Geoscience Reference
In-Depth Information
Buoyancy subrange (
k
23
)
Inertial subrange (
k
25/3
)
Viscous subrange (Steep!)
Log
k
Figure 3.35
Schematic diagram of passive scalar fluctuation power spectrum in the
atmosphere.
spectra are illustrated in Fig. 3.35. The buoyancy subrange drives the inertial
subrange and eventually energy reaches the viscous damping range. The buoy-
ancy scale
L
B
is determined by convection scales or gravity wavelengths. At small
wavelengths, the Kolmogorov microscale
μ
is a measure of the breakpoint to a
very steep slope in the spectrum at large
k
:
1
/
4
3
ν
μ
=
ε
where
is the energy dissipation rate. The wavelength at which the spectrum
breaks, called the inner scale, is estimated to be about an order of magnitude
larger than
ε
μ
. The dependence on
ε
is very weak, so increasing the energy cas-
cade only changes
by a small amount. The kinematic viscosity coefficient does
change dramatically in the atmosphere and dominates the variation of
μ
with
height. Hocking (1983) calculated these other parameters as a function of alti-
tude, as shown in Fig. 3.36. The inner scale increases from a few centimeters
near the ground to nearly 100m at 100 km altitude.
This latter result is very important because at this height the buoyancy scale
and the microscale are nearly equal. Without an inertial subrange turbulence
cannot exist and the atmosphere is no longer mixed. This height is called the tur-
bopause; above it the molecules separate by diffusion according to their mass. In
the transition region, turbulence is very patchy, and for any given profile, a patch
of turbulent atmosphere can actually be above a region of nonturbulent fluid.
An observation illustrating this phenomenon comes from pictures of chemilumi-
nescent meteor trails and is shown in Fig. 5.25b. The well-defined double trail
portion of the trail is below the very puffy, turbulent piece. The puffy portion
was found to expand at a rate consistent with turbulent diffusion, whereas the
lower turbulent portion exhibited molecular diffusion (Kelley et al., 2003b).
μ
Search WWH ::
Custom Search