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DYNAMICAL OCEANOGRAPHY
11.7. Exercises on chapter 11
(11.1) The Equatorial Under Current
Consider a column of water with a thickness h 0 below the Ekman layer. Water
moves from a location y 0 > 0 to the equator as a compensation of water which
flows northward in the upper layer. Assume that at y 0 , the relative vorticity is
small with respect to the planetary vorticity.
a. Show that from conservation of potential vorticity, it follows that
β 0 y − u ′
h
=
f 0
h 0
where h(y) is the thickness of the water column at location y and u(y) the
steady zonal velocity at the equator.
b. Determine the solution u(y) as a model for the Equatorial Under Current
and provide an estimate of the amplitude of the zonal velocity of this current.
c. Is this a good model to explain the existence of the Equatorial Under Current?
(11.2) Equatorial Counter Current
The model in section 11.2 does qualitatively indicate the existence of the Equatorial Counter Current (ECC). We have assumed that f 0 =0and computed the
flow on the equatorial β-plane. At latitudes between 4 ◦ N and 10 ◦ N, the Coriolis parameter f 0 is not strictly zero and one could compute the flow using a
midlatitude β-plane model such as presented in the chapters 5 and 6.
a. Use the dimensionless Sverdrup balance (6.5) to compute the zonal
velocity, meridional velocity and sea surface height for the same wind stress
as in Example 11.1.
b. Show that an ECC occurs at latitudes where the meridional gradient in the
sea surface height is negative.
DYNAMICAL OCEANOGRAPHY
11.7. Exercises on chapter 11
(11.1) The Equatorial Under Current
Consider a column of water with a thickness h 0 below the Ekman layer. Water
moves from a location y 0 > 0 to the equator as a compensation of water which
flows northward in the upper layer. Assume that at y 0 , the relative vorticity is
small with respect to the planetary vorticity.
a. Show that from conservation of potential vorticity, it follows that
β 0 y − u ′
h
=
f 0
h 0
where h(y) is the thickness of the water column at location y and u(y) the
steady zonal velocity at the equator.
b. Determine the solution u(y) as a model for the Equatorial Under Current
and provide an estimate of the amplitude of the zonal velocity of this current.
c. Is this a good model to explain the existence of the Equatorial Under Current?
(11.2) Equatorial Counter Current
The model in section 11.2 does qualitatively indicate the existence of the Equatorial Counter Current (ECC). We have assumed that f 0 =0and computed the
flow on the equatorial β-plane. At latitudes between 4 ◦ N and 10 ◦ N, the Coriolis parameter f 0 is not strictly zero and one could compute the flow using a
midlatitude β-plane model such as presented in the chapters 5 and 6.
a. Use the dimensionless Sverdrup balance (6.5) to compute the zonal
velocity, meridional velocity and sea surface height for the same wind stress
as in Example 11.1.
b. Show that an ECC occurs at latitudes where the meridional gradient in the
sea surface height is negative.