Geoscience Reference
In-Depth Information
(5.26)
of a conserved scalar diffusing to or from the surface is observed to be neg-
ligible. In this case the budget reduces to a simple balance between mean-gradient
production and molecular destruction,
2
wc
∂C
∂c
∂x
j
∂c
∂x
j
≤
∂z
=−
χ
c
=−
2
γ
0
.
(5.37)
Thus here the global constraint of
Eq. (5.15)
becomes a local one that requires
wc
and
∂C/∂z
to be of opposite sign.
In the steady flow downstream of a heated grid in a wind tunnel, the turbulent
transport of temperature variance is also negligible and the budget reduces to a
balance between streamwise mean advection and molecular destruction:
U
∂c
2
∂x
=−
χ
c
.
(5.38)
This provides a way of inferring
χ
c
from the rate of change of
c
2
with downstream
distance, which can be simpler and more reliable than measuring it directly from
its definition
(5.12)
(
Part III
).
5.4 The scalar flux and Reynolds stress budgets
5.4.1 The cu
i
budget
The same derivation procedure, plus scaling arguments for the molecular terms
(Appendix), yields the turbulent scalar flux budget:
∂cu
i
∂t
U
j
∂cu
i
∂x
j
=−
(
mean advection
)
u
j
u
i
∂C
∂x
j
−
(
mean-gradient production
)
−
cu
j
∂U
i
∂x
j
(
tilting production
)
(5.39)
∂cu
i
u
j
∂x
j
−
(
turbulent transport
)
c
∂p
∂x
i
(
pressure-gradient interaction
)
1
ρ
−
ν)
∂u
i
∂x
j
∂c
∂x
j
−
(γ
+
(
molecular destruction
).
