Geography Reference
In-Depth Information
Fig. 4.6
Two types of two-dimensional flow:
(a) linear shear flow with vorticity and
(b) curved flow with zero vorticity.
4.3
POTENTIAL VORTICITY
With the aid of the ideal gas law (1.17), the definition of potential temperature (2.44)
can be expressed as a relationship between pressure and density for a surface of
constant θ :
p
c
v
/c
p
(Rθ )
−
1
(p
s
)
R/c
p
Hence, on an isentropic surface, density is a function of pressure alone, and the
solenoidal term in the circulation theorem (4.3) vanishes;
dp
ρ
∝
ρ
=
dp
(1
−
c
v
/c
p
)
=
0
Thus, for adiabatic flow the circulation computed for a closed chain of fluid parcels
on a constant θ surface reduces to the same form as in a barotropic fluid; that is, it
satisfies Kelvin's circulation theorem, which may be expressed as
D
Dt
(C
+
2δAsin φ)
=
0
(4.10)
