56
DYNAMICAL OCEANOGRAPHY
This linear meridional variation of f is part of the β-plane approximation. The
characteristic time scale associated with the meridional variation of the Coriolis
acceleration is
τ β =
1
β 0 L
.
(3.11)
An interpretation in terms in vorticity is again possible (Fig. 3.1c). A water parcel
that moves northward in the northern hemisphere is deflected more strongly at a
more northerly position. This gives a contribution to the vertical component of
the vorticity with a magnitude of β 0 L.A t4 5 ◦ N, a value of τ β is 10 4 sforaflow
with a length scale L = 5000 km.
3.1.3. Stratification
Because the density of ocean water depends on temperature, salinity and pressure, ocean water is stratified. A characteristic quantity of the stratification is the
buoyancy (or Brunt-V¨ ais¨ al¨ a) frequency N ,givenby
N
2 = −
g
ρ
∂ρ
∂z
,
(3.12)
In a stably stratified water column (N>0), a fluid parcel can locally depart
from its equilibrium due to a perturbation, but because the restoring force always
counteracts its motion, the parcel will eventually return towards its equilibrium
position. It can, however, overshoot and this behavior will lead to a damped oscillation with an oscillation frequency N .
A stable stratification of the water column introduces a characteristic time scale
τ s = N
−1 .
(3.13)
The profile of N 2 along the WOCE A16 section is plotted in Fig. 3.4 (in cycle/hour). In the upper layers the profile follows that of salinity (see Fig. 1.6).
The time scale τ s increases from a minimum of 1/10 hr just below the ocean surface to about 1/2 hr at a depth of 2 km.
The ocean-atmosphere interface is deformable and it can be considered as a
special case of a stratified liquid in which there is a layer of air with thickness D
and constant density ρ a situated above a liquid layer also with depth D and density
ρ. The buoyancy frequency N 2 can for this case be approximated by
N
2 ≈ g(ρ − ρ a )/(Dρ),
(3.14)
and because ρ a /ρ ≪ 1 it follows that N 2 ∼ = g/D. This introduces the timescale
τ g =
D/g,
(3.15)
which is associated with oscillations in the ocean-atmosphere surface, i.e., long
gravity waves with phase speed c = D/τ g =
√ gD. Deformations of the air-sea
interface provide also a contribution to the vorticity balance, as we will see later.
DYNAMICAL OCEANOGRAPHY
This linear meridional variation of f is part of the β-plane approximation. The
characteristic time scale associated with the meridional variation of the Coriolis
acceleration is
τ β =
1
β 0 L
.
(3.11)
An interpretation in terms in vorticity is again possible (Fig. 3.1c). A water parcel
that moves northward in the northern hemisphere is deflected more strongly at a
more northerly position. This gives a contribution to the vertical component of
the vorticity with a magnitude of β 0 L.A t4 5 ◦ N, a value of τ β is 10 4 sforaflow
with a length scale L = 5000 km.
3.1.3. Stratification
Because the density of ocean water depends on temperature, salinity and pressure, ocean water is stratified. A characteristic quantity of the stratification is the
buoyancy (or Brunt-V¨ ais¨ al¨ a) frequency N ,givenby
N
2 = −
g
ρ
∂ρ
∂z
,
(3.12)
In a stably stratified water column (N>0), a fluid parcel can locally depart
from its equilibrium due to a perturbation, but because the restoring force always
counteracts its motion, the parcel will eventually return towards its equilibrium
position. It can, however, overshoot and this behavior will lead to a damped oscillation with an oscillation frequency N .
A stable stratification of the water column introduces a characteristic time scale
τ s = N
−1 .
(3.13)
The profile of N 2 along the WOCE A16 section is plotted in Fig. 3.4 (in cycle/hour). In the upper layers the profile follows that of salinity (see Fig. 1.6).
The time scale τ s increases from a minimum of 1/10 hr just below the ocean surface to about 1/2 hr at a depth of 2 km.
The ocean-atmosphere interface is deformable and it can be considered as a
special case of a stratified liquid in which there is a layer of air with thickness D
and constant density ρ a situated above a liquid layer also with depth D and density
ρ. The buoyancy frequency N 2 can for this case be approximated by
N
2 ≈ g(ρ − ρ a )/(Dρ),
(3.14)
and because ρ a /ρ ≪ 1 it follows that N 2 ∼ = g/D. This introduces the timescale
τ g =
D/g,
(3.15)
which is associated with oscillations in the ocean-atmosphere surface, i.e., long
gravity waves with phase speed c = D/τ g =
√ gD. Deformations of the air-sea
interface provide also a contribution to the vorticity balance, as we will see later.