Geoscience Reference
In-Depth Information
Derbyshire
(
1990
) interprets
Eq. (12.53)
as giving the maximum surface buoy-
ancy flux the steady SBL can have while remaining fully turbulent - i.e., without the
onset of turbulence intermittency and extinction at
Ri
0
.
25
(Subsection 12.1.1)
.
We can support that interpretation by rewriting
Eq. (12.53)
as
−
√
3
θ
0
Q
0
G
2
R
f
=
constant
.
(12.54)
|
f
|
The numerator of the fraction is proportional to the SBL-averaged rate of buoyant
destruction of TKE. Since
G
is the magnitude of the mean horizontal pressure
gradient, the MKE balance (
Chapter 5
,
Subsection 5.5.2
) shows that the denomina-
tor is proportional to the rate of production of mean flow kinetic energy (MKE). If
theMKE balance is in equilibrium, the denominator is also proportional to the SBL-
averaged rate of shear production of TKE. Thus as Derbyshire suggests,
Eq. (12.54)
can be interpreted as an estimate of the maximum “global” flux Richardson number
for the SBL - i.e., that beyond which it cannot support turbulence:
|
f
|
R
f
(
max
)
=
constant
SBL-averaged rate of buoyant destruction of TKE
SBL-averaged rate of shear production of TKE
∼
.
(12.55)
Nieuwstadt
(
2005
) provided some intriguing support for Derbyshire's notion of
a maximum flux Richardson number,
Eq. (12.55)
, through DNS of stably stratified
turbulent channel flow. He applied cooling at the bottom and allowed a surface
stress. At the channel top he used a “free slip” condition that caused the stress and
buoyancy flux to vanish there. Thus the flow was qualitatively like an SBL without
significant Coriolis effects. He found that the flow ceased to be turbulent when the
Monin-Obukhov length
L
became less than twice the channel depth. This can be
expressed as a constraint like
Eq. (12.55)
on the maximum global flux Richardson
number
(Problem 12.23)
.
The surface heat flux in the SBL over land is determined by the surface energy
balance, which in clear weather is dominated by radiative effects that are indepen-
dent of SBL dynamics. It appears that such SBLs are prone to such strong surface
cooling that excessive values of the global flux Richardson number are generated
and the turbulence is extinguished.
12.3.5 Insights from LES
Calculations of SBL structure with several different LES codes (
Beare
et al
.
,
2006
)
showed broad agreement at sufficiently high resolution, i.e., aminimumgrid dimen-
sion of 3 m and less. The test case was an SBL previously simulated by
Kosovic and
