Geography Reference
In-Depth Information
nonlinear balance equation (11.15) for the corresponding geopotential
, assuming that the Coriolis parameter is a constant corresponding to
its value at 30˚ N. Run this script for several values of the amplitude, A,
in the range 0.4
10
7
m
2
s
−
1
. Note how the geopotential
field depends on A. For the case A
10
7
to 4.0
×
×
10
7
m
2
s
−
1
use the
gradient
function in MATLAB to compute the geostrophic wind, and hence find
the ageostrophic wind. Plot these as quiver plots and explain why the
ageostrophic wind has the structure seen in your plot.
=
4.0
×
M11.4.
A simple model for the horizontal flow in the mixed layer on an equatorial
β plane forced by an equatorial wave mode is given by the following
equations:
∂u
∂t
=−
∂
∂x
+
−
αu
βyv
∂v
∂t
=−
∂
∂y
αv
−
βyu
−
where (x, y, t) is given by (11.32) for the appropriate mode. The MAT-
LAB script
equatorial mixed layer.m
solves these equations numeri-
cally for the horizontal velocity components and divergence field in the
mixed layer forced by a specified Rossby-gravity wave (n
0 mode)
geopotential perturbation corresponding to a w
est
ward propagating dis-
turbance of zonal wavelength 4000 km and
√
gh
e
=
=
18 m s
−
1
. Run the
code for a long enough time so that the solution becomes
per
iodic in time.
Rerun the model for zonal wavelength 10,000 km and
√
gh
e
=
36 m s
−
1
.
In each case compare the frequency of the oscillation with the Coriolis
parameter at the latitude of maximum convergence forced by the wave.
What can you conclude from these results?
M11.5.
Modify the MATLAB script of M11.4 to compute the mixed layer veloc-
ity and divergence pat
tern
for the n
=
1 Rossby mode for zonal wave-
length 4000 km and
√
gh
e
=
18 m s
−
1
using the formulas for frequency
and geopotential derived in Problem 11.8.
M11.6.
The MATLAB script
forced equatorial mode2.m
shows the time devel-
opment of the velocity and height perturbations produced by a transient
localized mass source for shallow water waves on an equatorial β-plane.
The model is based on equations (11.50), (11.51), and (11.53), but with
time tendency terms included (ε
0 is set here, but you can experiment
with different values if you wish). The source is located at the equator
at x
=
0. It rises smoothly in amplitude for the first 2.5 days and then
decreases to 0 at day 5. Modify the script to contour the divergence and
the vorticity. Run the script for a 10-day period and interpret the results
=
