Tornado-like non-stationary vortices: experimental modelling under laboratory conditions

doi:10.4236/ns.2011.311116

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Vol.3, No.11, 907-913 (2011) Natural Science

http://dx.doi.org/10.4236/ns.2011.311116

Tornado-like non-stationary vortices: experimental

modelling under laboratory conditions

Aleksei Y. Varaksin*, Mikhael E. Romash, Viktor N. Kopeitsev

Joint Institute of High Temperatures, Russian Academy of Sciences, Moscow, Russia; *Corresponding Author: [email protected]

Received 16 September 2011; revised 20 October 2011; accepted 30 October 2011.

ABSTRACT

The purposes of the paper are threefold: 1) to

show the fundamental possibility of physical

simulation of non-stationary wall-free concen-

trated air vortices (called here as tornado-like

vortices) under laboratory conditions without

using of the mechanical rotation, 2) to find the

heating rates of underlying surface and air tem-

poral and spatial temperature shear which lead

to the stable genesis of wall-free vortices, and 3)

to investigate the some parameters of the pro-

cess of generation of vortices and their char-

acteristics. The wall-free vortices were gener-

ated over underlying surface of aluminum sheet

due to its controlled heating from below as a

result of development of unstable stratifycation

of air.

Keywords: Vortex Flows; Tornado-Like Flows;

Physical Simulation

1. INTRODUCTION

As a global phenomenon, tornadoes have been re-

ported in many countries in the world, such as Australia,

Austria 1, Bermuda Islands, Britain 2, Canada, China,

England, France, Germany 3, Holland, Hungary, India,

Italy 4, Lithuania 5, Russia, Japan 6 and many oth-

ers. However, they are most frequent in spring and

summer during the late afternoon on the central plains

and in the South-Eastern states in the United States.

Each year an average of a thousand tornadoes are re-

ported in the United States.

Compared with other storms in the nature, a tornado is

the most violent one. It is estimated that tornadoes cause

about one billion dollars of damage per year in the

United States. Additionally to destroying everything on

its path the tornadoes lead to the human fatalities 7,8.

Some words about tornado study methods. The first

method to be introduced is tornado-chasing. Tornado-

chasing has become an important activity for many sci-

entists and weather enthusiasts to observe the tornado

dynamics and collect the data about real tornadoes. The

tornado videos recorded by tornado chasers offer us fur-

ther understandings about its appearance and formation.

Unfortunately, due to the difficulties to put the data re-

cording equipments into the tornado path, the real data

collection for tornado’s internal dynamics study is still

not much successful today. Tornado-chasing has great

disadvantage connected with significant risk for chaser’s

live during tornado observation.

Instead of chasing tornadoes, on the other hand, satel-

lite and radar images are also used to understand the

flow dynamics of tornadoes. But the cost is high in order

to build enough satellites and radars to monitor torna-

does.

Turbulent and vortex flows (including “bubble-type”

vortex) bounded by the walls are formed by way of tan-

gential nozzle delivery of medium, application of me-

chanical swirling devices (ventilators 9,10, guide swirl

vanes, screws, internal spiral ribbing, and the like), and

intensive rotation of body elements of channels (rotating

tubes, tables 11, tanks 12,13, rotating screen 9, and

the like). For the experimental and numerical studies in a

closed cylinder, techniques employed include small ro-

tating disk 14,15, rotating end wall 16, corotating end

walls 17,18 , counter-rotating end walls 19, independ-

ently rotating a small central rod 20, and the others.

In earlier work by Ward 9 the apparatus produced an

adjustably convergent airflow through a fine mesh cy-

lindrical wire screen, 8 ft in diameter, which imposes

controlled angular momentum by its rotation around the

perimeter. The convective flow was created by a vari-

able speed exhaust fan with the pressure deficit distrib-

uted over the top of the convective chamber, 6 ft in di-

ameter and 3 ft high. At the top of the chamber the air

passed through a relatively fine mesh honeycomb mate-

rial which effectively removed the tangential component

from the flow.

In 10 the experimental setup represented a closed

chamber having the shape of a parallelepiped with trans-

A. Y. Varaksin et al. / Natural Science 3 (2011) 907-913

908

parent walls made of organic glass. Rectangular plate

with central hole was mounted on the upper lid from

inside with some gap. The air was pumped out of the

chamber by a centrifugal ventilator (with propeller

driven by electric motor) via the central hole in plate and

directed back toward walls of the chamber via the gap

between the plate and the lid. The exit from the gap was

partly blocked so that air passed through a system of

directing pads with vertical axes arranged on the sides of

a rectangle symmetrically relative to centers of these

sides. The rotation of the pads by some angle about their

axes imparted a circular motion around the vertical axis

of the chamber to the flux outgoing from the gap.

The mentioned above vortex flows are convenient for

detailed experimental description; however, their char-

acteristics and, especially, behaviour may significantly

differ from the parameters of real vortex structures ob-

served in Earth atmosphere.

The study of wall-free concentrated (the vorticity is

localized in space) vortices is complicated by a number

of reasons such as spontaneity of formation, space-time

instability, practical impossibility of controlling the char-

acteristics, and so on. The difficulties identified above

account for the apparent absence of experimental studies

producing results in stability and dynamics of wall-free

concentrated vortices, which could be used for verifying

mathematical models 21-24.

In this paper we use the simple experimental setup al-

lowing to make controlled heating of aluminum plate top

surface (called here as underlying surface) and to gener-

ate the wall-free non-stationary swirl structures (called

as tornado-like vortices) over the plate due to the unsta-

ble air stratification (the warm air near the top surface

and the cold air over him). It is strictly emphasized that

in contrary of previous studies no mechanical rotation

devices and/or underlying surface rotation were used for

the vortices generation.

The paper is organized as follows. Section 2 presents

the description of experimental setup, measurement

procedure and principal parameters of thermal modes

employed for generation and study of the characteristics

of air vortices. In Section 3, the results of underlying

surface and air temperature measurements are given.

Section 4 is devoted to describing the information (ob-

tained by visualization) about the process of generation

of vortices and their characteristics. In Section 5 we gen-

eralize the different thermal modes by use of dimen-

sionless parameter, i.e. Rayleigh number. A conclusion

of the work is given in Section 6.

2. EXPERIMENTAL SETUP AND

MEASUREMENT PROCEDURE

The experimental setup is schematically shown in

Figure 1. It was located in a room with floor 1 6 by 6 m2

in area and ceiling 2 3.3 m high at a distance of 0.5 m

from one of walls 3. The experimental setup included a

deck 4 0.35 m high with three legs 5. The horizontal

surface of the deck 4 was a sheet of aluminium (Grade

D16AM) 1100 mm in diameter and 1.5 mm thick. The

top (underlying) surface of the aluminum sheet was

blackened with heat-resistant paint. Placed under the

deck was an electrically ignited gas burner 6 of maximal

thermal power of 3.5 kW. The diameter of flame 7 of the

burner was varied (for different modes of thermal power)

from 200 to 300 mm. A liquefied propane-butane mix-

ture required for the operation of the gas burner was

placed in a 27-liter vessel 8.

This experimental setup makes possible the controlled

heating of the underlying surface of aluminium sheet,

which leads to the generation of unsteady vortex struc-

tures 9 as a result of development of unstable stratifica-

tion of air. The vortex structures being formed were visu-

alized using tracer particles (micrometer-sized particles of

magnesia, chemical formula 4MgCO2Mg(OH)24H2O) or

vapour of special easily-boiling fluid (VDLSL5, Velle-

man company, Belgium) which were applied in a thin

layer onto the underlying surface prior to experiments.

A digital video camera (Sanyo VCC-6572P) was used

for video filming of vortices being generated.

An infrared thermometer (AZ8868) was used for

measuring the temperature of the underlying surface of

the sheet. The measurements of air temperature over un-

derlying surface were made by using of chromyl-alu-

mele thermocouples. The underlying surface temperature

measurements (along the radius) were performed at six

points with coordinates r = 0, 100, 200, 300, 400, and

Figure 1. Schematic of the experimental setup.

A. Y. Varaksin et al. / Natural Science 3 (2011) 907-913

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500 mm (r is the distance from the sheet centre). The air

temperature measurements were produced at the same

points of horizontal direction and at the different coor-

dinates y = 50, 100, 200 and 300 mm (y is the distance

from the sheet surface in the vertical direction).

Also monitored in the course of experiments was the

air temperature in the room. The initial (prior to experi-

ments) difference between the air temperature on the

level of underlying surface T1 and the vicinity of the

room ceiling T2 was ΔT = T2 – T1  1˚C. The maximal

increase in the air temperature in the vicinity of the ceil-

ing after a single experiment in one thermal mode (see

below) reached a value of ΔT



3˚C - 4˚C. Further ex-

periments were performed after complete “cooling off”

of the room to initial values of temperature.

The Table 1 gives the principal parameters of thermal

modes employed for generation and study of the charac-

teristics of air vortices.

3. UNDERLYING SURFACE AND AIR

TEMPERATURE MEASUREMENTS

The dependences of temperature on the radius of un-

derlying surface and a time in different modes were ob-

tained as follows: 1) monitoring of the “inadequate

heating” of the surface by way of measuring T = T(r) =

const; 2) switching on the gas burner; 3) heating of the

underlying surface during time h



(see Table 1) for

obtaining the distribution of (, )TTr



; 4) switching

off of the gas burner; 5) cooling of the underlying sur-

face during time c



(see Table 1) for obtaining the

distribution of (, )TTr



. The dependences of air tem-

perature on the horizontal and vertical directions and a

time (,,)

TTry



 were received by similar procedure.

Examples of the thus obtained distributions for se-

lected thermal modes are given in Figures 2-5.

Figure 2 gives the dependence of temperature at the

center of underlying surface on time ()



 for two

modes (no. 3 and 6). One can see from the data given in

the figure that these modes are characterized by the same

heating time (180



 s) and by the following values of

maximal temperature: max 500

T K (mode no. 3) and

max 610

T K (mode No. 6).

The temperature distributions along the radius of un-

derlying surface for mode no. 6 under heating are given

in Figure 3. Some decrease in temperature in the central

region of underlying surface (r < 100 mm), observed for

short times of heating (120



 s), is attributed to the

structural features of the employed gas burner.

Figure 4 gives the dependence of air temperature at

the center of underlying surface on time ()

ac ac





for y = 50 mm over surface for two modes (no. 3 and 6).

One can see from the data given in the figure that these

modes are characterized by the following values of

Table 1. Principal characteristics of experimental modes.

No. Mode of

heating

Heating time

τh, s

Cooling time

τc, s

Maximal temperature

Tcmax, K

1 60 600 420

2 120 900 470

Weak

180 1200 500

4 60 600 500

5 120 900 580

Strong

180 1200 610

240

280

320

360

400

440

480

520

560

600

0180 360540 720 90010801260



c

Figure 2. The temperature at the center of underlying

surface as a function of time: 1—mode No. 3; 2—mode

No. 6.

250

300

350

400

450

500

550

600

0100200 300 400500

rmm

Figure 3. The temperature as a function of the radius

of underlying surface and of time under heating (mode

no.6): 1—τh = 0; 2—τh = 30 s; 3—τh = 60 s; 4—τh =

120 s; 5—τh = 180 s.

maximal air temperature: max 315

T K (mode no. 3)

and max 334



K (mode no. 6).

The air temperature distributions along the radius of

A. Y. Varaksin et al. / Natural Science 3 (2011) 907-913

910

underlying surface for mode no. 6 under heating are

given in Figure 5. It is clearly seen, that the air tem-

perature distributions are not uniform. The maximal air

temperature shear is realized in a circular region (150

mm < r < 250 mm), i.e. in the same region of abrupt rise

of underlying surface temperature gradient (see Figure

3). Some increase in air temperature in the peripheral

region (r > 400 mm), is attributed, probably, to the exis-

tence of upstream flow of warm air from bottom part of

aluminum sheet due to gas burner operation.

4. VORTEX PARAMETERS STUDY BY

VISUALIZATION

The video filming and use of tracer (magnesia) and

vapour particles made it possible to visualize the vortex

structures arising above the underlying surface.

Frame-by-frame analysis (see Figure 6) of video re-

280

290

300

310

320

330

340

0180360 54072090010801260



Figure 4. The temperature of air as a function of time

(y = 50 mm, r = 0): 1—mode No. 3; 2—mode No. 6.

280

300

320

340

0100 200 300400500

rmm

1 2

3 4

Figure 5. The temperature of air as a function of the

radius of underlying surface and of time under heating

(mode no.6), y = 50 mm: 1—τh = 0; 2—τh = 30 s; 3—

τh = 60 s; 4—τh = 120 s; 5—τh = 180 s.

cords in different thermal modes (see Table 1) enables

one to obtain information about the following parame-

ters of the process of generation of vortices and their

characteristics: 1) the values of underlying and air tem-

peratures, at which the vortices are generated; 2) the

region of underlying surface, where the vortices are

generated; 3) the direction of rotation of vortex structure;

4) the number of vortices observed per experiment; 5)

the trajectory of travel of the base of vortex structure; 6)

the length of the trajectory of the vortex base; 7) the ve-

locity of travel of the vortex base; 8) the lifetime of vor-

tex structure; 9) the visible height of vortices; 10) the

visible diameter of vortices, and others.

Repeated experiments in different thermal modes gave

rise to the following inferences. A stable generation of

vortices was observed in all modes except for mode no.

1 (see Table 1). Vortex structures began to form in the

mode of heating of the underlying surface after the tem-

perature at its center reached a value of 470



The largest vortices were generated at a temperature at

the surface center 570



K. Vortex structures were

largely generated in a circular region (150 mm < r < 250

mm), i.e. in the region of abrupt rise of temperature gra-

dient. The preferable direction of rotation of vortices

was not observed. Up to ten vortex structures were ob-

served per experiment. Three types of trajectories of

motion of vortex base were identified. The majority of

vortex structures moved along spiral trajectories (trajec-

tories of the first type) within the circular region (150

mm < r < 250 mm) in which they were generated. Some

vortices moved in fact along the shortest, almost recti-

linear trajectories (trajectories of the second type) from

the region of their generation to the edge of underlying

surface where they disintegrated. Some vortices pro-

duced the wake in a form of “circle” (trajectories of the

Figure 6. A typical frame (negative) with a registered vortex

(mode No. 6); magnesia particles visualization, the image size

is 1.0 by 0.75 m.

A. Y. Varaksin et al. / Natural Science 3 (2011) 907-913

911911

third type). As a rule, such wakes were left by shortest-

lived vortices at a short time of heating of underlying

surface (120



 s).

The maximal length of trajectory of the base of vortex

structures was 60 - 100 cm with the time-averaged ve-

locity of travel of 2 - 20 cm/s. The limiting lifetime of

observed vortices was about 40 s. The maximum visible

height of generated vortices could be 2 m, and their

maximal visible diameter—0.2 m.

In the case of operation in “softer” modes (no. 2 and 3)

the geometric dimensions of observed vortices were

smaller and their lifetime was shorter than those in the

case of operation in “hard” modes (no. 4, 5 and 6).

The typical experimentally observed vortex structure

is given in a Figure 7(a) for the purpose of detailing its

basic parts (vortex core, peripheral region, vortex cas-

cade). Given in Figure 7(b) for comparison is a photo-

Vortex cascade (large particles

repulsed by centrifugal forces)

“Fork” (gives an idea of the

diameter of vortex core)

Peripheral

region

(left-handed

upward

motion of

articles)

(a)

(b)

Figure 7. Photographs of vortex structures: (a) frame with

recorded wall-free vortex (negative), 1.68 s after initiation,

(mode No. 6, magnesia particles visualization, the image size is

0.66 by 0.41 m); (b) air tornadoes in northern Lincoln County,

Washington (photographer Dawn Nelson, www.wrh.noaa.gov/

otx/photo_gallery/Jun6_Creston_tornadoes.php).

graph of real air tornadoes on June 6, 2009 in northern

Lincoln County, Washington. Initially only one tornado

was visible, but it appeared to split into two twisters.

The typical observed frames in the operation in “soft”

mode no. 3 by using of vapour particles are demon-

strated in Figures 8(a) and (b). Repeated experiments

show clearly, that the development of vortex structures

was as follows. Initially, the region with decreased

pressure is forming due to intensive air rotation (see

Figure 8(a)). The vapour particles concentrated in this

region and formed the vortex tube which is characterized

by up- stream air flow. Such vortex tube is an analog of

main stage of slender tornado 24. In case of weakening

of upstream flow the pressure is increased. Thus the

vortex tube during final stage becomes more thinner and

more curve and then its discontinued (see Figure 8(b)).

The mechanism described above is in agreement with

majority of real tornado descriptions and available pho-

tographs (see Figure 9).

(a)

(b)

Figure 8. Typical frame with vortex tube in (a) main stage, (b)

final stage (vapour visualization): 1—edge of underlying sur-

face; 2—vapour; 3—air vortex.

A. Y. Varaksin et al. / Natural Science 3 (2011) 907-913

912

(a)

(b)

Figure 9. Photographs of real tornado in Kansas during (a)

main stage, (b) final stage. (photographer Lanny Dean, www.

photolib.noaa.gov).

So, conducted experiments allowed to make the fol-

lowing important conclusion. In the case of operation in

“softer” modes (no. 2 and 3) the geometry of observed

vortices was the same with the structure of slender

(smooth) tornadoes, while in the case of operation in

“hard” modes (no. 4, 5 and 6) the observed vortices were

similar with fat (rough) tornadoes.

5. RAYLEIGH NUMBERS

The received distributions of underlying surface and

air temperature (see Section 3) allowed to find the values

of dimensionless number, i.e. Rayleigh number, for dif-

ferent thermal modes. This Rayleigh number has the

form

Ra a







.

Here, g is acceleration of gravity, h is the characteris-

tic distance in vertical direction where the temperature

difference exists, β is coefficient of volume expansion,

ΔT is the temperature difference (between underlying

surface and surrounding air) causing the convection, v is

the coefficient of kinematic viscosity, a is the thermal

diffusivity.

For the estimations, we take h, as the distance from

underlying surface in vertical direction to the place

where the air temperature exceeds the surrounding tem-

perature only for 10 K. The values of β, v and a were

taken for parameters of surrounding air.

Figure 10 gives the time dependence of Rayleigh

number at the centre of underlying surface for all six

operating thermal modes. A stable generation of vortices

was observed in all modes except for mode no. 1. There-

fore the Rayleigh number 7

10Ra  may be taken as a

minimal value at which the vortex structures began to

form. The largest vortices were generated in case of op-

eration in modes no. 5 and 6, which corresponds to

10Ra . There are two horizontal lines in Figure 10,

which correspond to 7

10Ra  and 9

10Ra  respect-

tively. By using these lines it is easy to define the time

of existence of relatively small (79

10 10Ra) and

large vortices (9

10Ra ) for the different operation

modes. Received ranges of Rayleigh number are in good

agreement with the experimental data on vortices gen-

eration on modes of heating and cooling of underlying

surface.

6. CONCLUSIONS

Some experimental results are given of observation of

wall-free concentrated air vortices (called here as tor-

nado-like vortices) under laboratory conditions without

application of mechanical swirling devices. It was found

Figure 10. Rayleigh numbers as a function of time for different

thermal modes; r = 0:1—mode No. 1; 2—No. 2; 3—No. 3;

4—No. 4; 5—No. 5; 6—No. 6.

A. Y. Varaksin et al. / Natural Science 3 (2011) 907-913

913913

the heating rates of underlying surface and air temporal

and spatial temperature shear which lead to the stable

generation of wall-free vortices. Video filming, as well

as the use of tracer (magnesia or vapour) particles were

used to visualize and to investigate qualitatively the dy-

namics and some integral parameters of vortices which

arise over heated underlying surface as a result of unsta-

ble air stratification.

In our opinion, further progress in studying the prob-

lems associated with generation, stability, and dissipa-

tion of vortex structures with a view to explaining a

number of natural phenomena (tornadoes, typhoons,

storms) will be based on the concept of two-phase nature

25,26 (the presence of droplets and solid particles) of

the atmospheric processes referred to above.

7. ACKNOWLEDGEMENTS

This study was supported in part by the programs for basic research

of the Division of Energetics, Machinery, Mechanics, and Control

Systems of the Russian Academy of Sciences on “The Investigation of

Fundamental Problems in Combustion and Detonation in Power Engi-

neering” and “Physicochemical Mechanics of Nonequilibrium Sys-

tems” and by the Russian Foundation for Basic Research (grant no.

11-08-00591).

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