Geoscience Reference
In-Depth Information
12.15 Explain the nature of the opportunities and hazards that the nocturnal jet
poses for wind power.
12.16 Discuss the important similarities and differences of the SBL and the
interfacial layer of the CBL.
12.17 Show that
Eq. (12.37)
for
R
f
follows from
Eq. (12.36)
.
12.18 Derive
Eq. (12.21)
.
12.19 Show that the Coriolis term in
Eq. (12.21)
is equivalent to a wind-turning
rate of 20 degrees per hour in mid-latitudes.
12.20 Explain why the jet exists in the
U
-component wind profile of
Figure 12.1
.
(Hint: in the coordinates used for that figure, integrate the lateral equation
of mean motion across the boundary layer.)
12.21 Use the equations of motion to discuss the mechanism through which in
clear weather the surface wind speed typically decreases as the bound-
ary layer transitions in late afternoon. What can you infer about
the
mechanism?
12.22 Show that integrating
Eq. (12.51)
from the surface to height
z
and evaluating
the result at
z
h
gives the geostrophic drag law,
Eq. (12.52)
.
12.23
Nieuwstadt
(
2005
) found his stably stratified, horizontally homogeneous
channel flow
(Subsection 12.3.4)
to be turbulent only for
L
=
≥
2
h,
with
L
the M-O length and
h
the channel depth.
(a) Assuming that the temperature flux decreases linearly from
Q
0
at the
surface to zero at the channel top, calculate the depth-averaged rate of
buoyant destruction of TKE per unit mass.
(b) Assume the MKE
equation (5.51)
reduces to a balance between the rate
of production of MKE by flow down the mean pressure gradient and the
rate of loss of MKE through shear production of turbulence. Recall from
Example
3.2.1
,
Chapter 3
, that the mean pressure gradient here does not
depend on
z
. Use this balance to express the depth-averaged rate of shear
production of TKE as the product of depth averaged mean velocity,
U
ave
,
and the mean kinematic pressure gradient.
(c) Use the streamwise mean momentum balance,
Eq. (3.10)
, the zero-stress
condition at
z
h
, and a high-
Re
approximation to neglect its viscous
term and express the mean kinematic pressure gradient in terms of
u
2
=
∗
and
h
.
(d) Use a friction factor
f
(as in the Moody chart,
Figure 1.2
)
to express
U
ave
in terms of
u
∗
.
(e) Write the global flux Richardson number, ratio of the depth-
integrated rates of buoyant production and shear production of TKE, in
terms of
h/L
. Relate your result to Nieuwstadt's finding that turbulence
cannot be supported for
h/L
≥
0
.
5
.
