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DYNAMICAL OCEANOGRAPHY
6.5. Exercises on chapter 6
(6.1) Sverdrup flow
Given is the dimensionless wind-stress field
τ =
τ x
τ y
=0.1
sin 6(y −
π
6 )
0
over an ocean basin with x ∈ [0, 1] and y ∈ [0,π]. The Sverdrup flow is
assumed to satisfy the kinematic condition at the eastern boundary.
a. Determine the Sverdrup streamfunction ψ 0 (x, y).
b. Draw (or plot) the streamline pattern for
π
12
12 and interpret the
result in terms of a vorticity balance.
(6.2) Sverdrup flow and Stommel boundary layer
Given is the same dimensionless wind-stress field as in exercise 6.1, over an
ocean basin with x ∈ [0, 1] and y ∈ [0,π].
a. Determine the dimensionless Stommel boundary layer solution for this
wind-stress field.
b. Determine now the dimensional pressure p ∗ , the sea surface elevation h ∗
and the meridional transport Φ ∗ (y ∗ ) defined by
Φ ∗ (y ∗ )=
L
0
ψ ∗ (x ∗ ,y ∗ ) dx ∗
where L is the basin length.
c. Sketch (or plot) these fields for typical values of the parameters as in Table 6.9. Is the flow in the Stommel boundary layer in geostrophic balance?
(6.3) Integral balance
Consider in the general situation of (6.22), i.e., with all physical processes
taken into account, a closed streamline C that encloses an area A,a si nt h e
figure below. Show that for Re →∞ , the velocity field u =( u, v) and the
DYNAMICAL OCEANOGRAPHY
6.5. Exercises on chapter 6
(6.1) Sverdrup flow
Given is the dimensionless wind-stress field
τ =
τ x
τ y
=0.1
sin 6(y −
π
6 )
0
over an ocean basin with x ∈ [0, 1] and y ∈ [0,π]. The Sverdrup flow is
assumed to satisfy the kinematic condition at the eastern boundary.
a. Determine the Sverdrup streamfunction ψ 0 (x, y).
b. Draw (or plot) the streamline pattern for
π
12
12 and interpret the
result in terms of a vorticity balance.
(6.2) Sverdrup flow and Stommel boundary layer
Given is the same dimensionless wind-stress field as in exercise 6.1, over an
ocean basin with x ∈ [0, 1] and y ∈ [0,π].
a. Determine the dimensionless Stommel boundary layer solution for this
wind-stress field.
b. Determine now the dimensional pressure p ∗ , the sea surface elevation h ∗
and the meridional transport Φ ∗ (y ∗ ) defined by
Φ ∗ (y ∗ )=
L
0
ψ ∗ (x ∗ ,y ∗ ) dx ∗
where L is the basin length.
c. Sketch (or plot) these fields for typical values of the parameters as in Table 6.9. Is the flow in the Stommel boundary layer in geostrophic balance?
(6.3) Integral balance
Consider in the general situation of (6.22), i.e., with all physical processes
taken into account, a closed streamline C that encloses an area A,a si nt h e
figure below. Show that for Re →∞ , the velocity field u =( u, v) and the