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radial direction, we then have
∂r (rv λ )
Assuming that the vertical scale is much larger than the radial scale, the Laplacian
in cylindrical coordinates can be approximated by
v λ
r
U
× ω
i λ
r
1
r
∂r
∂r
2
Thus, from (9.57) the dynamical component of the pressure perturbation in the
vortices (designated p dyn ) can be expressed as
r v λ 2
∂r
r
ρ 0
v λ ∂ (rv λ )
∂r
∂v λ
∂r
(9.58)
Integrating (9.58) with respect to r, we obtain the equation of cyclostrophic balance
(see Section 3.2.4):
1
r
∂r
∂p dyn
∂r
1
r
∂r
1
r
∂r
1
r
≈−
+
=
∂p dyn ∂r ∂r
v λ / r (9.59)
Hence, there is a pressure minimum at the vortex center irrespective of whether the
rotation is cyclonic or anticyclonic. The strong midtropospheric rotation induced
by vortex tube twisting and stretching creates a “centrifugal pump” effect, which
causes a negative dynamical pressure perturbation centered in the vortices in the
midtroposphere. This in turn produces an upward directed dynamical contribution
to the vertical component of the pressure gradient force, and thus provides an
upward acceleration, which produces updrafts in the cores of the counterrotating
vortices as depicted in Fig. 9.12. These updrafts are separated by a downdraft
that leads to a splitting of the storm and the development of two new centers of
convection that move to the right and left of the original storm (Fig. 9.12b).
As discussed in this section, the tilting and stretching of horizontal vorticity
associated with the vertical shear of the basic state wind can account for the devel-
opment of mesoscale rotating supercells. This process does not, however, appear to
be able to produce the large vorticities observed in the tornadoes that often accom-
pany supercell thunderstorms. Numerical simulations suggest that these tend to
involve tilting and stretching of especially strong horizontal vorticity produced by
horizontal gradients in buoyancy that occur near the surface along the gust front
where negatively buoyant outdrafts produced by convective downdrafts meet moist
warm boundary layer air.
ρ 1
0
9.6.2
The Right-Moving Storm
When the environmental wind shear is unidirectional, as in the case discussed
above (see also Fig. 9.13a), the anticyclonic (left moving) and cyclonic (right
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