manner, a sensible heat flux also independent of height can be derived as
T
H = ρcp w′T ′ = ρcp Kh
.
(7)
z
It states that the surface boundary layer is characterized essentially by the "constant flux layer."
B. Wind structure of the surface boundary layer
In the absence of buoyancy, the wind profile is given as
u u*
=
,
(8)
z kz
u* = τ / ρ = -u′w′ .
(9)
Upon integrating, the mean wind speed is
u*
z
u=
.
(10)
ln
zo
k
u* is employed as the reference velocity in the study of fluid flow over a rough surface. In general,
it increases with both u and the roughness of the surface zo, which is the height above the ground
(or surface) where the wind speed vanishes (this is also known as the roughness length, a character-
istic of the surface).
To take into account all stability conditions other than neutral, Monin and Obukhov (1954)
modified eq 8 by introducing a universal function, φm (z L), i.e.,
φm
u u*
z
=
(11)
L
z kz
in which L is the MoninObukhov stability length defined as
3
u*ρ cpT
3
L=-
.
(12)
kgH
For the case of neutral stability or when H = 0, we have set φm(0) = 1. If H is positive (the heat flux
is directed from the ground upward), then z/L is negative, indicating an unstable condition. On the
other hand, if H is negative, z/L is positive, indicating a stable condition.
The other two important stability parameters are the Richardson (Ri) and flux Richardson (Rif)
numbers, which are respectively defined as
T
z
g
Ri =
(13)
()
u 2
T
z
and
g w′T ′
gH
Rif =
=
.
(14)
u
u
-T cpτ
T u′w′
z
z
The sign of Ri is determined by the gradient of mean temperature, which is by convention
negative in lapse and positive in inversion profiles. A value of Ri of zero, negative, or positive
5
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