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:
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
9
8
5
3
1
2
7
6
4
Figure 1. Schematic of the experimental setup.

A. Y. Varaksin et al. / Natural Science 3 (2011) 907-913
909909
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 (,,)
aa
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 ()
cc
TT

 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
h

 s) and by the following values of
maximal temperature: max 500
c
T K (mode no. 3) and
max 610 c
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
h

 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
TT


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
3
Weak
180 1200 500
4 60 600 500
5 120 900 580
6
Strong
180 1200 610
240
280
320
360
400
440
480
520
560
600
0180 360540 720 90010801260

,
s
T
c
,
К
1
2

h
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
T,
K
1
2
3
4
5
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
ac
T K (mode no. 3)
and max 334
ac
T

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

,
c
T
ac
,
К
1
2

h
 c
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
T
a
,
K
1 2
3 4
5
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
c
T

K.
The largest vortices were generated at a temperature at
the surface center 570
c
T

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
h

 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
p
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
3
g
hT
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
9
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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