Turbulent Transport in the Atmospheric Surface Layer - Transport in the Atmosphere-Vegetation-Soil Continuum - page 87

ρ c p w' θ ' L v ρ w'q'

turbulent transport

H

L v E

surface flux
(non-turbulent)

Figure 3.8 Link between surface luxes (here luxes of sensible heat and water
vapour) and turbulent luxes. Surface luxes are relevant for the surface energy and
mass balance. Furthermore, they are the source/sink for the turbulent transport.

3.4 Turbulent Transport
3.4.1 Mean Vertical Flux Density
The turbulent transport engine presented in Section 3.3.1 involves the vertical trans-
port of quantities by the vertical motion of air. Thus, at a given location and time, the
transport of a quantity with speciic concentration X is wρX ( ρX is the volumetric
concentration, or density): a parcel of air with concentration ρX is moving vertically
with velocity w . But we are not interested in what happens at a certain moment, but
rather in the mean effect of all those parcels moving up and down. Hence we apply
the Reynolds decomposition ( Section 3.3.3 ). First we only decompose X :

′

(3.12)

FwXwXX w

ρ ρ w

X =

ρ ρ = ( += + ′ X X

The term wρ is the total transport of mass. If we neglect the exchange of mass at the
surface (in the form of release or uptake of water vapour and CO 2 ), the mass lux
can be assumed to be zero at the surface and in the surface layer (no air is entering
or leaving the solid surface). With this step (irst only decomposing X ) we partly get
rid of the mean vertical wind speed w , which is very hard to measure accurately but
can have a considerable impact on the luxes. Now in Eq. ( 3.12 ) only the second term
remains, which can be expanded as (applying Reynolds decomposition to w and ρ ,
and subsequently average):

( ) =

(3.13)

FwX

X =

ρ ′ = ++ ww wwX ρρρρ ρ ρ ′ ′ ′′ ′ ′ ′ ′ ′ ′ ′′ + w XwXwX + + ρ

where we used wρ ′≡0 to omit the irst term. It can be shown that the irst and the
last term on the right-hand side are small compared to the middle one, so that the lux
F X is simply the covariance of the vertical wind speed and the speciic concentration
X times the mean air density.