Geography Reference
In-Depth Information
Horizontal
stretching deformation
tends to advect the temperature field so that
the isotherms become concentrated along the axis of
dilation
(the x axis in Fig.
9.1b), provided that the initial temperature field has a finite gradient along the
axis of
contraction
(the y axis in Fig. 9.1b). That this effect is represented by the
second term on the right in (9.1) can be verified by noting from Fig. 9.1b that
∂T/∂y < 0 and ∂u
g
/∂x > 0.
The velocity field shown in Fig. 9.1b is a pure stretching deformation field. A pure
deformation field is both irrotational and nondivergent. Thus, a parcel advected
by a pure deformation field will merely have its shape changed in time, without
any rotation or change in horizontal area. The deformation field of Fig. 9.1b has
a streamfunction given by ψ
Kxy, where K is a constant. Such a field is
characterized by the rate at which advection changes the shape of a horizontal area
element. This can be illustrated by considering the rectangular element with sides
δx and δy. The shape can be represented by the ratio δx/δy, and the fractional rate
of change of shape can thus be expressed as
=−
1
(δx/δy)
D(δx/δy)
Dt
1
δx
Dδx
Dt
−
1
δy
Dδy
Dt
=
δu
δx
−
δv
δy
≈
∂u
∂x
−
∂v
∂y
=
It is easily verified that the fractional rate of change of δx/δy for the velocity field
in Fig. 9.1b equals
2K. Thus, a square parcel with sides parallel to the x and y
axes would be deformed into a rectangle as the sides parallel to the x axis stretch
and those parallel to the y axis contract in time at a constant rate.
Horizontal deformation at low levels is an important mechanism for the devel-
opment of both cold and warm fronts. In the example of Fig. 9.2 the flow near
point A has ∂u/∂x > 0 and ∂v/∂y < 0 so that there is a stretching deformation
field present with its axis of contraction nearly orthogonal to the isotherms. This
deformation field leads to strong warm advection south of point A and weak warm
advection north of point A.
Although, as shown in Fig. 9.2, the low-level flow in the vicinity of a developing
warm front may resemble a pure deformation field, the total flow in the upper
troposphere in baroclinic disturbances seldom resembles that of a pure deformation
field due to the presence of strong mean westerlies. Rather, a combination of
mean flow plus horizontal stretching deformation produces a
confluent
flow as
shown in Fig. 9.3. Such confluence acts to concentrate the cross-stream temperature
gradient as parcels move downstream. Confluent regions are always present in
the tropospheric jetstream due to the influence of quasi-stationary planetary-scale
waves on the position and intensity of the jet. In fact, even a monthly mean 500-
hPa chart (see Fig. 6.3) reveals two regions of large-scale confluence immediately
to the east of the continents of Asia and North America. Observationally, these
two regions are known to be regions of intense baroclinic wave development and
frontogenesis.
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