1. Non-Universal Turbulence in Planetary Boundary Layers
Igor N. Esau
Nansen Environmental and Remote Sensing Centre
Bergen, Norway

2. 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)

3. Universal Properties of Small Eddies
Universal motions
After Chapman, 1979, AIAA papers
After Larson, 1986, RISOE report

4. 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:

5. Small eddies exert stress and carry momentum
in classical boundary layers
How do large eddies look like?

6. Classical Large Eddies
Horseshoe vortices
Top view
Side view
Ejections of low speed fluid carry stress

7. Turbulence in PBLs Real world turbulence is different: Rough surface
Large scales
Stratification
Rotation

8. New View Internal wave radiation from PBL top (Zilitinkevich, 2000)
Eddy blocking and
distruction in
surface layer
(Hunt, 2000)

9. Fluxes of Turbulent Kinetic Energy
Classical view
New view
Turbulence Free Atmosphere
P=e=0
P=0 e>0
PBL Core
P<e
P<e
P=e
P>e
Surface Layer
P>e
Roughness Layer
P<e

10. Profiles of the Energy Flux
Surface layer
Roughness layer

11. 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

12. Turbulent Stress Turbulent stress Turbulent stress decreases
with the eddy size
Turbulent stress
does not change
with the eddy size
Critical eddy size

13. What determines the size of
large eddies?

14. 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

15. PBL Depth Imposed stability parameter
accounts for the size of large eddies
(Zilitinkevich, 2000)

16. Instant View

17. Why do we need this knowledge?
Anthropogenic
hazards
Weather forecast
Climate research
Why do we need this knowledge?
Air pollution
management
Understanding
of cloud structures

18. Geostrophic Drag and Geostrophic Angle
Larger eddies Smaller eddies
Larger eddies Smaller eddies

19. A and B Functions

20. 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

21. Thank you for your attention
Bergen, Norway
Thank you for your attention