Etudes et évaluation de processus océaniques par des hiérarchies ...

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Chapter 8
Equatorial Dynamics
tel-00545911, version 1 - 13 Dec 2010
The ocean dynamics near the equator is different from other places on our planet as the Coriolis
parameter f = 2Ω sin θ, measuring the vertical component of the rotation vector, a key
parameter in geophysical fluid dynamics, vanishes at the equator. We remind the reader that
the ocean currents are mostly horizontal and we can thus to first order neglect the horizontal
component of the rotation vector. The terms containing the horizontal component of the rotation
vector always involve the vertical component of the velocity vector due to the orthogonal
nature of the vector product Ω × u. Neglecting the horizontal component of the rotation vector
is called the traditional approximation . This does not mean that the effects of rotation can be
neglected when considering equatorial dynamics. Although the Coriolis parameter vanishes at
the equator its change with the respect to the meridional direction, β = 2(Ω/R) cos θ, where R
is the earths radius, is maximal at the equator. The equatorial dynamics is thus well described
by what is called the equatorial β-plane. The reduced gravity shallow water equations for the
equatorial β-plane are given by eqs. (5.38) - (5.40) with f = βy.
Another peculiarity of equatorial dynamics is the strong density stratification across the
thermocline. At the equator radiative forcing is strongest leading to warm waters and there
is also no cooling of the surface waters in winter time, a process important at high latitudes.
Precipitation is also strong near the equator freshening the surface waters. Both phenomena
lead to strong vertical density differences in the equator, which is responsible that the vertical
velocity shear is also more pronounced than in other regions of the ocean.
The first question we have to address is of course about the latitudinal extension of the
equatorial β-plane. If we compare the wave speed c = √ g ′ H to the value of β we obtain
the equatorial Rossby radius R eq = √ c/β. For barotropic dynamics H ≈ 4km we obtain
R eq ≈ 3000km. Due to the strong vertical density difference across the equatorial thermocline
most phenomena are, however, baroclinic in the tropics (at low latitude). For such dynamics
g has to be replaced by the reduced gravity g ′ = g∆ρ/ρ and the relevant thickness is this
of the layer above the thermocline. For this reduced gravity dynamics of the waters above
the thermocline c bc = 0.5ms −1 which leads to Req bc ≈ 300km. This gives a band extending
approximately 3 o to the north and south of the equator, a rather large area.
The easterly winds (winds coming from east) drive the westward (to the west) equatorial
current . These current causes a pileup of water at the western side of the basin, which leads
to a eastward equatorial undercurrent just below the waters directly influenced by the windstress.
The equatorial undercurrent is a band of eastward moving water at about 200m depth
which is about 100m thick and 300km large and which has maximal velocities of up to 1.5
ms −1 in the Pacific Ocean. The equatorial pile up of water at western side of the basin also
leads to eastward (counter) currents at the surface north and south of the equator, which are
called north equatorial counter current (NECC) and south equatorial counter current (SECC),
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