Geoscience Reference
In-Depth Information
Bouyancy
Turbulence is generated by
buoyancy near the ground
and throughout the ABL
but is destroyed near and
through the inversion layer
1.2
1.0
Transport
Turbulence near the
surface is transferred
upwards through the ABL
0.8
0.6
Dissipation
Turbulence is destroyed at
all levels but most strongly
near the ground
Shear generation
Turbulence is generated by
friction, mainly near the
ground
0.4
0.2
0
−
1.5
1.0
−
0.5
Relative size of terms in the TKE budget
0.5
1.0
1.5
Figure 18.6
Typical values of terms in the prognostic equation for Turbulent Kinetic Energy and their variation with
height relative to the top of the ABL in daytime conditions. Note that there is very substantial variability around these
typical values.
Because
e
is the sum of squared terms it is always positive, and −
e
, i.e., Term VI in
Equation (18.17), is always negative.
The physical meanings of the terms in Equation (18.17) are as follows:
TERM I
represents temporal change in the local 'storage' of TKE.
TERM II
is either a buoyant production o
r destru
ction term, depending on
the sign of the buoyancy flux
(
)
which is positive giving
production during the day and negative giving destruction of
turbulence at night.
w
q
′′
v
TERM III
describes the redistribution of TKE by pressure fluctuations.
TERM IV
describes the pro
ductio
n of turbulence by friction which is always
positive because
(
)
uw
is always negative while (∂
ū
/∂
z
) is always
positive, and which is greatest in regions where the momentum
flux and gradient of wind speed with height is large.
′′
TERM V
represents the turbulent transport of TKE between different
levels.
TERM VI
viscous dissipation of TKE.
The presence of TERM VI in Equation (18.17) means TKE is continually being
destroyed and will decay if not also continually created either by buoyant
production (TERM II) or by frictional production (TERM IV). Within the wide
observed ranges reported by Stull (1988), Fig. 18.6 illustrates the typical observed
relative strength of terms in the prognostic equation for TKE over flat, homogeneous
terrain in daytime conditions as a function of height relative to the top of the ABL.
