Geoscience Reference
In-Depth Information
-4
-5
-6
log
k
max
-2
-1
0
1
2
log
k
Fig. 3.9
Averaged (6h) component velocityvariance spectra from 20mbelow theice-water inter-
face duringastormatIce StationWeddellin1992. Envelope indicates95%confidence interval for
the
w
spectrum only. The vertical lineindicates the wave number at the maximum in the weighted
(area-preserving)
w
spectrum used to estimate mixing length. The horizontal line identifies the
spectral level used to estimate TKE dissipation (Reproduced from McPhee and Martinson 1994.
Withpermission American Association for the Advancement of Science)
energy at those scales depends only on the local wave number and dissipation
,
i.e., the rate at which energy is being cascaded to the small scales. Following the
notationofBarenblatt(1996),wheresquarebracketsdenotedimensions,we havea
dependent quantity (
w
spectral density) that depends on two governingparameters
withindependentdimensions.
ε
L
3
T
−
2
[
]=
S
w
dependentquantity
−−−−−−−−−−
L
−
1
[
k
]=
governingparameters
L
2
T
−
3
[
ε
]=
In this case, by the PI theorem a dimensionless quantity combining the dependent
andgoverningparametersmustequalaconstant,i.e.,
