Geography Reference
In-Depth Information
for a parcel lifted from the lowest level of the sounding. Modify this script
to plot profiles of the potential temperature, the equivalent potential tem-
perature, and the saturated potential temperature. Hint: Temperature at sat-
uration can be calculated by inverting the expression for saturation vapor
pressure, which is obtainable by integrating (D.4):
e s,tr exp L v
R v
1
T tr
1
T
e s =
10 6 Jkg 1 are the
saturation vapor pressure at the triple point temperature, the triple point
temperature, and the latent heat of vaporization, respectively.
where e s,tr =
6.11hPa, T tr =
273.16K, andL v =
2.5
×
M9.3. For the thermodynamic sounding of Problem M9.2 compute the CAPE and
the profile of vertical velocity for a parcel lifted from the lowest layer in the
absence of entrainment. What is the maximum vertical velocity, and what
is the distance that the parcel overshoots its level of neutral buoyancy?
M9.4. The MATLAB script lee wave 1.m uses the Fourier series approach to
solve for flow over an isolated ridge for the case of constant N and constant
mean zonal flow. For the case of
50 m s 1 determine by running the
script for various ridge widths what width is required for significant vertical
propagation (i.e., at what ridge width do phase lines of vertical velocity
begin to tilt with height)?
u
¯
=
M9.5. The script lee wave 2.m plots an approximate analytic solution for flow
over a mountain in the wide ridge limit. The height profile is given by
h 0 L 2 L 2
x 2
h(x)
=
+
where L is the width scale of the ridge and h 0 is the ridge height. For a
fixed ridge height of 2 km, vary the input zonal mean wind and comment on
the dependence of the contoured solutions. (Note that the vertical scale is
given in vertical wavelengths as in Fig. 9.7 in the text.) Modify the script to
vary the mountain height and determine what fraction of the vertical wave-
length the mountain height must have in order that wave breaking occur.
(The onset of wave breaking occurs when the streamlines become vertical.)
Suggested References
Durran (1990) reviews the dynamics of mountain waves and downslope windstorms.
Eliassen (1990) discusses the secondary circulation within frontal zones.
Emanuel, Atmospheric Convection is a graduate-level text covering the subject of convection,
including symmetric instability in great detail.
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