Geography Reference
In-Depth Information
where 0 (p) is the standard atmosphere geopotential dependent only on
pressure, is the magnitude of the geopotential wave disturbance, c is the
phase speed of zonal propagation of the wave pattern, and k and l are the
wave numbers in the x and y directions, respectively. If it is assumed that
the flow is in geostrophic balance, then the geopotential is proportional to
the stream function. Let the zonal and meridional wave numbers be equal
(k
k f 0 , where f 0
is a constant Coriolis parameter. Trajectories are then given by the paths
in (x, y) space obtained by solving the coupled set of ordinary differential
equations:
l) and define a perturbation wind amplitude U
=
Dx
Dt =
∂y =+
f 1
0
U sin [k (x
u
=−
ct)] sin ly
Dy
Dt =
∂x =+
f 1
0
U cos [k (x
v
=+
ct)] cos ly
[Note that U (taken to be a positive constant) denotes the amplitude of
both the x and y components of the disturbance wind.] The MATLAB script
trajectory 1.m provides an accurate numerical solution to these equations
for the special case in which the zonal mean wind vanishes. Three separate
trajectories are plotted in the code. Run this script letting U =
10 m s 1
5, 10, and 15 m s - 1 . Describe the behavior of the
three trajectories for each of these cases. Why do the trajectories have their
observed dependence on the phase speed c at which the geopotential height
pattern propagates?
=
for cases with c
M3.3. The MATLAB script trajectory 2.m generalizes the case of problem M3.2
by adding a mean zonal flow. In this cas e the geopotential distribution is
specified to be (x, y, t)
f 0 Ul 1 sin ly
sin [k (x
ct)]
cos ly. (a) Solve for the latitudinal dependence of the mean zonal wind
for this case. (b) Run the script with the initial x positi on specified as
x
=
0
+
10ms - 1 ,
2250 km a nd U =
15ms 1 . Do two runs, letting U
=−
=
10ms - 1 , respectively. Determine
the zonal distance that the ridge originally centered at x
5ms - 1
5ms - 1 , c
c
=
and U
=
=
2250 km
has propagated in each case. Use this information to briefly explain the
characteristics (i.e., the shapes and lengths) of the 4-day tra je ctories for
each of these cases. (c) What combination of initial position, U and c, will
produce a straight-line trajectory?
=−
M3.4. The MATLAB script trajectory 3.m can be used to examine the dispersion
of a cluster of N parcels initially placed in a circle of small radius for a
geopotential distribution representing the combination of a zonal mean jet
plus a propagating wave with NE to SW tilt of trough and ridge lines.
 
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