Houze Robert A., Jr. Cloud Dynamics

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(8.5)

8.5 Supercell Dynamics

289

which V

= - u

we obtain, according to the definition of the vertical vorticity

given in (2.56), the relation:

VxU

-"4"

In a strong vortex, (8.4) then implies that

* *

-v

(8.6)

That is, there is a dynamic pressure perturbation minimum associated with the

vortex (regardless of whether the vortex is cyclonic or anticyclonic). Another way

to look at this pressure perturbation development in the vortex is that, as the

vortex intensifies, the pressure field within it adjusts to a state of cyclostrophic

balance (2.46), which implies a pressure minimum in the center of the vortex

regardless of the sense of the rotation. Thus, strong midlevel rotation acts to lower

pressure at midlevels on each flank of the storm. The corresponding vertical

gradient of dynamic pressure perturbation then encourages updraft growth on

each flank of the storm, according to the first term on the right of (8.3). Because of

this effect, updrafts on the flanks are maintained and not choked off by downdraft

spreading.

Thus, the supercell type of thunderstorm organization is promoted by strong

environmental shear, which leads to strong midlevel vortices on the storm flanks.

The negative dynamic pressure perturbations in these vortices lead to vertical

acceleration and continual regeneration of the updrafts on the two flanks of the

storm. As the initial updraft shifts to the flanks of the splitting storm, the inflow

pattern shifts to that shown by the dashed arrows in Fig. 7.23b. This behavior

explains the quasi-steady, long-lived characteristic

the supercell, since this

vertical pressure gradient provides a mechanism for the continual regeneration of

the updraft on the flank of the storm. Since the vertical pressure gradient associ-

ated with the eddies occurs only on the flanks of the storm, and not on its leading

edge, this same mechanism also explains the splitting of the storm.

was sus-

pected for a long time that the storm splitting and propagation were in some way

caused by the precipitation-induced downdraft. However, numerical experiments

in which the precipitation is not allowed to fall also exhibit storm splitting and

continuous regeneration on the storm flanks, thus confirming that it is the vertical

pressure gradient associated with the eddies on the updraft flanks that is responsi-

ble for the splitting.

8.5.2 Directional Shear

Although storm splitting is essential to the formation of supercell storms, mirror-

image rotating thunderstorms are rare. In most of the supercell storm cases that

occur over the central United States, the right-moving storm dominates and the

left-moving member of the split is seldom observed.l'?

is easily verified by

numerical modeling that this behavior is not because of Coriolis effects.?" Rather

217 Davies-Jones (1986) found, using radar data taken at the U.S. National Severe Storms Labora-

tory in Oklahoma, that only 3 of 143 supercell storms rotated anticyclonically.

218 See Klemp and Wilhelmson (l978b).

(8.8)

290 8 Thunderstorms

it is associated with the directional shear of the wind, which up to now we have

ignored.

The effect of directional shear can be illustrated by linearizing (8.4) about a

mean velocity of

v = (ii,v,O), in which case we obtain

p; =

-2p

oS·

VHw (8.7)

where

is the horizontal gradient operator (ia/ax + ja/ay) and S is the vertical

shear of the mean horizontal wind, defined as

-n

- UI+VJ

Figure 8.20 Pressure and vertical velocity perturbations arising as an updraft in a supercell

thunderstorm interact with an environmental wind shear that (a) does not change direction with height

and (b) turns clockwise with height. The high (H) to low (L) horizontal pressure gradients parallel to

the shear vectors (flat arrows) are labeled along with the preferred location of cyclonic

(+)

and

anticyclonic

(-)

vorticity. The shaded arrows depict the orientation of the resulting vertical pressure

gradients. (From Klemp, 1987. Reproduced with permission from Annual Reviews, Inc.)

8.6 Transition of the Supercell to the Tornadic Phase

291

200

;>.

sfc

u (m 5-

Figure 8.21 Mean wind sounding (m

S-I)

in the vicinity of tornadic thunderstorms in the central

United States. The profile is an average of 62 cases. Heavy arrows indicate the direction of the shear

vector at each level labeled in millibars. The estimated mean storm motion is indicated by

(8).(Adapted

from Maddox, 1976. Reproduced with permission from the American Meteorological Society.)

The dot product 2S· VHw in (8.7) indicates that a maximum of pressure gradient

divergence (and, hence, a minimum of pressure) occurs in the zone of strong

horizontal gradient of vertical velocity on the downshear side of the updraft (Fig.

8.20a). Since the updraft (and the gradient of

w bounding it) is strongest at

midlevels, this pressure perturbation is strongest at midlevels, thus producing an

upward pressure-gradient acceleration in the lower troposphere on the downshear

side

ofthe

storm. In the unidirectional shear case, this effect induces a circulation

that reinforces inflow and overturning (Fig. 8.20a). However, it has no effect on

growth on the flanks of the storm, which has already been seen to be a nonlinear

effect. Neither side of the storm is favored.

In the part of the United States where most tornadic thunderstorms occur, the

wind shear in the storm environment is typically far from unidirectional. Normally

the hodograph exhibits "clockwise" turning of the shear, in which the direction of

the wind-shear vector (expressed in degrees from true north) increases with in-

creasing height (e.g., Fig. 8.21, from the surface to

-600

mb). In this case, the

high-to-Iow pressure gradient in the direction of the wind shear S favors growth of

the cyclonic (right-moving) member of the split, since the shear-induced vertical

gradient of pressure perturbation favors development on the south side of the

storm (Fig.

8.20b).219

This behavior is consistent with the climatological prefer-

ence for right-moving supercell storms in the United States.

219

was once thought by some that since the right-moving member of a splitting thunderstorm has

a cyclonically rotating updraft (Sec. 7.4.3), the Coriolis force might be directly responsible for favoring

the further development of the right-moving storms. Numerical-model simulations with the Coriolis

force included demonstrate, however, that this force has no significant effect (Klemp and Wilhelmson

1978b). Equation (8.7) further shows that the Coriolis force plays no direct role in determining whether

the right- or left-moving storm is favored. However, the large-scale shear S, which appears in (8.7) and

is specified as input to the model calculations, does, in reality, depend

ou f: Therefore, whether right-

or left-moving storms are favored does depend indirectly

onf.

292

8.6 Transition of the Supercell to the Tomadic Phase

The early stages of development of the supercell thunderstorm have been depicted

in Fig. 7.23 and Fig. 8.20. During these times, strong vortices (maxima and min-

ima of

0 are produced by tilting of the horizontal vorticity inherent in the environ-

mental wind shear. These processes are depicted again in Fig. 8.22a and b. In Sec.

7.4.3 we noted that, in the splitting storm, the vortex and updraft may become

collocated as a result

ofthe

combined effects of advection and tilting [recall (7.73)]

and that the rotating updraft thus formed is referred to as the mesocyclone (Fig.

8.22c). The mesocyclone, moreover, extends to low levels to a location on the

gust front (dotted line in Fig. 8.22d). The positioning of the center of the mesocy-

clone at low levels is determined by a complex combination of tilting, advection,

and stretching [i.e., all the terms in (2.59), except those involving

f, are impor-

tant]. The vorticity development at the gust front will be discussed further below.

The mesocyclone, formed between midlevels and the low-level gust front, is the

environment in which the main tornado of the supercell forms. Locating the

mesocyclone by Doppler radar is a useful method for short-term forecasting of

tornado occurrence.

In Figs. 8.9 and 8.10, the typical location of the tornado within the supercell

was seen, in plan view, to be near the leading point of the wedge of warm air

entering the storm at low levels. The schematic view of a tornadic thunderstorm

shown in Fig. 8.23 also shows this region as one of the most likely locations for a

tornado. This empirical model of storm structure near the ground includes a

second tornado location to the south as well as features labeled

FFD

and RFD,

which are the outflows of

forward-flank and rear-flank downdrafts. This schema

represents the storm after its transition to the tornadic phase. This transition

usually occurs relatively suddenly, on a scale

-10

min, after the supercell has

evolved slowly over a period of several hours. During the rapid transition, the

low-level rotation increases, the rear-flank downdraft forms behind the updraft,

and the cold outflow and warm inflow become intertwined at low levels.

Figure 8.22 Schematic of vorticity development in a supercell thunderstorm. Cloud boundary is

sketched. Precipitation is hatched. White tube represents a vortex tube. Heavy arrows are updrafts

and downdrafts. GF indicates gust front. Storms move over a horizontal surface shown in perspective.

Point 0 is fixed to the surface and is directly under the center of the cloud in (a). Storms move away

from 0 in time. Storm cross sections are in vertical planes outlined by dashed lines. In (b) a split

occurs. In (c) and (d), the two components of the storm move away from the center line of the

horizontal plane. In (c) divergence (DIY) and convergence (CONY) are indicated. In (d) the vortex at

the base of the downdraft is deleted because by this time it has been greatly weakened by the strong

divergence at low levels. The dotted line in (d) represents the center of the mesocyclone. (From Houze

and Hobbs, 1982.)

Figure 8.23 Schematic plan view of low-level structure of a tornadic thunderstorm. The thick line

surrounds the radar echo. The frontal symbol denotes the boundary between the warm inflow and cold

outflow. Low-level position of the updraft is finely stippled, while the forward-flank (FFD) and

rear-flank (RFD) downdrafts are coarsely stippled. Storm-relative surface flow is shown along with the

likely location of tornadoes. (Adapted from Lemon and Doswell, 1979. Reproduced with permission

from the American Meteorological Society.)

Figure 8.22

Figure 8.23

,------

r------::---l--

------,

: iJ((---

._--\

'B/--

"--""\

----.,..;.!---~

-- I

f : I ; I

I I I

I I ! I I I I

I _ -_1)7 :

GF __

----

GF (c )

u..---

STORMMOTION

(8.9)

294

8 Thunderstorms

Numerical simulations show that the increased vorticity at low levels induces a

minimum of pressure perturbation, according to (8.6). The low-level rotation in-

crease and tornado formation at the peak of the warm wedge (at the lower end of

the mesocyclone) are the result of a sequence of events beginning with the genera-

tion of a horizontal buoyancy gradient across the gust front separating the front-

flank downdraft and the warm sector. As discussed in Sec. 7.4.2, the buoyancy

gradient along the gust front is a source of horizontal vorticity along this gust front

to the east of the storm. The easterly relative wind in the vicinity of the gust front

advects the horizontal vorticity created along the gust front toward the center of

the storm. The remainder of the sequence of events can be understood with the

aid of Eq. (2.59), which expresses the time change of the vertical component of

vorticity.

Ifthe

Coriolis effect is ignored, (2.59) may be rewritten in Eulerian form

)

- =

-v·

(;w

71wx

(i) (ii) (iii)

where the terms on the right are the changes in the vertical component of relative

vorticity , associated with (i) advection, (ii) intensification by convergence

(stretching) of vortex tubes, and

(iii) tilting of horizontal components of vorticity

into the vertical. Once horizontal vorticity generated along the gust front is ad-

vected into the center of the storm, it is tilted into the vertical by the main storm

updraft [term (iii)]. The vertical vorticity thus created is then concentrated by the

convergence at low levels in the center of the storm to form an intense vortex

[term (ii)].

Thus, the storm's own gust front is the major source of the intense circulation

at low levels in the tornadic phase of the supercell. The horizontal vorticity

produced at the gust front is part of a positive feedback loop intrinsic to the

supercell circulation; it should not be confused with the horizontal vorticity con-

tained in the large-scale environment shear. The large-scale shear accounts for the

rotation in the upper part of the mesocyclone (upper end of dotted line in Fig.

8.22d) and is the source of rotation of the storm-wide circulation (as discussed in

Sec. 7.4.3). The latter circulation first produces a gust front, which in turn pro-

duces strong horizontal vorticity in a location where it can be advected into the

center of the storm circulation. There it is tilted and stretched to produce a more

intense low-level circulation, which constitutes the lower end of the mesocyclone

and ultimately the

tornado-when

the lower part of the mesocyclonic circulation

is sufficiently stretched by the gust-front convergence.

Numerical simulations further show that the rear-flank downdraft is a

result of

the intensified circulation at low levels.

For

many years, there was a difference of

opinion as to whether the rear-flank downdraft was the cause or an effect of the

transition of the supercell to its tornadic phase. This dispute appears to have been

resolved by modeling studies.P' which show that the increased rotation at low

levels, according to (8.6), produces a minimum of pressure at the ground. The

220 For further discussion, see Klemp (1987).

8.7 Nonsupercell Tornadoes and Waterspouts

295

resulting downward-directed vertical pressure-gradient acceleration induces the

rear-flank downdraft. Part of the diverging outflow from the rear-flank downdraft

spreads forward rapidly enough that the main updraft and its associated tornado

become cut off from the warm inflow. A new storm updraft center forms to the

south. This location coincides with the southern tornado location in Fig. 8.23. The

cutting off of the main updraft by the outflow from the rear-flank downdraft is

sometimes referred to as

"occlusion."

Since the processes that create the tornado

also lead to the rear-flank downdraft and the cutting off of the main updraft from

its source of warm air, the tornado is usually associated with a weakening super-

cell updraft.

After the old updraft is cut off and the new one forms, all the processes can

repeat, with new updraft, new tornado, and new rear-flank downdraft. Repetition

of these processes can lead to sequences of tornadoes, as indicated in Fig. 8.24.

8.7 Nonsupercell Tornadoes and Waterspouts

So far we have considered only tornadoes that occur in the context of supercell

thunderstorms. A large number of intense vortices that form in association with

cumulus congestus or developing cumulonimbus are not of the supercell variety.

Over water these usually take the form of waterspouts. Generally, these vortices

are weak in comparison to a supercell tornado. However, especially over land,

vortices associated with nonsupercell convective clouds can occasionally reach

tornado strength and be quite damaging. An empirical model of the life cycle of a

nonsupercell tornado over land is shown in Fig. 8.25. This type of tornado occurs

when a developing convective cloud is located above a spot of intensified local

vertical vorticity in the boundary layer. Often these local maxima of boundary-

layer vorticity are found along convergence lines in the boundary layer, as indi-

cated at points A, B, and C in Fig. 8.25. The same convergence line may provide

the uplift for convective cloud development. However, the cloud may develop for

other reasons and simply became located over the convergence line. Also, the

boundary-layer vorticity maximum could be produced at other types of locations.

For

example, it might be topographically produced.P' Regardless

ofthe

origins of

the cloud and the boundary-layer vorticity maxima, once a developing cloud and a

vorticity maximum become vertically aligned, tornado development can occur, as

shown in Fig. 8.25c at location C. The mechanism of development is thought to be

vortex stretching [i.e.,

term (ii) in (8.9)]. Strong convergence, and hence

stretching, occurs between the strong updraft at cloud base (where

W - 1-10 m

S-I)

and the ground (where W = 0). The tornado formed in this manner is observed

221 On 9 April 1991, a nonsupercell tornado occurred over the coast of Puget Sound, near Silver-

dale, Washington.

appears that this tornado occurred when boundary-layer vorticity was produced

by flow around steep jagged terrain along the coastal area (Colman, 1992).When a developing cumulus

congestus or small cumulonimbus cloud moved over this region of boundary-layer vorticity, the

tornado developed and was seen from the Atmospheric Sciences-Geophysics Building at the Univer-

sity of Washington.

C~~f

(fj;j-

""7

Figure8.24 Conceptual model of the evolution of the mesovortex core (L) of a tornadic supercell

thunderstorm. Thick lines show gust-front position. Shaded areas are tornado tracks. Inset shows the

tracks of the tornadoes

(T"

, T

)

associated with successive mesovortex redevelopment. Small

square is the region expanded in the main figure. (From Burgess et al., 1982. Reprinted with

permission from the American Meteorological Society.)

Figure8.25 Empirical model of the life cycle of a nonsupercell tornado over land. The black line is

a radar-detectable convergence zone in the boundary layer. Low-level vortices are labeled with letters.

Open arrows indicate air motion. Clouds are sketched. (From Wakimoto and Wilson, 1989. Reprinted

with permission from the American Meteorological Society.)

8.8 The Tornado

297

to build upward from the ground until it establishes a connection to cloud base.

This behavior is also observed in dust devils, which appear to differ from the

model in Fig. 8.25 only in that they form in connection with dry thermals instead

of cloud updrafts.

The mechanism depicted in Fig. 8.25 requires no dynamical attribute of the

cumulus cloud other than its updraft. The vortex originates in the boundary layer

independent of the cloud. However, as is evident from our previous discussions of

the vorticity in convective clouds (Sec. 7.4.3, Sec. 8.5, and Sec. 8.6), vortices that

result from tilting of environmental horizontal vorticity into the vertical [term (iii)

in (8.9)] are typically present in the vicinity of the cumulus updraft (Fig. 7.23). As

a result of advection and/or stretching [terms

(i) and (ii) in (8.9)], it is possible for

the updraft to become collocated with one of the vorticity maxima. One example

of this collocated updraft vortex is the mesocyclone of the splitting storm, de-

scribed by (7.73).

Just

as the mesocyclone of the supercell forms a favorable

environment for tornado formation, so could a rotating updraft in a smaller con-

vective cloud. If the updraft in the cloud of Fig. 8.25 were rotating, it would

provide another source

vorticity for a tornado-like vortex, in addition to inde-

pendently existing boundary-layer vortices, such as those depicted along the con-

vergence line in Fig. 8.25. Convergence, such as that along the convergence line,

would concentrate the vorticity of the rotating updraft, possibly into a narrow

tornado-like vortex extending below cloud base. This type of explanation has been

offered for the development of waterspouts from cumulus congestus or small

cumulonimbus clouds over an ocean surface (Fig. 8.26). Waterspouts tend to form

in the vicinity of gust front outflows from nearby convective rain showers. The

strong convergence at the gust front is envisaged to concentrate the vorticity of a

rotating updraft into a narrow waterspout vortex.

The difference between Fig. 8.25 and Fig. 8.26 is that in the former the conver-

gence line provides the vorticity and the cloud provides the convergence for the

stretching [term (ii) in (8.9)], while in the latter the convergence line (gust front)

provides the convergence while the cloud provides the vorticity for the stretching.

Either process is feasible, and which is dominant probably has to be evaluated on

a case-by-case basis.

Waterspouts appear to occur in clouds whose circulations resemble qualita-

tively the air motions in supercell storms. The airflow below clouds producing

waterspouts disrupts the structure of the ocean surface in such a way that tracers

of the air motions can be seen from a distance as shading on the water. An

empirical model of a developing waterspout, its accompanying low-level flow, and

the pattern of shading on the ocean is shown in Fig. 8.27 and Fig. 8.28. The

proximity of the waterspout funnel to a nearby rain shower is seen in Fig. 8.27.

The

"shear

band"

indicated in both figures is a windshift line that is the analog of

the gust front and flanking line of the supercell seen Figs. 8.9, 8.10, and 8.23. The

waterspout vortex in Figs. 8.27 and 8.28 is also in a similar location to the super-

cell tornado in Figs. 8.9, 8.10, and 8.23. The scales and intensities of all of the flow

features in the case of the waterspout, however, are much reduced in comparison

to the supercell storm.

298 8 Thunderstorms

8.8 The Tornado

8.8.1 Observed Structure and Life Cycle

The structure of a supercell tornado observed at several stages of its life cycle is

illustrated schematically in Fig. 8.29. The

organizing stage was characterized by a

visible funnel touching the ground intermittently, though the damage path was

continuous. In the

mature stage, the tornado was largest. In the shrinking stage,

the entire funnel decreased to a thin column. The decaying stage was character-

SEA

SURFACE:

SPtML

STAGE

Figure 8.26

250

750

500

1000m

, I

I I

\: LONGER

/FUNNEL

I,'

/1~XWi~~E

, COLUMN

I 1

Figure 8.27 Figure 8.28