Non-Universal Turbulence inPlanetary Boundary Layers
Igor N. Esau([email protected])
Nansen Environmental and Remote Sensing CentreBergen, Norway
Classical ViewTurbulent boundary layers consist of random eddies (Kolmogorov 1941)
Small eddies produce the shear stress and transportheat, 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)
Universal Properties of Small Eddies
After Chapman, 1979, AIAA papers
Universal motions
After Larson, 1986, RISOE report
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:
Small eddies exert stress and carry momentumin classical boundary layers
How do large eddies look like?
Classical Large Eddies
Top view
Side view
Horseshoe vortices
Ejections of low speed fluid carry stress
Turbulence in PBLs
Real world turbulence is different:● Rough surface● Large scales● Stratification● Rotation
New View
Internal waveradiation from PBL top(Zilitinkevich, 2000)
Eddy blocking anddistruction in surface layer(Hunt, 2000)
Fluxes of Turbulent Kinetic Energy
Roughness Layer
Classical view New view
P> P<
Surface Layer
PBL Core
Turbulence Free Atmosphere
P=
P<
P=
P>
P<
P=0
Profiles of the Energy Flux
Roughness layer
Surface layer
Maximum of Non-dimensional TKE
Small eddies Large eddies
Small stress
Large stress
Measurementsin shallow
near-neutral PBLs(Hogstrom, 1990)
Measurementsin deep
near-neutral PBLs(Pennel, LeMone, 74)
LES data
Turbulent Stress
Turbulent stress decreases
with the eddy size
Critical eddy size
Turbulent stress does not change
with the eddy size
What determines the size of large eddies?
Coherent Structures in Sheared Flow
Typical size ofthe first characteristic eddy
is close to the critical eddy size for the stress fall-off.
Lc~ 600 meters in atmospheric boundary layer
PBL Depth
Imposed stability parameteraccounts for the size of large eddies
(Zilitinkevich, 2000)
Instant View
Why do we need this knowledge?
Anthropogenic hazards
Weather forecast Climate research
Air pollution management
Understandingof cloud structures
Geostrophic Drag and
Geostrophic Angle
Larger eddies Smaller eddies Larger eddies Smaller eddies
A and B Functions
ConclusionsTurbulent planetary boundary layer consists of 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
Small eddies produce little shear stress and relate to large eddies
Thank you for your attention
Bergen, Norway