GUIDE WAVE ANALYSIS AND FORECASTING - WMO

26
Gr G
Gr
∇p C Cnf ∇p C Cnf ∇p C
Low High
Figure 2.4 — Balance of forces for basic types of frictionless
flow (northern hemisphere) (Gr = gradient
wind, G = geostrophic wind, ∇p = pressure
gradient force; C = Coriolis force and
Cnf = centrifugal force)
⎛ δug
δvg⎞g
⎛ δT
δT
⎞
⎜ , ⎟ = ⎜ – , ⎟ . (2.6)
⎝ δz
δy
⎠ T ⎝ δy
δx
⎠
In the southern hemisphere the left hand side of the
equation needs to be multiplied by –1.
It is clear from Equation 2.6 that the geostrophic
wind increases with height if higher pressure coincides
with higher temperatures (as in the case of mid-latitude
westerlies) and decreases with height if higher pressure
coincides with lower temperatures. Furthermore, if the
geostrophic wind at any level is blowing towards warmer
temperatures (cold advection), the wind turns to the left
(backing) as the height increases and the reverse happens
(veering) if the geostrophic wind blows towards lower
temperatures (warm advection).
The vector difference in the geostrophic wind at
two different levels is called the “thermal wind”. It can
be shown geometrically that the thermal wind vector
represents a flow such that high temperatures are located
to the right and low temperatures to the left. The thermal
wind, through linear vertical wind shear, can be incorporated
directly into the solution of the Ekman layer, and
thus incorporated in the diagnostic models which will be
described in more detail below.
2.3.4 Isallobaric wind
In the above discussions, the wind systems have been
considered to be evolving slowly in time. However, when
a pressure system is deepening (or weakening) rapidly, or
moving rapidly, so that the local geostrophic wind is
changing rapidly, an additional wind component
becomes important. This is obtained through the isallobaric
wind relation. An isallobar is a line of equal
pressure tendency (time rate of change of pressure). The
strength of the isallobaric wind is proportional to the isallobaric
gradient, and its direction is perpendicular to the
gradient — away from centres of rises in pressure and
toward centres of falls in pressure. Normally, this component
is less than 5 kn (2.5 m/s), but can become greater
than 10 kn (5 m/s) during periods of rapid or explosive
cyclogenesis.
GUIDE TO WAVE ANALYSIS AND FORECASTING
The isallobaric wind component is given by:
⎡ ⎛ p⎞
⎛ p⎞
⎤
⎢δ
⎜ ⎟ ⎜ ⎟
1 ⎝ t ⎠ ⎝ t ⎠ ⎥
( ui, vi)
= – 2 ⎢ , ⎥ . (2.7)
ρa
f ⎢ x y ⎥
⎣⎢
⎦⎥
The modification of the geostrophic wind field
around a moving low pressure system is illustrated in
Figure 2.5.
δ
δ
δ
δ
δ
δ
δ
2.3.5 Difluence of wind fields
Difluence (confluence) of isobars also creates flows that
make the winds deviate from a geostrophic balance.
When a difluence of isobars occurs (isobars spread
apart), the pressure gradient becomes weaker than its
upstream value, so that as an air parcel moves downstream,
the pressure gradient is unbalanced by the
Coriolis force associated with the flow speed. This then
results in the flow being deflected towards high pressure
in an effort to restore the balance of forces through an
increase in the pressure gradient force. In the case of
converging isobars, the pressure gradient increases from
it upstream value. Hence, the pressure gradient force
becomes larger than the Coriolis force and the flow turns
towards the low pressure in a effort to decrease the pressure
gradient force. In either case, it is clear that a
non-geostrophic cross-isobaric flow develops of a
magnitude U dG/ds (Haltiner and Martin, 1957), where
G is the geostrophic speed, U is the non-geostrophic
component normal to the geostrophic flow that has
developed in response to the confluence or difluence of
the isobars, and s is in the direction of the geostrophic
flow.
+2
G
I I
+4 Low
G
G
G
Figure 2.5 — Examples of the isallobaric wind field. Solid
line = isobar, dashed line = isallobar, G = (u g,
v g) = geostrophic wind, and I =(u i, v i) = isallobaric
wind
I
I
G
G
G G
I
I
I
-4
I
-2