Geoscience Reference
In-Depth Information
stability (as characterized by an as yet undefined dimensionless measure of
buoyant production) its value may change.
We return to this point later, but meanwhile next consider how it is possible
to define other dimensionless gradients of atmospheric entities, including
f
H
corresponding to kinematic sensible heat flux and virtual potential temperature,
and
f
V
corresponding to kinematic moisture flux and specific humidity. Bearing
in mind the purpose these dimensionless functions serve (i.e., to modify the effec-
tive average mixing length of the turbulent eddies operating in the surface layer),
by analogy with Equation (20.3) it is possible to re-write Equation (19.28) in the
form:
⎛
⎞
∂
q
v
q¢ ¢
wku
=−
()(
f
−
1
z
−
d
)
(20.4)
⎜
⎟
*
v
H
∂
⎝
⎠
which can then be rearranged to define the dimensionless gradient of virtual
potential temperature thus:
kz d
(
−
)
∂
q
v
f
=
(20.5)
H
q
∂
*
where:
−
(
q¢ ¢
v
w
)
q
=
(20.6)
*
*
Similarly Equation (19.29) can be re-written as:
⎛⎞
∂
q
qw ku
¢¢
=−
()(
f
−
1
z d
−
)
(20.7)
⎜⎟
∂
⎝⎠
*
V
z
which can be rearranged to define the dimensionless gradient of specific
humidity:
kz d
q
(
−
)
∂
q
f
=
(20.8)
V
z
∂
*
where:
−
(
qw
u
¢¢
)
q
=
*
*
(20.9)
As is the case for the dimensionless wind speed gradient, when written in the
dimensionless form of Equations (20.5) and (20.8), respectively, the gradient of
