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DYNAMICAL OCEANOGRAPHY
b. This pressure gradient sets up a zonal flow through geostrophy with a
characteristic velocity U . Explain why this flow causes a zonal pressure
gradient Δp Z .
c. Explain why Δp Z ≈ Δp M .
d. Describe how the meridional flow can be driven by a meridional density
difference.
(16.5) Scaling
As a sequel to exercise (16.4), we try to find a scaling relation between the
strength of the meridional overturning circulation ψ M and the meridional
density difference Δρ.
a. Scale U according to the geostrophic balance and use the scale of Δp M
from exercise (16.4) to show that
U =
DgΔρ
fL
,
where f is the average Coriolis parameter over the flow domain.
b. Use the advection diffusion balance for the thermocline, i.e.,
w ∗
∂ρ ∗
∂z ∗
= K V
∂ 2 ρ ∗
∂z ∗
2
,
to show that
U =
K V L
D 2 .
c. Show that ψ M ≈ (Δρ)
1
3 .
DYNAMICAL OCEANOGRAPHY
b. This pressure gradient sets up a zonal flow through geostrophy with a
characteristic velocity U . Explain why this flow causes a zonal pressure
gradient Δp Z .
c. Explain why Δp Z ≈ Δp M .
d. Describe how the meridional flow can be driven by a meridional density
difference.
(16.5) Scaling
As a sequel to exercise (16.4), we try to find a scaling relation between the
strength of the meridional overturning circulation ψ M and the meridional
density difference Δρ.
a. Scale U according to the geostrophic balance and use the scale of Δp M
from exercise (16.4) to show that
U =
DgΔρ
fL
,
where f is the average Coriolis parameter over the flow domain.
b. Use the advection diffusion balance for the thermocline, i.e.,
w ∗
∂ρ ∗
∂z ∗
= K V
∂ 2 ρ ∗
∂z ∗
2
,
to show that
U =
K V L
D 2 .
c. Show that ψ M ≈ (Δρ)
1
3 .