non-universal turbulence in planetary boundary layers

Non-Universal Turbulence inPlanetary Boundary Layers

Igor N. Esau(igore@nersc.no)

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