Geography Reference
In-Depth Information
ocean while the isopycnic surfaces (surfaces of constant density) will slope down-
ward toward the land. To compute the acceleration as a result of the intersection
of the pressure-density surfaces, we apply the circulation theorem by integrating
around a circuit in a vertical plane perpendicular to the coastline. Substituting the
ideal gas law into (4.3) we obtain
DC
a
Dt
=−
RT d ln p
For the circuit shown in Fig. 4.3 there is a contribution to the line integral only for
the vertical segments of the loop, as the horizontal segments are taken at constant
pressure. The resulting rate of increase in the circulation is
R ln
p
0
p
1
(T
2
−
DC
a
Dt
=
T
1
)>0
Letting
v
be the mean tangential velocity along the circuit, we find that
D
v
R ln(p
0
/p
1
)
2(h
=
(T
2
−
T
1
)
(4.7)
Dt
+
L)
10
◦
C,L
If we let p
0
=
1000 hPa, p
1
=
900 hPa, T
2
−
T
1
=
=
20 km, and
10
−
3
ms
−
2
. In the absence
of frictional retarding forces, this would produce a wind speed of 25 m s
−
1
in
about 1 h. In reality, as the wind speed increases, the frictional force reduces
the acceleration rate, and temperature advection reduces the land-sea temperature
contrast so that a balance is obtained between the generation of kinetic energy by
the pressure-density solenoids and frictional dissipation.
h
=
1 km, (4.7) yields an acceleration of about 7
×
4.2
VORTICITY
Vorticity, the microscopic measure of rotation in a fluid, is a vector field defined as
the curl of velocity. The absolute vorticity
ω
a
is the curl of the absolute velocity,
whereas the relative vorticity
ω
is the curl of the relative velocity:
ω
a
≡
∇
×
U
a
,
ω
≡
∇
×
U
so that in Cartesian coordinates,
∂w
∂y
−
∂v
∂z
,
∂u
∂w
∂x
,
∂v
∂u
∂y
ω
=
∂z
−
∂x
−
