Xin Xi

1
Xin Xi
2
1946 Obukhov Length, as a universal length scale
for exchange processes in surface layer. 1954
Monin-Obukhov Similarity Theory, as a starting
point for modern micrometeorology.
3
(No Transcript)
4
Interpretation of Obukhov Length

• In 1946, Obukhov length was first proposed as a
  length scale (of order one to tens of meters) to
  characterize the dynamical surface layer. It
  gives a relation between the parameters that
  describe the dynamic, thermal and buoyant
  processes.

NOT potential T
Constant momentum/temperature flux (with height)
assumption in the surface layer
5

• A dimensionless length scale z/L is further used
  to describe the stability of surface layer

6
Dimensional analysis of TKE budget equation
Surface layer turbulent kinetic energy (TKE)
budget equation
1
4
5
6
2
3
TKE tendency
virtual temperature (10.61q)T
fluctuating wind velocity x-component
1 rate of change of TKE due to mean wind
advection 2 TKE production/loss due to wind
shear. Usually a positive contribution to TKE 3
flux divergence of TKE represents the turbulent
transport of TKE by w 4 divergence of pressure
flux describe the redistribution of TKE by
pressure perturbation (e.g., buoyancy, gravity
waves) 5 TKE production/loss due to buoyancy
depends on the sign of the heat flux 6 loss of
TKE due to viscosity or dissipation (e.g.,
conversion of TKE to heat)
7

• Assuming constant flux (with height) in surface
  layer (variation within 10), one can use the
  surface values of heat and momentum fluxes to
  define turbulence scales and nondimensionalize
  the TKE equation.
• The momentum flux at the surface (shear stress)

The logarithmic velocity law in the constant-flux
layer
Therefore, the dimensionless stability parameter
is given by
Obukhov length
8
Monin-Obukhov Similarity Theory
Similarity theory is based on the assumption that
dimensionless groups of variables (V, T) may be
arranged in terms of functional relationships to
the flow field, and where the number of variables
is reduced to a closed set for easy application.
Monin-Obukhov similarity theory is developed
based on the following findings
Note zero-plane displacement is the height above
the ground where the wind approaches zero due to
flow obstacles, e.g., building, vegetation, etc
9

• The similarity theory gives the profile of any
  bulk quantity (X) which satisfies the assumptions
  in the theory

For wind speed and temperature
Universal functions of the dimensionless
stability parameter, z/L
OR
Dimensionless wind and temperature gradients
10

• Integration of these two formulae between the
  surface and a certain reference layer
  (observational level or the first model level)
  gives

Logarithmic wind profile
Universal stability functions (of z/L) Have
different forms in different situations
(stable/unstable)
Z0 and Z0T are the surface roughness length for
momentum and heat, respectively
11

• Rearrangement of the two equations gives

CD bulk transfer coefficient for momentum, or
drag coefficient CH bulk transfer coefficient
for heat
12
Questions for discussion

• 1. Stability parameter z/L Richardson Number?
• 2. Monin-Obukhov similarity theory
• the large eddy simulation method
• 3. (scale issue / assumption breakdown) how is
  vegetation considered currently in applying the
  similarity theory in vegetated area (in terms of
  surface roughness, stability function, etc)? And
  how is this combined with other parts, such as
  soil thermodynamics, plant evapotranspiration
  (hydrological cycle).

13
(No Transcript)