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4 An Electric Force Facilitator in Descending TVS
6 Forest S. Patton and Gregory D. Bothun, Department of Physics, University of Oregon
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12 Corresponding author:
13 Dr. Forest Sun Patton
14 University of Oregon
15 Department of Physics
16 Eugene, OR 97403
17 Email: [email protected]
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19 Patton 2
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20 Abstract. We present a novel explanation of the physical
21 processes behind tornadogenesis. We suggest that charge
22 separation found in supercell thunderstorms serves to condense
23 the existing angular momentum through the additional process of
24 the electric force. Based on this, we present a plausible
25 geometry that explains why many tornadoes begin at storm mid-
26 levels and build downward. We show that this geometry can
27 explain the observations that ground level tornadoes thrive in
28 regions with high shear and large convective available potential
29 energy (CAPE). A simple model based on this geometry leads to
30 rational time scales spanning from the birth of a supercell to the
31 touchdown of a tornado. We make some predictions of specific
32 measurable quantities.
33 Patton 3
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35 1. Motivation
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37 Many of the physical conditions required to initiate tornadoes are well understood on
38 a broad qualitative level but many quantitative details remain unknown. On the
39 qualitative level, it is apparent that the deep rotation of a supercell thunderstorm along
40 with a buoyant updraft and a rain-driven downdraft create a probable environment for
41 tornadogenesis. Yet, we still do not quantitatively understand the full range of energy
42 inputs which allow particular storms to spawn tornadoes while other storms with
43 similar macroscopic properties do not. Furthermore, we cannot currently predict the
44 length (minutes to hours) or intensity of the tornadoes that do form [Davies-Jones,
45 2001]. This suggests the presence of one or more physical thresholds in the system
46 that, once crossed, spawn a tornado. Systems in which the relevant threshold is not
47 achieved, therefore fail to form a tornado. As an example, evidence indicates that a
48 certain amount of boundary layer shear in conjunction with a certain level of
49 convective available potential energy (CAPE) is required for a tornado to occur
50 [Rasmussen, 1998].
51 One clear attribute is that most tornadoes spawn from supercells and associated
52 convective activity. In particular, Trapp et al. [2005] showed that 79% of all
53 tornadoes for the years 1998-2000 came from supercells. We also know that around
54 two-thirds of this 79% of supercell-spawned tornadoes begin their rotation aloft (2-7
55 km) and then descend to form ground level tornadoes in what is known as a Patton 4
56 descending “tornado vortex signature” (TVS) [Trapp, 1999]. This means that
57 roughly half of all tornadoes begin in a supercell cloud and then descend to make
58 ground level tornadoes. This further suggests the existence of a triggering
59 mechanism which we explore in this paper.
60 While current theories adequately take into account the large-scale rotation and
61 potential buoyancy associated with a supercell (see Davies-Jones et al. [2001] for a
62 review) they do not yet include any effects from the potentially massive amounts of
63 energy stored in charge separation. In this paper we link the condensation of angular
64 momentum beginning in the heart of the supercell with an electrical force that
65 naturally exists in all supercells due to charge separation. We qualitatively show how
66 this embryonic tornado structure, enhanced by its electrical properties, can lead to a
67 central downdraft that will build the condensation of rotation downward. We then
68 use a simple numerical model to demonstrate that the time scales associated with the
69 development of the tornado are similar to empirical observation (e.g. minutes). We
70 finish by showing how latent heat release and preexisting boundary layer shear in
71 conjunction with the central downdraft can lead to the formation of a stable ground
72 level tornado.
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74 Patton 5
74 2. History
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76 As the large-scale lightning/thunder associated with supercells is clearly due to
77 massive amounts of charge separation, the basic idea of charge exchange and
78 movement having some bearing on tornadic activity has precedent. Lucretius [circa
79 60 BC] and Francis Bacon [1622], observing that lightning sometimes precedes a
80 tornado, wrote about the idea. Later, Peltier [1840] and Hare [1837] independently
81 put forth theories that tornadoes are conduits for charge exchange in the atmosphere.
82 The quantitative ability to accurately measure the electrical properties of
83 thunderstorms let alone tornadoes (e.g. charge densities, charge separation length
84 scales, etc) did not exist when these theories were presented. This fact caused the
85 subsequent neglect of these theories.
86 Bernard Vonnegut [1960] revived the idea by hypothesizing that electrical heating
87 (through ohmic dissipation) might be able to sustain the intense winds observed in a
88 tornado. He conjectured that electrical heating from a continuous electrical current
89 could create temperature gradients strong enough so that air would be accelerated to
90 tornadic speeds. Cobine [1978], along with Watkins and Vonnegut, later undertook a
91 laboratory experiment which showed that a vortex discharge alone could not account
92 for total tornado wind intensity; there was simply not enough current energy density
93 in a thunderstorm to maintain the required constant arc.
94 We agree that Vonnegut’s theory is untenable due to the massive amount of
95 continuous current required to make it work. Qualitatively, however, there is
96 certainly energy associated with the electrical field in tornadoes and the conversion of Patton 6
97 that energy into other forms may be one of the triggers or threshold mechanisms that
98 spawn the tornado. The simple fact that 79% of all tornadoes come from supercell
99 thunderstorms, the largest and most intense class of thunderstorms, suggests a
100 connection. Furthermore, there are significant observations that link electrical
101 activity to tornadoes.
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103 Patton 7
103 3. Electrical Connection
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105 Numerous eyewitness accounts within the last one hundred years report various
106 noteworthy electrical phenomena associated with tornadoes including St. Elmo’s fire,
107 glowing funnel, glowing patches of cloud, etc. Church and Barnhart [1979] compiled
108 the eyewitness reports from 67 separate tornadoes between 1787 and 1975 into one
109 paper. Despite their quantity, eyewitness reports are not quantitative and therefore do
110 not provide conclusive proof of an electrical phenomenon. These eyewitnesses are
111 not trained scientists, and this provides further grounds to question their testimony.
112 The sheer number of independent reports does, however, point to some sort of
113 association between tornadoes and luminous electrical phenomena which is worthy of
114 further investigation.
115 Visual evidence and supporting eyewitness accounts of luminous electrical
116 phenomena were presented by Vonnegut and Weyer [1966]. Their evidence was a
117 nighttime picture that showed what appeared to be two glowing funnels at the
118 approximate position where a tornado passed. Eyewitnesses also reported that the
119 funnels were glowing and told of other electrical activity near the funnels. Further
120 evidence of electrical activity associated with tornadoes has been collected in
121 numerous studies in the form of electromagnetic (EM) noise called sferics (see
122 MacGorman and Rust [1998]). These high frequency emanations are traditionally
123 related to lightning and come in pulses coincident with lightning discharges. Both
124 before and during a tornado remarkably intense sferics have been observed. During
125 the lifecycle of the tornado the sferic pulse repetition rate becomes so high as to be Patton 8
126 almost constantly emitted. Sferic data suggests that in about 80% or more of tornadic
127 storms there is an increase in total sferic rates near the time of the tornado
128 [MacGorman, 1989]. Furthermore, sferics with frequencies above 1 MHz were found
129 to increase in intensity and become most extreme in the time leading up to and during
130 a ground level tornado [MacGorman, 1989]. At the very least, this suggests some
131 form of increase in total electrical activity within the system prior to and during a
132 ground level tornado. Observed radiation during tornadoes seems to indicate that a
133 semi-continuous mode of lightning is occurring. MacGorman et al. [1989] suggested
134 that the increase in the measured sferic intensities is dominated by inter-cloud
135 lightning; this is similar to what has been observed recently in what are called lighting
136 holes.
137 Lightning holes are essentially lightning free regions within supercells that have
138 been observed in association with strong updrafts (bounded weak echo regions)
139 [Lang, 2004]. They are identifiable because they occur in the deepest part of the
140 thunderstorm surrounded by vigorous lightning. In at least one case a lightning hole
141 has been found to be spatially coincident with a tornado; the lightning hole appeared
142 before tornado touchdown and became the most pronounced during the tornado
143 [Zhang, 2004]. Furthermore, the authors found that “The lightning channels of
144 inter-cloud lightning discharge exhibit clockwise rotary structures and do not have
145 clear bi-level structures in the vicinity of the tornado”. This phenomenon may
146 support a charge relaxation mechanism but is not yet well understood.
147 Overall, there seems to be appreciable evidence to indicate that there is a
148 heightened level of electrical activity associated with and in the vicinity of tornadoes. Patton 9
149 From the sferic data and the lightning hole measurements there seems to be electrical
150 activity preceding and concurrent with a ground level tornado. Other authors
151 [Vonnegut, 1960; Winn, 2000] have compiled other electrical facts not mentioned in
152 this paper. Motivated by evidence for a more direct electrical connection, we will
153 now propose a mechanism through which charged airflow leads to the organization of
154 a TVS.
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156 Patton 10
156 4. The Tornado Vortex Signature
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158 A TVS is a low resolution Doppler radar image of an embryonic or fully
159 developed tornado. This structure, which is evidence of strong axial rotation,
160 generally develops before a tornado touches down, intensifies while the tornado goes
161 through its mature stage, and dissipates as the tornado dies [Brown, 1978]. Trapp et
162 al. [1999] found that roughly half of all TVSs form aloft (median height of 4-5 km)
163 and then build downward (mode I) while the other half either start near the ground
164 and build upward quickly or form simultaneously over several kilometers of depth
165 (mode II). Both modes are precursors to ground level tornado formation but do not
166 necessarily lead to tornadoes [Trapp, 1999]. Likewise, a measurable TVS does not
167 precede all tornadoes. Davies-Jones [1986] suggested that this might be due to
168 limitations in radar resolution and/or the stringency of the automated detection
169 algorithms. For simplicity, we will concentrate on mode I formation, but will touch
170 on mode II a little as well. The charge structure of the parent cloud gives important
171 clues to the nature of these extra physics influences.
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173 Patton 11
173 5. The Supercell Mesocyclone Charge Structure
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175 Initially, local weather conditions spawn a convective supercell. The defining
176 characteristics of the supercell are large charge separations and a persistent large-
177 scale rotation known as the mesocyclone. The spatial scale of this rotation is between
178 3 and 9 kilometers in diameter [Davies-Jones, 2001] and generally extends to the
179 vertical limit of the storm [MacGorman and Rust 1998 p. 236].
180 Supercells are “charge stratified,” meaning that alternating regions of positive and
181 negative charge layers are stacked on top of each other. Stolzenburg et al. [1998b]
182 reported that supercell storms generally have 4 alternating charge layers in the strong
183 updraft region and up to 8 outside the main updraft region. In the strong updraft
184 region the lowest two layers consist of a deep (1-4 km), low-density positive charge
185 region between about 4 and 8 km above mean sea level (msl) with a shallow, dense
186 negative charge layer residing between 8 and 10 km above msl. Marshal et al. [1995]
187 were the first to report this phenomena and to note a very fast electric-field change at
188 the boundary between the lowest two regions. This electric-field anomaly, also
189 observed in charged particle measurements by Stolzenburg et al. [1998a], is evidence
190 of a highly charged bi-layer that resides at the interface between the lower positive
191 region and the main negative charge region above. Termed “benchmark charge
192 regions”, these layers were found to contain charge densities on the order of ~10 nC
193 m-3 [Marshall, 1995]. However, there are not many reliable measures of charge
194 density at this level, so the true variation around this order of magnitude of observed Patton 12
195 values is unknown. For instance, at certain times, the charge densities could be
196 significantly higher.
197 Another aspect of these “benchmark charge regions” that will become important
198 later is their temperature profile. At this level in the cloud the temperature crosses the
199 freezing point of water with cold air higher than the warm air. The temperature turns
200 over at the point of interaction between the two charge layers. The mixing of liquid,
201 ice, and graupel may be responsible for the thunderstorm’s largest charge separation
202 through the non-inductive collisional process (see MacGorman [1998] for an
203 overview). The change in overall particle composition and size within an evolving
204 thunderstorm is quite complex but also strongly suggests that there should be
205 significant evolution in charge densities as the charge carriers themselves are
206 evolving, changing size and even changing phase.
207 Consider the idealized situation: two large charge regions with a highly charged
208 bi-layer at the interface within a rotating system (Figure 1a). The rotation will tend to
209 centrifuge everything outward causing a lower-pressure region to form near the axis.
210 Let us imagine that our charged bi-layer dips downward (Figure 1b). This could
211 happen due to a downdraft, a drainage effect due to the density stratified rotating
212 system, or because this leads to a lower energy configuration of the electromagnetic
213 system. As the bi-layer deforms, the central negatively charged air sinking down
214 finds itself surrounded by positively charged rotating air. The electric force now
215 begins to draw the positively charged air inward while allowing the uncharged air to
216 filter outward. The decrease in radius leads to faster rotation through conservation of
217 angular momentum as well as a lower pressure on axis and draws the dipping Patton 13
218 negative region downward further (Figure 1c). The negative charges of the core will
219 also be drawn outward aiding the creation of a low-pressure core.
220 Another important process occurring to maintain the coherence of the nascent
221 TVS is latent heating. The lower positive region is slightly warmer than freezing
222 while the upper negative region is made up of ice particles. When the cold air moves
223 down the center and then mixes with the incoming wet air then the water will freeze
224 releasing its latent heat to the surrounding parcel of air. This heating will buoy the
225 parcel upward and out of the system. The core downdraft will be re-supplied from
226 above and the lower air has enough rotating air that can move inward to sustain the
227 exchange. This is a very similar situation to what happens at ground level as will be
228 discussed later.
229 In the positive outer sheath, particles are kept in orbit around the core by the
230 effects of the pressure gradient force, the electric force, and latent heating. Mixing of
231 the sheath and the core will occur at the boundary causing charge neutralization,
232 heating, and then removal of the mixed air from the system by being buoying upward
233 and centrifuged outward. This does not stop the charge flow. In fact, the exit of this
234 air from the system will help drive the flow because the neutralized air will be
235 centrifuged outward and upward allowing more negatively charged cold air from the
236 upper layer to descend.
237 As the negative central downdraft delves deeper into the positive region the
238 attraction of opposite charges as well as latent heating condenses the angular
239 momentum at each successive level, lowering the axial pressure, drawing down more
240 negatively charged air from above, which again condenses the angular momentum of Patton 14
241 the rotating wet positive region at the next lowest level. This runaway reaction will
242 intensify rotation and build the TVS downward. It represents a plausible threshold
243 scenario in which the amount of charge separation and water content determines the
244 rate at which the TVS can grow. As stated earlier, few electrical measurements exist
245 in this region of the storm, but it seems reasonable that charge separation densities in
246 these systems may have a large range of values. Systems with insufficient charge
247 density to induce a strong enough electrical force will fail to develop beyond their
248 embryonic stage. It is therefore beneficial to attempt to understand what this
249 threshold is in a quantitative manner.
250 Patton 15
250 6. Model and Calculations
251
252 As an ideal model, we assume a core cylinder of negative charge at the center
253 around which a sheath of positive charge rotates at a constant rate. To simplify the
254 model further, we consider a single charged particle rotating around the core at some
255 initial radius. If there were no charges on either body then the rotating particle will
256 remain in orbit around the core at the same radius due to the pressure gradient force;
257 we neglect any turbulent effects for now. With the addition of charges there will be
258 an imbalance of forces and the charged particle will be drawn inward (for the sake of
259 this estimate we assume that the core is static). The balance of forces then reduces to
260 a one-dimensional equation with axial forces:
2 2 U R q Uair ACDv 261 ma eq. 1 2H 0r 2
262 where the first term on the right is the electric force that a cylindrical volume of charge
263 has on a charged particle at some radius, and the second term is the drag force of a
264 particle moving through the air dependent on the square of its velocity. The symbols
265 refer to:
266 ¾ȡ-=the charge density in the central downdraft;
267 ¾R=the radius of the cylindrical core;
268 ¾q+=the charge on the single orbiting particle;
269 ¾m=the mass of the orbiting positive particle;
270 ¾r=the initial radius from the axis of the orbiting particle;
271 ¾İ0=the permeability of free space;
272 ¾ȡair= density of air; Patton 16
273 ¾CD=drag coefficient;
274 ¾A=the cross-sectional area of the particle;
275 ¾v=radial velocity of the particle.
276 ¾a=the observed acceleration of the particle
277 We solve for acceleration and then are able to numerically integrate twice to find
278 position as a function of time. With a time-dependent position, we can estimate the time
279 it takes for the particle to reach the outer radius of the core. We do this by starting the
280 particle from rest, calculating the instantaneous acceleration, allowing the particle to
281 accelerate at that rate for a set time step, and then recalculating the acceleration and
282 velocity. Repeatedly stepping through this routine, we track position (relative to the axis
283 of the system), radial velocity, time, and acceleration. For our model the time step was
284 set to one second; making it smaller did not change the resulting condensation time
285 appreciably. Other variables listed above were given realistic values, based on available
286 observations, and will be explained presently.
287 The highest measured benchmark charge regions from Marshall et al. [1995] were
288 13.4 nC m-3 and the inferred charge densities from measurements of a multicell severe
289 thunderstorm by Byrne et al. [1987] in MacGorman and Rust (1998 p.239) are -17 nC m-
3 -3 290 . Therefore, a core charge density of ȡ-§-10 nC m is a reasonable estimate of what
291 really occurs in a supercell.
292 The estimate of charge on our single particle is a little more difficult to make. No
293 data exist (to our knowledge) on either the size or charge of particles (water droplet,
294 hailstone, graupel, etc) within supercells near the Rear Flank Downdraft. It has been
295 shown however, that different types of thunderstorms (New Mexican thunderstorms, Patton 17
296 Mesoscale Convective Systems, and Supercells) have the same basic charge structures
297 [Stolzenburg, 1998c]. The same researchers found that highly charged layers in the weak
298 updraft region of New Mexican thunderstorms are very similar in charge density to the
299 benchmark regions found by Marshall et al [1995]. The temperature profile in both
300 storms at that layer is the same: the temperature crosses zero near the middle of the bi-
301 layer. Also, both studies indicated that the lower layer’s charge is carried on precipitation
302 particles. For these reasons we believe that the particle size and charge found on
303 individual particles in the New Mexican thunderstorm should be similar to those found in
304 analogous layers in a typical supercell; the difference in a supercell would be that the
305 spatial extent is larger and the system is rotating. Stolzenburg et al. [1998a] reported a
306 mean single positive particle charge in the layer between 6-6.6 km height (analogous to
307 Marshall et al.’s benchmark region) as being -29.3 pC. We therefore use an estimate of -
308 30 pC for the charge on our orbiting particle. Stolzenburg et al. [1998a] also report an
309 average droplet diameter of 2.1 mm. Using this diameter and the density of water, we
310 can estimate the mass of these particles (assuming a spherical shape) and use this radius
311 to find the cross-sectional area.
312 Positively charged particles will start at some radius from the axis of the supercell
313 rotation and “fall” inward to the final (core) radius. Initially we will set the beginning
314 radius to be 3000 meters (consistent with observations of large scale rotation) and we will
315 set the final radius to be 500 meters. These values are on the scale of mesocyclone
316 rotations (diameter ~6 km) and echo free central vaults (diameter ~1 km).
317 If we use these estimates of the physical parameters in combination with the force
318 balance equation derived above, we can derive a relation between core charge density and Patton 18
319 particle transit time (e.g. from 3 km to ½ km). Figure 2 shows that the time needed for
320 condensation of a charged particle, in minutes, is consistent with time scales TVSs form
-3 321 on. Also we assume ȡair=1 kg m and CD=1 (due to estimates of the Reynolds number
322 associated with our moving particle).
323 If we arbitrarily state that any angular condensation that takes more than ~15 minutes
324 will fail to develop due to turbulent dissipation then we can say that any core charge
325 densities higher than ~5 nC m-3 indicate a high probability of TVS formation and high
326 tornado danger. This statement must be tempered by the fact that supercells with a highly
327 coherent large scale rotation will be able to form TVSs on longer time scales, while more
328 turbulent cells will not remain stable long enough for the concentration of angular
329 momentum to fully mature. This indicates that there should be some parameter space in
330 which charge density and cloud rotation can predict the probability of TVS formation.
331 This is well beyond the scope of this calculation and model and is left for future
332 investigation. Overall, however, our model and calculation has returned a condensation
333 timescale that is consistent with storm timescales. This fortifies our main scientific point:
334 once the charge density reaches a critical value, there is a significant probability that
335 tornadogenesis will occur.
336
337 Patton 19
337 7. Ground-Level Tornadoes and Latent Heating
338
339 Once the nascent tornado has formed in the cloud as a TVS, the runaway process
340 explained above will build the vortex downward until either the reaction runs out of
341 energy (either rotational energy or charge separation energy) and decays, or the
342 vortex reaches close enough to the ground to tap into the massive convective
343 available potential energy (CAPE). When the vortex descends this far, the cold
344 downdraft core will mix with moist air causing immediate buoyancy of the mixed
345 parcel. It has been found that enhanced levels of CAPE, as well as boundary layer
346 shear, are present at the time of tornado formation [Rasmussen, 1998]. The CAPE
347 number represents the energy density of moist air if all the water were condensed and
348 the energy released via latent heating. Boundary layer shear is a measure of the
349 change in velocities from one radar bin to the next in the lowest 6 km of a supercell;
350 higher values indicate faster rotation. Typical values of CAPE at the ground near
351 tornadoes average 1300 J kg-3 but can be up to around 3000 J kg-3. The values of
352 boundary layer shear have been found to be around 18 m s-1 on average with a
353 maximum of 29 m s-1 [Rasmussen, 1998].
354 Introduction of a descending TVS with a cold central core (on the order of -10ºC)
355 into an area with large CAPE and sufficient boundary layer shear will form a ground
356 level tornado. If the cold air core of a TVS reaches low enough to come into contact
357 with air containing a lot of moisture then this may be a “sudden” source of energy
358 which can act as a trigger. The subsequent latent heating could occur relatively
359 immediately leading to a violent upwelling from the ground rather than from higher Patton 20
360 in the cloud. This process leads to a stable flow because the preexisting rotation of
361 the ground level air ensures that the converging air will go into orbit around the core,
362 mix with core air lowering the temperature to 0 degrees C (or below), gain heat due to
363 the release of CAPE, and then move upward quickly. This behavior allows the
364 central downdraft to remain intact while keeping the pressure at the axis of rotation
365 low enough to facilitate the continual descent of the low-pressure core. The air of the
366 cold downdraft is continually lost to mixing with the ground level air, but it will also
367 be replaced continually from the reservoir above. This geometry is stable as long as
368 both air reservoirs are not depleted.
369 This configuration can also explain the long life of single tornadoes or multiple
370 track tornadoes. If the ground level air runs out of enough CAPE to continue the
371 reaction, or the tornado entrains too much mass to rotate fast enough to maintain the
372 low pressure core, the ground level tornado can break up and ascend into the clouds
373 only to return minutes (or tens of minutes) later when more CAPE is available or the
374 rotation has simply rid itself of the debris it was carrying; the cloud level TVS never
375 stops its rotation. Assuming that charge exchange continues to fuel the TVS in the
376 cloud, the ground level tornado can persist as long as the storm continually moves
377 through areas with high ground level CAPE.
378 Another possible scenario occurs when enough ground level boundary layer sheer
379 and enough CAPE exists that the rotation may be able to create a low enough
380 pressure core to draw down cold air from above. This may spawn a ground level
381 tornado through the same latent heat release as above but without the aid of any
382 electric force. This mode of formation should be more short-lived, as it will not have Patton 21
383 the organizing effect of the electric force from the cloud above. This may be a good
384 explanation as to what happens in mode II tornadogenesis. Indeed, viable numerical
385 models have demonstrated tornado-like behavior without the presence of any electric
386 forces [Lewellen, 1997].
387
388 Patton 22
388 8. Discussion
389
390 Assuming that there is sufficient rotational energy in the pre-tornadic mesocyclone to
391 accelerate air to TVS speeds, we have presented a novel theory that suggests an electrical
392 mechanism plays a crucial role in allowing the cloud level condensation of angular
393 momentum. Cloud level TVSs would occur when enough rotational coherence is
394 coupled with the required charge separation. Through consideration of the organizing
395 role of charge density, we have outlined a plausible runaway effect for accelerating and
396 sustaining a rotating column of air building from mid-cloud towards the ground.
397 Furthermore, we have shown in a simplified model that observed charge densities lead to
398 inward forces that result in reasonable condensation time scales. We have further
399 presented a plausible explanation for ground level tornadic stability. The geometry
400 shows that latent heating can result in a hydrodynamic sink sustaining the concentration
401 of angular momentum at ground level as well as keeping the axial pressure low enough to
402 continually draw down cold air from above.
403 This ground level tornadic flow known as a “two-celled” structure (a central
404 downdraft with an upward moving outer sheath) has been suspected for many years
405 [Davies-Jones, 1986; Whipple, 1982], and stable solutions to the Navier-Stokes
406 equation with this geometry have been presented [Kuo, 1966; Sullivan, 1959].
407 Furthermore, an echo free region (i.e. free of liquid hydrometeors) at the core of
408 larger tornadoes is known to exist and has been directly observed through the use of
409 the Doppler On Wheels (DOW) [Bluestein, 2003; Wurman, 2002]. Our theory goes Patton 23
410 one-step further by plausibly explaining the development of the central downdraft and
411 TVS.
412 The suggested geometry has three specific testable attributes:
413 ¾Significant central negative charge density;
414 ¾A horizontal temperature profile above the ground with strong transition
415 regions between warm and cold air;
416 ¾ A low-pressure core;
417 The first attribute may only be testable 2-8 kilometers above the ground since as the
418 core descends its charges will migrate outward toward the sheath and neutralize.
419 Lightning holes may be evidence of this configuration but are not yet understood well
420 enough to be used as conclusive proof. The second and third attributes are more easily
421 probed near ground level. The horizontal temperature cross section of a tornado above the
422 ground will look something like Figure 3 (the levels are not meant to be exact, but
423 represent the general trends that will be observed).
424 Heated mixing regions where CAPE is being released are represented by the two
425 upward bumps and should be warmer than both the core and the ambient. The cool core
426 is at the center and should be colder than the freezing point of water. Outside of the
427 heated bumps the temperature approaches ambient conditions. The resolution of this
428 cross section is worse closer to the ground because of boundary layer turbulence. The
429 best measurement will come from a large tornado with good ground contact ensuring the
430 presence of a substantial core near the ground that sustains itself for a few minutes.
431 The third measurable parameter is pressure. Our model has a core reaching the
432 ground that is pulling air from high cloud levels where the temperature is below freezing. Patton 24
433 If this is the case, then the pressure in the core should be the same as that of where the air
434 is originating. This means that the core pressure near ground level should be less than
435 half that of the ambient ground level pressure. The pressure at the ground will be subject
436 to boundary layer conditions and therefore must be a mix of ground level and high-level
437 air. The core pressure near ground level will depend on the diameter of the tornado at the
438 ground and how well the core is screened from the ambient pressure by the rising walls of
439 the tornado. The pressure deficit will be most measurable in large long-lived tornadoes.
440
441 Patton 25
441 Acknowledgments
442
443 We thank Nikki Bowen, Dr. Brian Smith, Dr. Daniel DePonte, Dr. Alan VanDrie, and
444 Geri Infante for many discussions and support. We would like to than Dr. Winn for
445 helpful thoughts and advice. We further thank Dr. Stephen Kevan for understanding that
446 there is more to life than condensed matter physics.
447 Patton 26
447 References 448 449 Bacon, F., Natural History of Winds - Extraordinary Winds and Sudden Blasts, in The 450 Works of Francis Bacon, pp. 449, Carey and Hart, 1844, Philadelphia, 1622. 451 Bluestein, H.B., C. C. Weiss, W. C. Lee, M. Bell, and A. L. Pazmany, Mobile Doppler 452 Radar Observations of a Tornado in a Supercell near Bassett, Nebraska, on 5 June 453 1999. Part II: Tornado-Vortex Structure., Monthly Weather Review, Vol. 131 454 (Issue 12), 2968-2984, 2003. 455 Brown, R.A., L. R. Lemon, and D. W. Burgess, Tornado detection by pulsed doppler 456 radar, Monthly Weather Review, 106, 29-39, 1978. 457 Byrne, G.J., A. A. Few, M. F. Stewart, A. C. Conrad, and R. L. Torczon, In situ 458 measurements and radar observations of a severe storm: electricity, kinematics, 459 and precipitation, Journal of Geophysical Research, 92, 1017-1031, 1987. 460 Church, C.R., and B. J. Barnhart, A review of electrical phenomena associated with 461 tornadoes. Preprints, in 11th Conf. on Severe Local Storms, pp. 342-377, 462 American Meteorological Society, 1979. 463 Davies-Jones, R., R.J. Trapp, and H. B. Bluestein, Tornadoes and Tornadic Storms, in 464 Severe Convective Storms, Meteor. Monogr., pp. 167-221, Amer. Meteor. Soc., 465 2001. 466 Davies-Jones, R.P., Tornado Dynamics, in Thunderstorm Morphology and Dynamics, 467 edited by E. Kessler, pp. 197-236, University of Oklahoma Press, Norman, 1986. 468 Hare, R., On the causes of the tornado or waterspout, American Journal of Science and 469 Arts, 32, 153-161, 1837. 470 Kuo, H.L., On the dynamics of convective atmospheric vortices, Journal of the 471 Atmospheric Sciences, 23, 25-42, 1966. 472 Lang, T., L. J. Miller, M. Weisman, S. A. Rutledge, L. J. Barker III, V. N. Bringi, V. 473 Chandrasekar, A. Detwiler, N. Doesken, J. Helsdon, C. Knight, P. Hrehbiel, W. 474 A. Lyons, D. MacGorman, E. Rasmussen, W. Rison, W. D. Rust, and R. J. 475 Thomas, The severe thunderstorm electrification and precipitation study, Bulletin 476 of the American Meteorological Society, 85, 1107-1125, 2004. 477 Lewellen, W.S., D.C. Lewellen, and R.I. Sykes, Large-eddy simulation of a tornado's 478 interaction with the surface, Journal of the Atmospheric Sciences, 54 (5), 581- 479 605, 1997. 480 Lucretius, C.T., De Rerum Natura, 260 pp., E. P. Dutton, 1950, New York, circa 60 BC. 481 MacGorman, D., and W. Rust, The Electrical Nature of Storms, Oxford University Press, 482 New York, 1998. 483 MacGorman, D., D. W. Burgess, V. Mazur, W. D. Rust, W. L. Taylor, and B. C. 484 Johnson, Lightning rates relative to tornadic storm evolution on 22 May 1981, 485 Journal of the Atmospheric Sciences, 46 (2), 221-250, 1989. 486 Marshall, T.C., W. D. Rust, and M. Stolzenburg, Electrical structure and updraft speeds 487 in thunderstorms over the southern great-plains, Journal of Geophysical 488 Research-Atmospheres, 100 (D1), 1001-1015, 1995. 489 Peltier, J.C.A., American Journal of Science and Arts, 38, 73-86, 1840. 490 Rasmussen, E.N., and D. O. Blanchard, A baseline climatology of sounding-derived 491 supercell and tornado forecast parameters, Weather and Forecasting, 13, 1148- 492 1164, 1998. Patton 27
493 Stolzenburg, M., and T. C. Marshall, Charged precipitation and electric field in two 494 thunderstorms, Journal of Geophysical Research, 103 (D16), 19777-19790, 495 1998a. 496 Stolzenburg, M., W. D. Rust, and T. C. Marshall, Electrical structure in thunderstorm 497 convective regions 2. Isolated storms, Journal of Geophysical Research, 103 498 (D12), 14079-14096, 1998b. 499 Stolzenburg, M., W. D. Rust, and T. C. Marshall, Electrical structure in thunderstorm 500 convective regions 3. Synthesis, Journal of Geophysical Research, 103 (D12), 501 14097-14108, 1998c. 502 Sullivan, R.D., A two-cell vortex solution of the Navier-Stokes equations, Journal of the 503 Aero/Space Sciences, 767-768, 1959. 504 Trapp, R.J., E. D. Mitchell , G. A. Tipton , D. W. Effertz , A. Watson , D. L. Andra , and 505 M. A. Magsig, Descending and nondescending tornadic vortex signatures detected 506 by WSR-88Ds, Weather and forecasting, 14 (5), 625-639, 1999. 507 Trapp, R.J., S. A. Tassendorf, S. A. Godfrey, and H. E. Brooks, Tornadoes from squal 508 lines and bow echoes. Part 1: Climatological distributions, Weather and 509 Forecasting, 20, 23-34, 2005. 510 Vonnegut, B., Electrical theory of tornadoes, Journal of Geophysical Research, 65 (1), 511 203-212, 1960. 512 Vonnegut, B., and J. R. Weyer, Luminous phenomena in nocturnal tornadoes, Science, 513 153, 1213-1220, 1966. 514 Watkins, D.C., J. D. Cobine, and B. Vonnegut, Electrical discharges inside tornadoes, 515 Science, 199, 171-174, 1978. 516 Whipple, A.B.C., Storm, Time-Life Books, New York, 1982. 517 Winn, W.P., S. J. Hunyady, and G. D. Aulich, Electric field at the ground of a large 518 tornado, Journal of Geophysical Research, 105 (D15), 20145-20153, 2000. 519 Wurman, J., The multiple-vortex structure of a tornado, Weather and Forecasting, 17 (3), 520 473-505, 2002. 521 Zhang, Y., Q. Meng, P. R. Krebiel, X. Liu, and X. Zhou, Spatial and temporal 522 characteristics of VHF radiation source produced by lightning in supercell 523 thunderstorms, Chinese Science Bulletin, 49 (6), 624-631, 2004. 524 525 Patton 28
525 Figure Captions
526
527 Figure 1. The series shows the progression from the benchmark charge region
528 rotating (arrows with ring) with the storm (a), to a central low-pressure dip (b), and
529 finally the attraction of positive to negative resulting in the condensation of angular
530 momentum (c).
531
532 Figure 2. The time dependence of a particle to reach the core radius as a function of
533 central down draft charge density.
534
535 Figure 3. Theoretical temperature profile through the core of a tornado. (O.W.=Outer
536 Wall where water is condensed)
537 Patton 29
537 Figures
538
539
540
541
542 Figure 1
543
544 Patton 30
544
545 Figure 2
546 Patton 31
546
547 Figure 3