Non-Universal Turbulence in Planetary Boundary Layers

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Non-Universal Turbulence inPlanetary Boundary
Layers

• Igor N. Esau
• (igore_at_nersc.no)
• Nansen Environmental and Remote Sensing Centre
• Bergen, Norway

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Classical View
Turbulent boundary layers consist of random
eddies (Kolmogorov 1941)
Small eddies produce the shear stress and
transport heat, scalars and momentum, therefore
- active (Townsend 1961)
Large eddies do not produce the shear stress and
do not transport heat, scalar and momentum,
therefore - inactive (Townsand 1961)
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Universal Properties of Small Eddies
Universal motions
After Larson, 1986, RISOE report
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Universal Properties of Small Eddies
Kolmogorov's law for the energy spectrum
Structure function for the turbulent stress

Smagorinsky-Lilly eddy-viscosity relation for the
turbulent stress
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Small eddies exert stress and carry momentum in
classical boundary layers
How do large eddies look like?
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Classical Large Eddies
Horseshoe vortices
Top view
Side view
Ejections of low speed fluid carry stress
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Turbulence in PBLs

• Real world turbulence is different
• Rough surface
• Large scales
• Stratification
• Rotation

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New View
Internal wave radiation from PBL
top (Zilitinkevich, 2000)
Eddy blocking and distruction in surface
layer (Hunt, 2000)
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Fluxes of Turbulent Kinetic Energy
Classical view
New view
Turbulence Free Atmosphere
P0 egt0
Pe0
Plte
PBL Core
Plte
Pgte
Pe
Surface Layer
Pgte
Roughness Layer
Plte
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Profiles of the Energy Flux
Surface layer
Roughness layer
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Maximum of Non-dimensional TKE
Measurements in shallow near-neutral
PBLs (Hogstrom, 1990)
Small stress Large stress
LES data
Measurements in deep near-neutral PBLs (Pennel,
LeMone, 74)
Small eddies Large eddies
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Turbulent Stress
Turbulent stress does not change with the eddy
size
Turbulent stress decreases with the eddy size
Critical eddy size
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What determines the size of large eddies?
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Coherent Structures in Sheared Flow
Typical size of the first characteristic eddy is
close to the critical eddy size for the stress
fall-off.
Lc 600 meters in atmospheric boundary layer
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PBL Depth
Imposed stability parameter accounts for the size
of large eddies
(Zilitinkevich, 2000)
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Instant View
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Anthropogenic hazards
Weather forecast Climate research
Why do we need this knowledge?
Air pollution management
Understanding of cloud structures
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Geostrophic Drag andGeostrophic Angle
Larger eddies Smaller eddies
Larger eddies Smaller eddies
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A and B Functions
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Conclusions
Turbulent planetary boundary layer consists of
large eddies
Small eddies produce little shear stress and
relate to large eddies
Large eddies exert the most of the shear stress
and transport the most of heat, scalar and
momentum
Large eddies are limited by (I) the PBL depth,
which is the most important factor in real
PBLs and (II) the characteristic size of
coherent eddies
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Bergen, Norway
Thank you for your attention