Geography Reference
In-Depth Information
Equation (4.6) indicates that in a barotropic fluid the relative circulation for a closed
chain of fluid particles will be changed if either the horizontal area enclosed by the
loop changes or the latitude changes. Furthermore, a negative absolute circulation
in the Northern Hemisphere can develop only if a closed chain of fluid particles
is advected across the equator from the Southern Hemisphere. The anomalous
gradient wind balances discussed in Section 3.2.5 are examples of systems with
negative absolute circulations (see Problem 4.6).
Example . Suppose that the air within a circular region of radius 100 km centered
at the equator is initially motionless with respect to the earth. If this circular air
mass were moved to the North Pole along an isobaric surface preserving its area,
the circulation about the circumference would be
2π r 2
C
=−
[
sin(π/2)
sin(0)
]
Thus the mean tangential velocity at the radius r
=
100 km would be
7ms 1
V
=
C/(2πr)
=−
r
≈−
The negative sign here indicates that the air has acquired anticyclonic relative
circulation.
In a baroclinic fluid, circulation may be generated by the pressure-density
solenoid term in (4.3). This process can be illustrated effectively by considering
the development of a sea breeze circulation, as shown in Fig. 4.3. For the situation
depicted, the mean temperature in the air over the ocean is colder than the mean
temperature over the adjoining land. Thus, if the pressure is uniform at ground
level, the isobaric surfaces above the ground will slope downward toward the
Fig. 4.3
Application of the circulation theorem to the sea breeze problem. The closed heavy solid
line is the loop about which the circulation is to be evaluated. Dashed lines indicate surfaces
of constant density.
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