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In-Depth Information
We found that
A
was close to unity. By assuming that
at 4m (the upper-
mostturbulencecluster),theestimatefor
c
λ
wasabout0.85,slightlylargerthanthe
neutralvaluessuggestedbyBuschandPanofsky(0.8).Fromthisweconstructedan
estimate of mixing length based on the wave number at the peak in the average
w
spectraat5 levelsduringthe ISWstorm(McPheeandMartinson1994):
λ
=
κ
|
z
|
λ
peak
=
c
λ
/
k
max
(5.2)
Anindependentestimateofthemixinglengthmaybemadefromturbulencespectra
byassumingthatlocallyTKEproductionrateequalsdissipation,where
ε
isderived
fromspectrallevelsintheinertialsubrange(Hinze1975)
3
2
/
3
k
5
/
3
ε
=
S
ww
(
k
)
(5.3)
4
α
ε
where
51 is the Kolmogorov constant for turbulent kinetic energy. The
process is essentially an inversion of the inertial-dissipation method for estimat-
ing stress in the atmospheric surface layer (e.g., Edson et al. 1991), where instead
of using
α
ε
=
0
.
in the surface layer) to estimate stress, we use
u
∗
ob-
tainedfromthecovariancemeasurementsand
ε
and
κ
z
(i.e.,
λ
ε
fromtheinertialsubrangetocalcu-
late
λ
:
3
k
ε
S
ww
(
−
3
/
2
u
∗
3
k
ε
)
3
λ
ε
=
u
∗
/
ε
=
(5.4)
4
α
ε
k
ε
where
u
∗
is the local friction velocity,
k
ε
is a wave number chosen in the
−
2
/
3regionofthe
w
spectrum, and
S
ww
(
k
ε
)
is the spectral density evaluated
at
k
ε
.
With measurementsoftemperature-velocitycovarianceand TKEdissipation,an
analogous
thermal mixing length
,
λ
T
maybe derivedby equatingtemperaturevari-
anceproductionwith thermaldissipation(see Section3.7)
=
2
u
∗
λ
T
=
ε
T
=
ε
w
T
∂
w
T
1
/
3
T
k
5
/
3
ε
S
TT
(
k
ε
)
(5.5)
∂
z
α
T
=
.
where
79 (Edson et al. 1991) is the Komogorov constant for temperature
variance, and
S
TT
α
0
T
(
k
ε
)
is the spectral level for temperature variance at a specific
wavenumberin theinertialsubrange.
EstimatesofthethreedifferentmixinglengthsfortheISW-92storm,summarized
along with TKE and thermal variance dissipation rates in Fig. 5.2, are generally
similar throughout the IOBL, and all depart markedly from surface layer
|
)
scaling.Theseresultssuggestthatmixinglengthremainsrelativelyconstantthrough
the IOBL, once past a relatively shallow surface layer where it is proportional to
distancefromtheboundary.Thisobservationformsthebasisforthehypothesisthat
eddyviscosity inthe wellmixedportionof theIOBL beyondthe surfacelayermay
berepresentedby
(
κ
|
z
K
=
λ
u
∗
(5.6)
