Geography Reference
In-Depth Information
In general, midlatitude synoptic systems move eastward as a result of advection
by upper level westerly winds. In such cases there is a local turning of the wind
due to the motion of the system even if the shape of the height contour pattern
remains constant as the system moves. The relationship between R
t
and R
s
in
such a situation can be determined easily for an idealized circular pattern of height
contours moving at a constant velocity
C
. In this case the local turning of the wind
is entirely due to the motion of the streamline pattern so that
∂β
∂t
=−
C
∂β
C
R
s
C
·∇
β
=−
∂s
cos γ
=−
cos γ
where γ is the angle between the streamlines (height contours) and the direction
of motion of the system. Substituting the above into (3.23) and solving for R
t
with
the aid of (3.20), we obtain the desired relationship between the curvature of the
streamlines and the curvature of the trajectories:
R
s
1
−
1
C cos γ
V
R
t
=
−
(3.24)
Equation (3.24) can be used to compute the curvature of the trajectory anywhere
on a moving pattern of streamlines. In Fig. 3.7 the curvatures of the trajectories for
parcels initially located due north, east, south, and west of the center of a cyclonic
system are shown both for the case of a wind speed greater than the speed of
movement of the height contours and for the case of a wind speed less than the
speed of movement of the height contours. In these examples the plotted trajectories
are based on a geostrophic balance so that the height contours are equivalent to
streamlines. It is also assumed for simplicity that the wind speed does not depend
on the distance from the center of the system. In the case shown in Fig. 3.7b there is
a region south of the low center where the curvature of the trajectories is opposite
that of the streamlines. Because synoptic-scale pressure systems usually move at
speeds comparable to the wind speed, the gradient wind speed computed on the
basis of the curvature of the height contours is often no better an approximation to
the actual wind speed than the geostrophic wind. In fact, the actual gradient wind
speed will vary along a height contour with the variation of the trajectory curvature.
3.4
THE THERMAL WIND
The geostrophic wind must have vertical shear in the presence of a horizontal
temperature gradient, as can be shown easily from simple physical considerations
based on hydrostatic equilibrium. Since the geostrophic wind (3.4) is proportional
to the geopotential gradient on an isobaric surface, a geostrophic wind directed
along the positive
y
axis that increases in magnitude with height requires that the
