Turbulent Transport in the Atmospheric Surface Layer - Transport in the Atmosphere-Vegetation-Soil Continuum - page 86

is called the Richardson number (or lux-Richardson number, to distinguish it from
other variants):

g

θ θ
v

w

′′

buoyancy production
shear production

Ri ≡− =

(3.11) f

∂
∂

u
z

uw ′′

Note that within the ASL, where turbulent luxes change little with height (see Section
3.4.3 ), the only height dependence stems from the wind shear: close to the ground
shear is larger than at some larger height, leading to a larger contribution of shear
production close to the surface.
A number of situations can be distinguished:

• Ri f ≈ 0: There is no buoyancy production/destruction of TKE, only shear production
( neutral conditions).
• Ri f < 0: TKE is produced both by shear and by buoyancy ( unstable conditions).
• Ri f > 0: TKE is produced by shear but destroyed by buoyancy ( stable conditions).
• |Ri f | is large: The effect of buoyancy dominates over shear production (either very unsta-
ble (convective) or very stable, depending on the sign of Ri f ).

This analysis already gives a hint about the observations made with respect to the
diurnal cycle of the turbulent diffusivity in Figure 3.3 . The fact that at night K h was an
order of magnitude smaller than during daytime can be understood from the fact that
at night time the sensible heat lux is negative, hence Ri f > 0, and TKE is destroyed by
buoyancy. Because turbulent motion is needed for eficient transport, the hampering of
turbulence by buoyancy will decrease the turbulent diffusivity. The reverse argument
holds for daytime conditions with a positive heat lux and enhanced turbulence.

Question 3.7: Suppose we have a low with the following characteristics:

u (m s -1 ) v (m s -1 ) w (m s -1 )

Mean 4 2 0

Standard deviation 0.3 0.2 0.2

a) Compute the mean kinetic energy.
b) Compute the turbulent kinetic energy.
c) What are the units of the kinetic energies computed under (a) and (b)?
d) The units given under (c) are not the units of energy. With what quantity should the
kinetic energies computed under (a) and (b) be multiplied to obtain a real energy
(with the correct units)?

Question 3.8: Verify that the shear production term in Eq. ( 3.10 ) is indeed a positive
term (and hence a production term).