Geoscience Reference
In-Depth Information
temperature is weaker than it is for momentum. We will see in
Chapter 11
that
at greater heights in the convective boundary layer this coupling disappears for
conserved scalars.
10.4.5 The
uθ
budget
From
(8.70)
in quasi-steady conditions this is, using local isotropy and the
Bradley
et al.
(
1982
) measurements to drop the molecular destruction term,
uw
∂
θw
∂U
∂
∂z
wuθ
ρ
0
θ
∂p
1
∂z
+
∂z
+
=−
∂x
.
(10.51)
The Kansas results show that in the near-neutral surface layer the turbulent transport
term is small and the budget further reduces to
uw
∂
∂z
θw
∂U
∂z
ρ
0
θ
∂p
1
+
=−
∂x
,
(10.52)
a balance between the two rates of production and the rate of destruction by turbulent
pressure gradients.
On measuring turbulent pressure signals
Bradshaw
(
1994
) has written:
Pressure fluctuations within a turbulent flow are one of the Great Unmeasureables: they are
of the order of
ρu
2
and so, unfortunately, are the pressure fluctuations induced on a static
pressure probe by the velocity field. That is, the signal-to-noise ratio is of the order of one.
To say that signals cannot be educed even with
S/N
O(
1
)
is itself a fallacy, but in this
case the attempts made to do so have not met with general acceptance.
=
Nonetheless, armed with evidence that their pressure probe could measure pres-
sure fluctuations with a signal-to-noise ratio better than 1 (
Wyngaard et al.
,
1994
),
Wilczak and Bedard
(
2004
) confirmed that the turbulent transport term in
Eq.
(10.51)
is small, and found excellent agreement between the pressure covariance
inferred from measurements of the left sides of
Eqs. (10.52)
and
(10.51)
and their
direct measurements of it.
Appendix
Length scales near the surface
Since
w
vanishes at the surface, near the surface we can write from our zero-
divergence model of the fluctuating velocity
z
∂u
∂y
(x,y,z
,t)
dz
.
∂v
∂x
(x,y,z
,t)
+
w(x,y,z,t)
=−
(10.53)
0
