6 Equatorial Dynamics of the Thermocline:
The Equatorial Undercurrent
6.1 Introduction
The Coriolis parameter vanishes at the equator, and this distinguishes the
dynamics of the equatorial zone from the oceanic dynamics at higher latitudes.
Although the Coriolis acceleration due to the tangential component of the
earth's rotation vector remains different from 0 at the equator, for the large
scales of motion under consideration in this chapter its effect is negligible.
Whereas the horizontal pressure gradient outside the tropical zone is balanced
by the Coriolis acceleration, its absence at the equator leaves the pressure
gradient free to produce large relative accelerations.
The geostrophic approximation is the dynamical starting point and
foundation of all the theories of the ocean circulation discussed in the preceding chapters, and its breakdown at the equator signifies that the theoretical
results previously obtained cannot be carried directly to the equator. The
theories must be modified before the equatorial zone can be included in our
overall picture of the oceanic circulation.
The modification occurs on the level of the vorticity balance as well as the
momentum balance. The parameter which measures the size of the relative
acceleration with respect to the Coriolis acceleration is the Rossby number,
defined in (1.2.2) as:
u
Ro = -
(6.1.1)
fL
where Lis the scale of the motion and U that of the velocity, such that U/L is a
measure of the relative vorticity. Near the equator:
f = 2Q sin8 >::; 2Q8 >::; 2 ~ (R8) = f3y
( 6.1.2)
where y = R8 is the distance poleward from the equator and where f3 is the
equatorial value of the f3 parameter, 20/ R.
Suppose a motion which straddles the equator has the meridional scale L.
Then the characteristic value off for the motion would be f3L. Thus, in the
equatorial zone:
The Equatorial Undercurrent
6.1 Introduction
The Coriolis parameter vanishes at the equator, and this distinguishes the
dynamics of the equatorial zone from the oceanic dynamics at higher latitudes.
Although the Coriolis acceleration due to the tangential component of the
earth's rotation vector remains different from 0 at the equator, for the large
scales of motion under consideration in this chapter its effect is negligible.
Whereas the horizontal pressure gradient outside the tropical zone is balanced
by the Coriolis acceleration, its absence at the equator leaves the pressure
gradient free to produce large relative accelerations.
The geostrophic approximation is the dynamical starting point and
foundation of all the theories of the ocean circulation discussed in the preceding chapters, and its breakdown at the equator signifies that the theoretical
results previously obtained cannot be carried directly to the equator. The
theories must be modified before the equatorial zone can be included in our
overall picture of the oceanic circulation.
The modification occurs on the level of the vorticity balance as well as the
momentum balance. The parameter which measures the size of the relative
acceleration with respect to the Coriolis acceleration is the Rossby number,
defined in (1.2.2) as:
u
Ro = -
(6.1.1)
fL
where Lis the scale of the motion and U that of the velocity, such that U/L is a
measure of the relative vorticity. Near the equator:
f = 2Q sin8 >::; 2Q8 >::; 2 ~ (R8) = f3y
( 6.1.2)
where y = R8 is the distance poleward from the equator and where f3 is the
equatorial value of the f3 parameter, 20/ R.
Suppose a motion which straddles the equator has the meridional scale L.
Then the characteristic value off for the motion would be f3L. Thus, in the
equatorial zone: