Supercells - Severe Convective Storms and Tornadoes: Observations and Dynamics - page 163

gradients ((2.63) and (2.70)) begin to play a significant role and affect the location
and intensity of vertical accelerations. In this chapter we will consider what this
threshold is and how the behavior of convective storms is modified by dynamic
vertical perturbation pressure gradients. For a restricted range of environmental
conditions (vertical shear and potential buoyancy, the latter represented by
CAPE) a convective cell (storm) that is relatively long lived, three dimensional, has
a rotating updraft (vertical vorticity is correlated with vertical velocity), and is
quasi-steady can form. In these storms, ''supercells'', some of their behavior and
dynamics are identical to that of ordinary-cell/multicell storms, but the unique
aspects of the supercell are a result mainly of the effects of strong (deep) vertical
shear. While both ordinary cells and supercells can produce severe weather,
including tornadoes, supercells are more prolific in terms of inflicting damage and
often the most damaging. In short, supercells are relatively long lived and have a
rotating updraft, while ordinary-cell/multicell storms are not long lived and do not
have a rotating updraft.

4.1 SUPERCELLS AND THE BULK RICHARDSON NUMBER

We now consider under what restricted range of environmental conditions (vertical
shear and potential buoyancy—CAPE) an isolated convective cell (storm) can
develop into a supercell. To do so, we first consider the frictionless, vertical equa-
tion of motion in terms of buoyancy and the dynamic and buoyancy vertical
perturbation pressure terms (2.70)
Dw p 0 d =@ p 0 b =@ = Dt ¼ 1 = @ z þ½ð 1 = Þ@ z þ B ð 4 : 1 Þ

Suppose that the vertical dynamic perturbation pressure gradient term

p 0 d =@ = ð 1 z Þ is approximately the same magnitude as the inertial term on the

LHS of (4.1), and also the same order of magnitude as the ''effective'' buoyancy
term ( ½ð 1

@

p 0 b =@ z þ B ). If the aspect ratio of the buoyant air parcel in the

storm is on the order of unity, then it follows from (2.75) that
j Dw

= Þ@

2 Þ
where W is the scale of vertical velocity; H is the vertical scale (the depth of the
tropopause, which is the typical vertical scale for deep convection); and the advec-
tive time scale is H

= Dt j W =ð H = W Þ B = 2 ð 4 :

= W. (For a spherical bubble, our analysis showed that the

2

RHS of (4.2) is

3 B, cf. (2.133); if water loading is considered, then the factor
multiplying B on the RHS of (4.2) is even less, so a factor of

1
2

is reasonable.)

Then

B 2W 2

= H ð 4 : 3 Þ

From (3.7) and the above, it is seen that when the LFC is not too high,
W 2

1

2 BH 2 CAPE

ð 4 : 4 Þ