Geography Reference
In-Depth Information
M8.3.
The MATLAB script
twolayer model 3b.m
shows the propagation of a
wave packet composed of the sum of nine eastward propagating neutral
waves of the two-layer model, ranging in wave number from 0.6 to 1.6k,
where k
1850 km. Run the script and estimate from
the animation the characteristic phase velocity and the characteristic group
velocity for the cases of U
T
=
2π/L, and L
=
15 and 30 ms
−
1
.
=
M8.4.
Suppose that a meridional dependence is included in the eddy fields in the
two-layer model so that (8.17) becomes
A cos (my ) e
ik(x
−
ct)
B cos (my ) e
ik(x
−
ct)
ψ
m
=
;
ψ
T
=
where m
3000 km. Determine the zonal wavelength of
the most unstable wave. Solve for the fields ψ
m
,ψ
T
,
and ω
2
and plot (x, y)
cross sections of these fields using the MATLAB script
contour sample.m
as a template.
Hint:
The solutions in this case are similar to those of Prob-
lems 8.6-8.8 but with k
2
=
2π/L
y
and L
y
=
replaced by k
2
m
2
+
everywhere.
M8.5.
The MATLAB script
eady model 1.m
shows vertical and meridional cross
sections of the solution for the Eady model (Section 8.4.3) for the most
unstable wave mode at time t
0. Modify this script to plot the solution
for the Eady wave corresponding to the neutral stability condition given
in (8.69). Explain the vertical structure in this case in terms of quasi-
geostrophic theory.
=
Suggested References
Charney (1947) is the classic paper on baroclinic instability. The mathematical level is advanced,
but Charney's paper contains an excellent qualitative summary of the main results which is very
readable.
Hoskins, McIntyre, and Robertson (1985) discuss cyclogenesis and baroclinic instability from a poten-
tial vorticity perspective.
Pedlosky,
Geophysical Fluid Dynamics
(2nd ed.), contains a thorough treatment of normal mode
baroclinic instability at a mathematically advanced level.
Pierrehumbert and Swanson (1995) review numerous aspects of baroclinic instability, including
spatiotemporal development.
