Turbulence Energetics in Stably Stratified Atmospheric Flows

1
Turbulence Energetics in Stably Stratified
Atmospheric Flows

• Sergej Zilitinkevich
• Division of Atmospheric Sciences, Department of
  Physical Sciences
• University of Helsinki and Finnish Meteorological
  Institute
• Helsinki, Finland
• Tov Elperin, Nathan Kleeorin,
• Igor Rogachevskii
• Department of Mechanical Engineering
• The Ben-Gurion University of the Negev
• Beer-Sheva, Israel
• Victor Lvov
• Department of Chemical
  Physics
• ITI Conference on Turbulence III, 12-16 October
  2008, Bertinoro, Italy

2
Stably Stratified Atmospheric Flows
Production of Turbulence
Heating
by Shear
Destruction of Turbulence
Cooling
by Heat Flux
3
Laminar and Turbulent Flows
Laminar Boundary Layer
Turbulent Boundary Layer
4
Boussinesq Approximation
5
Budget Equation for TKE
Balance in R-space
6
TKE Balance for SBL
7
Observations, Experiments and LES
Blue points and curve meteorological field
campaign SHEBA (Uttal et al., 2002) green lab
experiments (Ohya, 2001) red/pink new
large-eddy simulations (LES) using NERSC code
(Esau 2004).
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Budget Equations for SBL

• Turbulent kinetic energy
• Potential temperature fluctuations
• Flux of potential temperature

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Budget Equations for SBL
10
Total Turbulent Energy
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Budget Equations for SBL
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Critical Richardson Number
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No Critical Richardson Number
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Budget Equations for SBL
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Turbulent Prandtl Number vs.
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Budget Equations for SBL with Large-Scale
Internal Gravity Waves
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Turbulent Prandtl Number vs. Ri
(IG-Waves)
Meteorological observations slanting black
triangles (Kondo et al., 1978), snowflakes
(Bertin et al., 1997) laboratory experiments
black circles (Strang and Fernando, 2001),
slanting crosses (Rehmann and Koseff, 2004),
diamonds (Ohya, 2001) LES triangles
(Zilitinkevich et al., 2008) DNS five-pointed
stars (Stretch et al., 2001). Our model with
IG-waves at Q10 and different values of
parameter G G0.01 (thick dashed), G 0.1 (thin
dashed-dotted), G0.15 (thin dashed), G0.2
(thick dashed-dotted ), at Q1 for G1 (thin
solid) and without IG-waves at G0 (thick solid).
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vs. (IG-Waves)
Meteorological observations slanting black
triangles (Kondo et al., 1978), snowflakes
(Bertin et al., 1997) laboratory experiments
black circles (Strang and Fernando, 2001),
slanting crosses (Rehmann and Koseff, 2004),
diamonds (Ohya, 2001) LES triangles
(Zilitinkevich et al., 2008) DNS five-pointed
stars (Stretch et al., 2001). Our model with
IG-waves at Q10 and different values of
parameter G G0.01 (thick dashed), G 0.1 (thin
dashed-dotted), G0.15 (thin dashed), G0.2
(thick dashed-dotted ), at Q1 for G1 (thin
solid) and without IG-waves at G0 (thick
solid).
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vs. Ri (IG-Waves)
Meteorological observations squares CME, Mahrt
and Vickers (2005), circles SHEBA, Uttal et al.
(2002), overturned triangles CASES-99, Poulos
et al. (2002), Banta et al. (2002), slanting
black triangles (Kondo et al., 1978), snowflakes
(Bertin et al., 1997) laboratory experiments
black circles (Strang and Fernando, 2001),
slanting crosses (Rehmann and Koseff, 2004),
diamonds (Ohya, 2001) LES triangles
(Zilitinkevich et al., 2008) DNS five-pointed
stars (Stretch et al., 2001). Our model with
IG-waves at Q10 and different values of
parameter G G0.01 (thick dashed), G0.04 (thin
dashed), G 0.1 (thin dashed-dotted), G0.3
(thick dashed-dotted), at Q1 for G0.5 (thin
solid) and without IG-waves at G0 (thick
solid).
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vs. Ri (IG-Waves)
Meteorological observations squares CME, Mahrt
and Vickers (2005), circles SHEBA, Uttal et al.
(2002), overturned triangles CASES-99, Poulos
et al. (2002), Banta et al. (2002), slanting
black triangles (Kondo et al., 1978), snowflakes
(Bertin et al., 1997) laboratory experiments
black circles (Strang and Fernando, 2001),
slanting crosses (Rehmann and Koseff, 2004),
diamonds (Ohya, 2001) LES triangles
(Zilitinkevich et al., 2008) DNS five-pointed
stars (Stretch et al., 2001). Our model with
IG-waves at Q10 and different values of
parameter G G0.001 (thin dashed), G0.005
(thick dashed), G 0.01 (thin dashed-dotted),
G0.05 (thick dashed-dotted), at Q1 for G0.1
(thin solid) and without IG-waves at G0 (thick
solid).
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vs. (IG-Waves)
Meteorological observations overturned triangles
CASES-99, Poulos et al. (2002), Banta et al.
(2002) laboratory experiments diamonds (Ohya,
2001) LES triangles (Zilitinkevich et al.,
2008). Our model with IG-waves at Q10 and
different values of parameter G G0.2 (thick
dashed-dotted), at Q1 for G1 (thin solid) and
without IG-waves at G0 (thick solid for
) and (thick dashed for
).
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Anisotropy vs. (IG-Waves)
Meteorological observations squares CME, Mahrt
and Vickers (2005), circles SHEBA, Uttal et al.
(2002), overturned triangles CASES-99, Poulos
et al. (2002), Banta et al. (2002), slanting
black triangles (Kondo et al., 1978), snowflakes
(Bertin et al., 1997) laboratory experiments
black circles (Strang and Fernando, 2001),
slanting crosses (Rehmann and Koseff, 2004),
diamonds (Ohya, 2001) LES triangles
(Zilitinkevich et al., 2008) DNS five-pointed
stars (Stretch et al., 2001). Our model with
IG-waves at Q10 and different values of
parameter G G 0.01 (thick dashed), G0.1 (thin
dashed-dotted), G0.2 (thin dashed), G0.3 (thick
dashed-dotted), at Q1 for G1 (thin solid) and
without IG-waves at G0 (thick solid).
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References

• Elperin, T., Kleeorin, N., Rogachevskii, I., and
  Zilitinkevich, S. 2002 Formation of
  large-scale semi-organized structures in
  turbulent convection. Phys. Rev. E, 66, 066305
  (1--15)
• Elperin, T., Kleeorin, N., Rogachevskii, I., and
  Zilitinkevich, S. 2006 Tangling turbulence
  and semi-organized structures in convective
  boundary layers. Boundary Layer Meteorology,
  119, 449-472.
• Zilitinkevich, S., Elperin, T., Kleeorin, N., and
  Rogachevskii, I, 2007 Energy- and
  flux-budget (EFB) turbulence closure model for
  stably stratified flows. Boundary Layer
  Meteorology, Part 1 steady-state homogeneous
  regimes. Boundary Layer Meteorology, 125,
  167-191.
• Zilitinkevich S., Elperin T., Kleeorin N.,
  Rogachevskii I., Esau I., Mauritsen T. and Miles
  M., 2008, Turbulence energetics in stably
  stratified geophysical flows strong and weak
  mixing regimes. Quarterly Journal of Royal
  Meteorological Society, 134, 793-799.

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Conclusions

• Budget equation for the total turbulent energy
  (potential and kinetic) plays a crucial role
  for analysis of SBL flows.
• Explanation for no critical Richardson number.
• Reasonable Ri-dependencies of the turbulent
  Prandtl number, the anisotropy of SBL turbulence,
  the normalized heat flux and TKE which follow
  from the developed theory.
• The scatter of observational, experimental, LES
  and DNS data in SBL are explained by effects of
  large-scale internal gravity waves on
  SBL-turbulence.

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• THE END