Geography Reference
In-Depth Information
9.6.1
Development of Rotation in Supercell Thunderstorms
The supercell thunderstorm is of particular dynamical interest because of its ten-
dency to develop a rotating mesocyclone from an initially nonrotating environment.
The dominance of cyclonic rotation in such systems might suggest that the Coriolis
force plays a role in supercell dynamics. However, it can be shown readily that the
rotation of the earth is not relevant to development of rotation in supercell storms.
Although a quantitative treatment of supercell dynamics requires that the den-
sity stratification of the atmosphere be taken into account, for purposes of under-
standing the processes that lead to development of rotation in such systems and
to the dominance of the right-moving cell, it is sufficient to use the Boussinesq
approximation. The Euler momentum equation and continuity equation may then
be expressed as
D
U
Dt
=
∂
U
∂t
+
1
ρ
0
∇
·∇
=−
+
(
U
)
U
p
b
k
∇·
=
U
0
Here,
U
is the three-dimensional
del operator, ρ
0
is the constant basic state density, p is the deviation of pressure
from its horizontal mean, and b
≡
V
+
k
w is the three-dimensional velocity,
∇
gρ
/ρ
0
is the total buoyancy.
It is convenient to rewrite the momentum equation using the vector identity
≡−
U
·
U
(
U
·∇
)
U
=
∇
−
U
×
(
∇
×
U
)
2
to obtain
p
ρ
0
+
∂
U
∂t
=−
∇
U
·
U
+
U
×
ω
+
b
k
(9.53)
2
Taking
(9.53) and recalling that the curl of the gradient vanishes, we obtain
the three-dimensional vorticity equation
∇
×
∂
∂t
=
∇
×
(
U
×
ω
)
+
∇
×
(b
k
)
(9.54)
Letting ζ
(9.54), we
obtain an equation for the tendency of ζ in a nonrotating reference frame:
=
k
·
ω
be the vertical component of vorticity and taking
k
·
∂ζ
∂t
=
k
·
∇×
(
U
×
ω
)
(9.55)
Note that buoyancy only affects the horizontal vorticity components.
