Geoscience Reference
In-Depth Information
In boundary-layer meteorology coherent structures are apt to be called
secondary
flows
. Examples include “convective rolls,” large, counter-rotating, horizontal vor-
tices that can be visible through the “cloud streets” they induce at their top (
LeMone
,
1973
). Because of their relatively large size and intensity they can be important
in applications such as atmospheric dispersion.
Morrison
et al
.
(
2005
) point to
their prevalence in the hurricane boundary layer. We'll discuss these atmospheric
boundary layer examples in
Chapter 11
.
Questions on key concepts
2.1
Since turbulence varies continuously in time and in the three spatial
directions, how can it ever be steady and homogeneous?
2.2
Describe the physical nature of the top of the atmospheric boundary layer.
2.3
Under what conditions does a time average converge to an ensemble average?
Ex
p
lain in physical terms why this convergence occurs.
If
u
T
is the time average (over time interval
T
) of a stationary random
function
2.4
u(t)
whose ensemble average is
U
,then
˜
2
u
2
τ
T
(u
T
−
U)
2
=
,
(1)
where
u
2
U)
2
=
(
u
˜
−
is the variance of
u(t)
. Explain physically the
˜
dependence on
u
2
,
τ
,and
T
.
2.5 Explain on physical grounds why we can roughly estimate
τ
in
Eq. (1)
as
/U
.
2.6 Explain why atmospheric turbulent flows tend to have much larger required
averaging times than engineering flows. What does this say about the relative
scatter in measurements in the two types of flows?
2.7 Why is averaging time
T
apt to be limited in atmospheric flows but not in
engineering flows?
2.8 Explain why we use the ensemble average in formal developments, even
though the time average can converge to it.
2.9 Explain some of the key differences between turbulent and molecular
diffusion. Explain their interplay.
2.10 Explain the concept of
u(r)
. How might one measure it?
2.11 Explain the concept of Reynolds-number similarity. Why is it important?
2.12 The eddy-diffusivity model has been criticized on the grounds that visual
observation of turbulence gives no support to the notion that it diffuses prop-
erties down their local mean gradients. Is this a legitimate point of view?
Discuss.
