Geography Reference
In-Depth Information
latitude. Compare this scale with the Rossby radius of deformation defined
in the text. (Note that gH
s
-
2
400 m
2
=
in this example.)
M7.6.
This problem examines the variation of phase velocity for Rossby waves
as the zonal wavelength is varied. Run the MATLAB program
rossby 1.m
with zonal wavelengths specified as 5000, 10,000 and 20,000 km. For each
of these cases try different values of the mean zonal wind until you find
the mean wind for which the Rossby wave is approximately stationary.
M7.7.
The MATLAB script
rossby 2.m
shows an animation of the Rossby waves
generated by a vorticity disturbance initially localized in the center of the
domain, with mean wind zero. Run the script and note that the waves
excited have westward phase speeds, but that disturbances develop on the
eastward side of the original disturbance. By following the development of
these disturbances, make a crude estimate of the characteristic wavelength
and the group velocity for the disturbances appearing to the east of the
original disturbance at time t
7.5 days. (Wavelength can be estimated by
using
ginput
to measure the distance between adjacent troughs.) Compare
your estimate with the group velocity formula derived from (7.91). Can
you think of a reason why your estimate for group velocity may differ from
that given in the formula?
=
M7.8.
The MATLAB script
rossby 3.m
gives the surface height and meridional
velocity disturbances for topographic Rossby waves generated by flow
over an isolated ridge. The program uses a Fourier series approach to
the solution. Ekman damping with a 2-day damping time is included to
minimize the effect of waves propagating into the mountain from upstream
(but this cannot be entirely avoided). Run this program for input zonal
mean winds from 10 to 100 m/s at 10-m/s intervals. For each run use
ginput
to estimate the scale of the leeside trough by measuring the zonal
distance between the minimum and maximum in the meridional velocity.
(This should be equal approximately to one-half the wavelength of the
dominant disturbance.) Compare your results in each case with the zonal
wavelength for resonance given by solving (7.93) to determine the resonant
L
x
=
2π
k, where K
2
π
8
10
6
in units of 1/m. (Do
not expect exact agreement because the actual disturbance corresponds to
the sum over many separate zonal wavelengths.)
k
2
l
2
and l
=
+
=
×
Suggested References
Hildebrand,
Advanced Calculus for Applications
, is one of many standard textbooks that discuss the
mathematical techniques used in this chapter, including the representation of functions in Fourier
series and the general properties of the wave equation.
