Geography Reference
In-Depth Information
zonal wavelength is for vertical propagation to occur in the upper part of
the domain (above the 6-km level). (c) Determine how the amplitudes
of the momentum flux and momentum flux convergence at z
6km
change as the zonal wavelength is increased from 20 to 100 km. Do enough
different wavelengths so that you can plot graphs of the dependence of the
magnitudes of the momentum flux and zonal force on the wavelength of
the sinusoidal topography. Use MATLAB to plot these two graphs.
M7.4.
The script
geost adjust 1.m
together with the function
yprim adj 1.m.
illustrates one-dimensional geostrophic adjustment of the velocity field
in a barotropic model for a sinusoidally varying initial height field. The
equations are a simplification of (7.69), (7.70), and (7.71) in the text for the
case of no y dependence. Initially u
=
=
v
=
0,φ
gh
=
9.8 cos(kx).
The final balanced wind in this case will have only a meridional component.
Run the program
geost adjust 1.m
for the cases of latitude 30 and 60
◦
choosing a time value of at least 10 days. For each of these cases choose
values of wavelength of 2000, 4000, 6000, and 8000 km (a total of eight
runs). Construct a table showing the initial and final values of the fields
u
,v
,φ
and the ratio of the final energy to the initial energy. You can
read the values from the MATLAB graphs by using the
ginput
command
or, for greater accuracy, add lines in the MATLAB code to print out the
values needed. Modify the MATLAB script to determine the partition of
final state energy per unit mass between the kinetic energy (v
2
/2) and the
potential energy φ
2
/(2gH). Compute the ratio of final kinetic energy to
potential energy for each of your eight cases and show this in a table.
M7.5.
The script
geost adjust 2.m
together with the function
yprim adj 2.m
.
extends Problem M7.4 by using Fourier expansion to examine the geo-
strophic adjustment for an isolated initial height disturbance of the form
h
0
(x)
≡
+
x
L
2
. The version given here uses 64 Fourier
modes and employs a fast Fourier transform algorithm (FFT). (There are
128 modes in the FFT, but only one-half of them provide real information.)
In this case you may run the model for only 5 days of integration time (it
requires a lot of computation compared to the previous case). Choose an
initial zonal scale of the disturbance of 500 km and run the model for
latitudes of 15, 30, 45, 60, 75, and 90
◦
(six runs). Study the animations
for each case. Note that the zonal flow is entirely in a gravity wave mode
that propagates away from the initial disturbance. The meridional flow
has a propagating gravity wave component, but also a geostrophic part
(cyclonic flow). Use the
ginput
command to estimate the zonal scale of the
final geostrophic flow (v component) by measuring the distance from the
negative velocity maximum just west of the center to the positive maximum
just east of the center. Plot a curve showing the zonal scale as a function of
h
m
1
=−
