60
DYNAMICAL OCEANOGRAPHY
The length scale L D is the internal Rossby deformation radius, given by
L D =
ND
f
,
(3.26)
and with N =1 0 −3 s −1 as a typical value in the midlatitude surface ocean and
D =4km, the scale L D =5 0km. For motions on this length scale, the deformations of isopycnal (constant density) surfaces provide accelerations that are
comparable to the Coriolis acceleration.
Ex. 3.3
For deformations of the ocean-atmosphere interface with the approximation
(3.14), the Burger number S transforms into the rotational Froude number F with
F
−1 =
gD
f 2 L 2 =
R 2
D
L 2 .
(3.27)
Here R D is referred to as the external Rossby deformation radius given by
R
2
D =
gD
f 2
0
,
(3.28)
with typical midlatitude values of R = 1000 km. Deformations of the oceanatmosphere interface on this scale cause accelerations comparable to the Coriolis
acceleration.
Additional Material
B: On the Coriolis acceleration and its counter-intuitive effects, see Stommel
and Moore (1989) and chapter 2 of Cushman-Roisin (1994). All the other
processes here are also part of many textbooks such as Cushman-Roisin
(1994). An overview of all processes in which turbulence is involved is provided in Thorpe (2005).
D: In the sections 10.1-10.5 of Vallis (2006), a thorough discussion is given
on turbulent transport. The modern formulation of mixing processes of momentum and heat/salt in ocean models is discussed systematically in Griffies
(2004). At this point, his chapter 7 would be useful to read.
3.2. Large-scale balances
In the chapters 1 and 2, we obtained a first impression of the large-scale ocean
circulation and the distribution of ocean temperature and salinity. To understand
these flows our starting point are the local conservation laws on a typical ocean
domain such as a sector of the sphere (Fig. 3.5) which rotates with angular velocity
Ω=|Ω|.
DYNAMICAL OCEANOGRAPHY
The length scale L D is the internal Rossby deformation radius, given by
L D =
ND
f
,
(3.26)
and with N =1 0 −3 s −1 as a typical value in the midlatitude surface ocean and
D =4km, the scale L D =5 0km. For motions on this length scale, the deformations of isopycnal (constant density) surfaces provide accelerations that are
comparable to the Coriolis acceleration.
Ex. 3.3
For deformations of the ocean-atmosphere interface with the approximation
(3.14), the Burger number S transforms into the rotational Froude number F with
F
−1 =
gD
f 2 L 2 =
R 2
D
L 2 .
(3.27)
Here R D is referred to as the external Rossby deformation radius given by
R
2
D =
gD
f 2
0
,
(3.28)
with typical midlatitude values of R = 1000 km. Deformations of the oceanatmosphere interface on this scale cause accelerations comparable to the Coriolis
acceleration.
Additional Material
B: On the Coriolis acceleration and its counter-intuitive effects, see Stommel
and Moore (1989) and chapter 2 of Cushman-Roisin (1994). All the other
processes here are also part of many textbooks such as Cushman-Roisin
(1994). An overview of all processes in which turbulence is involved is provided in Thorpe (2005).
D: In the sections 10.1-10.5 of Vallis (2006), a thorough discussion is given
on turbulent transport. The modern formulation of mixing processes of momentum and heat/salt in ocean models is discussed systematically in Griffies
(2004). At this point, his chapter 7 would be useful to read.
3.2. Large-scale balances
In the chapters 1 and 2, we obtained a first impression of the large-scale ocean
circulation and the distribution of ocean temperature and salinity. To understand
these flows our starting point are the local conservation laws on a typical ocean
domain such as a sector of the sphere (Fig. 3.5) which rotates with angular velocity
Ω=|Ω|.