Non-Universal Turbulence in Planetary Boundary Layers Igor N. Esau (igore@nersc.no) Nansen Environmental and Remote Sensing Centre Bergen, Norway

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)

Universal Properties of Small Eddies Universal motions After Chapman, 1979, AIAA papers 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 momentum in classical boundary layers How do large eddies look like?

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

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

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

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

Profiles of the Energy Flux Surface layer Roughness layer

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

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

What determines the size of large eddies?

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

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

Instant View

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

Geostrophic Drag and Geostrophic Angle Larger eddies Smaller eddies Larger eddies Smaller eddies

A and B Functions

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

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