Geography Reference
In-Depth Information
10.12.
Show by considering ∂u/∂t for small perturbations about the equilibrium
points in Fig. 10.17 that point B is an unstable equilibrium point while
points A and C are stable.
MATLAB EXERCISES
M10.1.
The MATLAB script
topo wave 1.m
uses finite differencing to solve the
linearized vorticity equation (7.99) on a midlatitude β plane for the case
of a constant mean zonal wind and forcing by a circular mountain with
mountain height given by h
T
(x, y)
y
2
−
1
, where
h
0
and L are constants characterizing the mountain height and horizontal
scale, respectively. Run the script for mean zonal winds of 5, 10, 15,
and 20 m s
−
1
. In each case estimate the horizontal wavelength and group
velocity of the northward and southward Rossby wave trains that form
in the lee of the mountain. Compare your results with the corresponding
expressions given in Section 10.5.1.
h
0
L
2
L
2
x
2
=
+
+
M10.2.
The two-meridional-mode version of the Charney and Devore (1979)
model described in Section 10.6.1 is given in the MATLAB script
C D model.m
. Solutions for this model may be steady state, periodic
in time, or irregularly varying, depending on the forcing of the first mode
zonal-mean streamfunction (zf(1) in the script) and the initial amplitude
of this mode (zinit(1) in the script). Run this script for forcing values of
zf(1)
0.1, 0.2, 0.3, 0.4, 0.5. In each case do two runs with initial con-
ditions zinit(1)
=
0.1, respectively. For each of the
10 cases, note whether the solution is steady, periodic, or irregular. Com-
pute the time average of the zonal mean zonal wind for nondimensional
time interval 2000 <t<3000 for each of these cases. Are your results
consistent with Fig. 10.17 in the text? Note for each case whether the
streamfunction tends to be in phase or out of phase with the topography
and whether the results are qualitatively consistent with the solution for
topographic Rossby waves given in Section 7.7.2.
=
zf(1) and zinit(1)
=
M10.3.
The MATLAB script
baroclinic 1.m
provides a simple illustration of
the effect of baroclinic eddies on the mean flow. The script extends the
two-level baroclinic instability model discussed in Section 8..2 by cal-
culating the evolution of the mean zonal flow components U
m
and U
T
caused by meridional vorticity and heat fluxes associated with unstable
baroclinic waves. The calculation is done for a midlatitude β plane with
weak Ekman layer damping. The eddies are governed by the linearized
model of Section 8.2 (with fixed zonal wavelength of 6000 km), but the
zonal-mean flow is affected by eddy-mean flow interactions and evolves
