Geoscience Reference
In-Depth Information
Using (
4.16
), we can determine t
he tu
rbulent viscosi
ty i
n a real flow if we mea-
sure the turbulent momentum flux
u
w
∂
u
∂
z
as it has been done by
Campistron et al. (
1991
). While the shear as a mean quantity is relatively eas-
ily available from SODAR measurements, it is very difficult to get the turbulent
momentum flux from remote-sensing data (see above).
Looking for a surrogate for the turbulent momentum flux, Emeis (
2004
) proposes
to use the findings fr
om
Stull (
1988
) or, e.g. from data presented in Emeis et al.
(
1995
) that
and the shear
σ
w
2
and
u
w
are proportional in the surface layer. In the case of near
neutral and stable thermal stratification of the air over homogeneous terrain, this
gives
w
1.6
u
w
,
σ
=
(4.18)
Inserting this proportionality into (
4.16
) we get
2
w
1.6
∂
u
∂
σ
ν
t
=
,
(4.19)
z
(4.19) is valid only for a near neutral or stable surface layer. Above this layer
the situation is more complicated. For a near neutral mixed layer where mechan-
ical production of turbulence dominates, both
σ
w
and the turbulent momentum
flux decrease with height. Using again information from Stull (
1988
, his equations
9.5.2b, 9.5.3f, and 9.5.3j), we get with the mixing layer height
z
i
(this is identical to
MLH above)
1.6
1
−
0.5
z
z
i
2
u
w
,
σ
w
=
−
(4.20)
which, if the factor 1.6 from Stull's (1988) equation 9.5.3j is used in his equation
9.5.
3f co
nverges to (
4.18
)for
z
against zero. For
z
σ
w
2
=
0.5
z
i
the factor between
and
u
w
is 2.26, for
z
=
0.9
z
i
it is 5.06. By inserting (
4.20
)into(
4.16
), this leads
to an approximation for
ν
t
w
σ
ν
t
=
,
(4.21)
z
i
)
−
0.5
∂
u
z
1.6(1
−
∂
z
(4.21) should not be used very close to the top of the mixed layer. For a stable
mixed layer, equations 9.4.2c and 9.4.3f in Stul
l (
19
88
) suggest a more or less height
independent, constant ratio between
σ
w
2
and
u
w
of the order 2.5. Thus, a rough
compromise between this finding, eq. (
4.19
), and eq. (
4.21
)mustbeused
w
a
∂
u
∂
z
σ
ν
t
=
,
(4.22)
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