(Giordani et al.,
2005)
All the fields are at 20 m depth and
averaged during
the period May-
August 2006.
Units are in m/day²
Derivation of the Vertical Velocity EquationWe start from the divergence equation (Holton, 1992):
The first term on the r.h.s. is expanded as:
for which the vorticity and zonal momentum equations are used. Then, by using the continuity equation, we obtain the following vertical velocity equation:
The r.h.s. of this equation is composed of 18 terms, which were grouped in external (independent of w or D) and internal (dependent on w or D) forcing terms. External forcings (first three lines) are due to the stress (terms 7, 8, 10), the pressure (terms 2, 3, 9, 12) or the horizontal current (terms 1, 4, 5, 6, 11); internal terms (last two lines) represent the negative feedback of the ocean to the external forcings.
zv
yw
zu
xwD
xv
yu
yv
xuP
zDwDU
zPuf
tD
hhh 22.1.1 22
t
tt dttu
tfufuf
00)()(
dzzv
yw
zu
xwD
zDwDU
dzdtxw
zu
ywf
zv
yw
xwf
zuw
zfwdzdt
zwff
dzPxv
yu
yv
xu
z
dzdtPkfz
fkz
UUfUfvxP
dzPufztw
zh
t
z
t
z
zhh
t
z
xhh
zt
02
0
0
0
0
0
0
0
2
02
0
2.
)()(
.12
..2
1)(
3
1
4 5 6
10
13(vortex stretching)
1211 (deformation of D)
9 (baroclinic term of the vorticity)
87
14 15 16 (tilting)
17 18 (deformation of D)
2
Term 7Zonal wind-stress
Term 8Stress-curl
Term 10Stress divergence
Term 1 – Term 2Imbalance between the circulation and pressure
Term 4Planetary vorticity advection by the meridional current
Terms 1 to 12
External forcings
Terms 13 to 18
Internal forcings
Term 13Vortex stretching
Terms 14 to 18Non linear terms