THEORETICAL AND EXPERIMENTAL MODELLING OF INTENSIVE ATMOSPHERIC VORTICES

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Warwick Turbulence Symposium Workshop "Environmen
tal Turbulence from Clouds through the
Ocean" March 13-17, 2006
THEORETICAL AND EXPERIMENTAL MODELLING OF
INTENSIVE ATMOSPHERIC VORTICES
Galina Levina1,2 1 Institute of Continuous
Media Mechanics UB RAS, Perm 2 Space Research
Institute RAS, Moscow Financial support Russian
Foundation for Basic Research NN 03-05-64593,
04-05-64315 International Science and Technology
Center, Project 2021
THE AIM OF THE INVESTIGATION Theoretical,
laboratory and numerical modelling
is intended to study large-scale intensive
vortices formation in the atmosphere and
physical mechanisms involved in the
cyclogenesis
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OUTLINE

• 1. Motivation
• 2. Large-scale a-like instabilities.
• 3. Turbulent vortex dynamo in convectively
  unstable fluid.
• 4. Theoretical model. Mean-field equations.
• 5. Numerical simulation of helical-vortex
  convection
• - helical-vortex effects in Rayleigh-Bénard
  convection with large aspect
• ratio.
• Parameterization of helical convective turbulence
  for numerical
• meteorological models.
• 7. A way to examine the hypothesis of turbulent
  vortex dynamo in simulation
• of tropical cyclogenesis.
• SUMMARY

Experimental Modelling --- poster
LARGE-SCALE SPIRAL VORTEX DRIVEN BY LOCAL
HEATING IN A SLOWLY ROTATING TURBULENT
FLUID G.P. Bogatyryov, V.G. Batalov, P.G. Frick,
I.V. Kolesnichenko, G.V. Levina, and A.N.
Sukhanovsky
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Large-Scale Alpha-Like Instabilities in Turbulent
Media
Origin

• Specific properties of small-scale turbulence
  displaying a symmetry break
• Helical Turbulence generated by pseudovector
  forces magnetic, Coriolis force fields
• Alpha-Effect in Magnetohydrodynamics
  Steenbeck, Krause, and Rädler (1966)
• Helical-Vortex Instability in non-MHD
  Hydrodynamics
• Moiseev, Rutkevich, Sagdeev, Tur, Khomenko, and
  Yanovsky (1983-1988)
• Turbulent Vortex Dynamo in the Moist Atmosphere
  Kurgansky (1998)
• Anisotropic Turbulence lacking parity-invariance
  generated by a special forcing
• Anisotropic Kinetic Alpha (AKA) Effect
• illustrated by full simulation in 3D Frisch,
  She, and Sulem (1987)

Examples
Turbulent helicity evidence
The first measurements in the atmospheric
boundary layer B. Koprov, V. Koprov, V.
Ponomarev, O. Chkhetiani (2005)
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DRY VORTICES VOLUMETRIC HEATING BY HOT
SOLID PARTICLES
TURBULENT VORTEX DYNAMO THEORY
Gives a threshold for the large-scale vortex
instability
Results in suggesting the generation of positive
feedback between the horizontal
and vertical circulation Condition for
non-zero dynamo-effect in a convectively unstable
rotating fluid volumetric heat release
additionally to the heating from below
Rutkevich (1993),
Kurgansky (1998)
MOIST VORTICES VOLUMETRIC HEATING BY
LATENT HEAT RELEASE
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TURBULENT VORTEX DYNAMO IN CONVECTIVELY UNSTABLE
FLUID MEAN-FIELD EQUATIONS Space Research
Institute, Moscow Moiseev et al. , Rutkevich
(1983-1993)
C characterizes the intensity of helical
feedback and depends on rotation O and internal
heat release intensity B, and characteristics of
small-scale convective turbulence

• With the helical feedback introducing (C?0)
• C-terms generate a new instability,
• there exists a threshold of instability,
• feedback enhancing results in the threshold
  decrease and
• horizontal dimensions of convective structures
  increase

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P.B. Rutkevich. Equation for vortex instability
caused by convective turbulence and the Coriolis
force (1993), JETP, v. 77, pp. 933-938
O background rotation, E - density of
turbulence energy, ?, t - the most energetic
scale and characteristic time of the turbulent
velocity correlation, A - constant
temperature gradient between the horizontal
boundaries, B - coefficient characterizing
the power of internal heat sources, h -
layer height, ? - molecular coefficient of
kinematic viscosity, ?T - coefficient of
turbulent viscosity on the large scale, ? -
dimensionless parameter specifying the aspect
ratio (of typical vertical to horizontal
dimension) for small-scale convective structures. 
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NUMERICAL SIMULATION OF HELICAL-VORTEX
CONVECTION
Burylov, Firulyov, Levina
Model force simulates the influence of
small-scale helical turbulence generated by joint
effect of the Coriolis force and internal heat
release
is applied to developed convective flows

• has the identical tensor structure with C-terms
  responsible for generation of new instability in
  the mean-field equation,
• makes the flow helical,
• generates a positive feedback between the
  poloidal and toroidal components of the velocity
  field.

Linear Stability Analysis helical force
operates favouring the large scale flow
generation and decreasing the threshold of
instability
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Boussinesq Convection with Helical Force

• The helical force
• works and can pump an additional energy,
• z-component is a necessary element to close
• the feedback loop between the horizontal
  and
• vertical circulation in a forming vortex
  structure

• Laminar Rayleigh-Bénard convection produces a
  great number of similar convective cells
• that can be considered as structures of an
  intermediate scale.
• Helical force pumping the energy into the
  system simulates the influence of small-scale
• helical turbulence.
• An intriguing idea arises is it possible to
  simulate any signs of large-scale instability in
  these relatively simple conditions ?

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Energy and Helicity Balance in Helical-Vortex
Convection
Helical force operates contributing to both
energy and helicity balances. Numerical analysis
is the most effective way to give quantitative
estimations for different terms in balance
equations.
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Helical-Vortex Effects in Laminar Convection 3D
Laminar Rayleigh-Bénard convection, AR 10
Computational domain
?z
BOUNDARY CONDITIONS
T
Impenetrable, rigid, no-slip Heating from below, lateral surface is adiabatic
PHYSICAL FIELDS
Temperature, azimuthal velocity, vorticity,
stream function
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Integral Characteristics
Convection flows at Ra 3000, Pr 1, Ta  100
Ek EkT EkP H Nu Um Vm Wm Cells Number
Stationary convection S 0 236 6 230 7 1.56 10.8 3.6 10.1 9
Stationary helical Convection S 6 914 507 407 -7801 1.77 17.3 28.0 16.3 6
Scheme of flow intensification through the
helical feedback linking the toroidal VT and
poloidal VP circulation
Stream function, tangential velocity and
temperature fields without (left), with
(right, S6)
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Cells Merging
Stream function field S6.5, Ra1100
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• the booklet summarizes results on proposed
  numerical
• approach for simulating the large-scale
  helical-vortex
• instability in rotating Boussinesq
  convection with
• internal heat sources

OPINIONS ABOUT GEOPHYSICAL APPLICATIONS Alexan
der Khain (University of Jerusalem, Israel),
April 2005 You have to make other people who
are in Tropical Cyclone modeling be
interested. This effect may have a potential
importance for the problem of development of
tropical depressions. Kerry Emanuel (MIT,
USA), April 2005 I think your work has
great potential applicability to dust
devils. While this may seem like a trivial
phenomenon, it is proving to be quite otherwise
on Mars.

• NEXT STEPS
• DNS with/without the helical force for
  Boussinesq convection
• Examination of helical-vortex effects in
  tropical cyclogenesis
• - with/without the helical force to
  parameterize the helical features of
• convective atmospheric turbulence in
  numerical meteorological models.

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PARAMETERIZATION OF HELICAL CONVECTIVE
TURBULENCE TO INCLUDE IN NUMERICAL
METEOROLOGICAL MODELS
O background rotation, E - density of
turbulence energy, ?, t - the most energetic
scale and characteristic time of the turbulent
velocity correlation, A - constant
temperature gradient between the horizontal
boundaries, B - coefficient characterizing
the power of internal heat sources, h -
layer height, ? - molecular coefficient of
kinematic viscosity, ?T - coefficient of
turbulent viscosity on the large scale, ? -
dimensionless parameter specifying the aspect
ratio (of typical vertical to horizontal
dimension) for small-scale convective structures. 
O   10-4 s-1 , ?  102 m2/s2 , ?  103 m,
t  103 s, ?  10-2 K/m, h  104 m, ?
 10-5 m2/s, ?T 102-103 m2/s, ?2  10,
C ? 101-102 B
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A WAY TO EXAMINE THE HYPOTHESIS OF TURBULENT
VORTEX DYNAMO IN MODELLING OF TROPICAL
CYCLOGENESIS
Examining the helical-vortex effects at initial
stages of tropical cyclone evolution may result
in a finding of threshold for the large-scale
vortex instability
Research Program proposed within a visit to
Colorado State University (Fort Collins,
February, 2006)

• concept of vortical hot tower (VHT) route to
  tropical cyclogenesis of
• M.T. Montgomery et al. (2006), JAS,
  represents the most appropriate
• basis to take into account helical features of
  convective atmospheric turbulence

• numerical realization
• - non-hydrostatic mesoscale models -- MM5,
  RAMS
• - near-cloud-resolving simulation, 2-3 km
  horizontal grid spacing
• - applying both DNS and proposed
  parameterization,
• - meteorological database on TC observation and
  investigation.

Visiting Scientist Program N00014-06-1-4011
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SUMMARY
I. With applying the helical force to the
Boussinesq convection 1. The existence of
threshold for large-scale instability has been
shown. 2. New effects have
been found - non-zero helicity generation,
- flow intensification through the positive
feedback loop between the horizontal and
vertical circulation, - merging of helical
vortex cells, - intensification and qualitative
change in heat transfer. Explanation is
given how the energy of the additional helical
source can be effectively converted into
the energy of intensive large-scale vortex
flow. 3. Some features of tropical cyclone
can be simulated - generation of
intensive tangential velocity field,
- enlargement of horizontal structure scale by
cells merging. II. Parameterization of helical
features of convective atmospheric
turbulence and way to examine the hypothesis of
turbulent vortex dynamo in simulation of
tropical cyclogenesis have been proposed.