QG theory Flashcards
The QG framework simplifies the equation of motions into a set of diagnostic equations
- QG omega equation
- QG geopotential tendency
geostrophic balance represents the
fundamental balance condition for mid-latitude synoptic-scale flow
The geostrophic wind approximation is only strictly valid in
regions of zero wind acceleration
There are two broad categories of flow in the atmosphere that will violate geostrophic balances
- Wind speed changes along the flow (i.e. jet streaks, regions of speed convergence/divergence)
- Wind direction changes along the flow (i.e. troughs and ridges, regions of confluence/diffluence)
Define ageostrophic wind
The degree of departure from geostrophic balance that characterizes synoptic-scale motions can be assessed by considering the difference between the actual wind at a location and the calculate geostrophic wind at the same point.
Ageostrophic wind is defined mathematically as
………………………, this implies that the geostrophic wind is non-divergent.
Because all divergence/convergence necessarily implies an acceleration of the wind field,
ALL…………………… in the synoptic-scale………………………………. is due to the presence of ageostrophic motion.
divergence , wind field
ALL divergence in the synoptic-scale wind field is due to the
presence of ageostrophic motion.
all vertical motion is due to the presence of
ageostrophic motion.
ageostrophic wind is entirely responsible for
- the distribution of cyclones,
- anticyclones,
- clouds,
- and precipitation in the atmosphere.
Despite the fact that the mid-latitude atmosphere is predominately in geostrophic balance, all of the important weather with which we are confronted develops as a direct result of the ……………………………….
often relatively small ageostrophic portion of the wind.
if the geostrophic wind is nondivergent, we have
the equation is for
relationship between ageostrophic wind and vertical motion
the equation means
divergece of ageostrophic wind in upper air causes upward motion
Equation for ageostrophic wind and horizontal acceleration:
Equation for ageostrophic wind and horizontal acceleration
Explain the following equation
Vag = Acceleration term in momentum equation and 1/f
Based on the equation we conclude three properties
- The ageostrophic wind is a measure of the horizontal acceleration in the atmosphere
- The ageostrophic wind is perpendicular to the horizontal acceleration vector
- The ageostrophic wind is directed to the left of the acceleration vector in the Northern Hemisphere.
To derive the relationship between ageostrophic wind and vertical motion, we first will write the
continuity equation in isobaric coordinates.
Centripital acceleration
ageostrophic wind
The ageostrophic winds converge on ……………………….of the upper trough (on its ………………side)
the western side, upstream
The ageostrophic winds converge on the western side of the upper trough (on its upstream side), leading to ………………..
downward vertical motion.
The ageostrophic winds divergence on the …………………side of the upper trough (on its …………………………side),
eastern , downstream
The ageostrophic winds divergence on the eastern side of the upper trough (on its downstream side), leading to …………………..vertical motion.
upward
……………………………………. explains why there tends to be cloudy/stormy weather downstream of an upper level trough
divergence on the eastern side of the upper trough (on its downstream side), leading to upward vertical motion.
obtain the geostrophic wind equations
based on the properties of the previous mathematical derivation, we see that the ageostrophic wind vector has three properties:
The following is an example of
Curvature in the wind field
The following is an example of
Speed change in the wind field
Under such circumstances, the acceleration of the wind will be entirely a consequence of ………………………….
speed changes.
A parcel of air located on the western edge of the entrance region would experience an acceleration in the……………………………
direction of the flow at that location
It can be shown that the rate of change of vorticity is strongly dominated by two processes
(change of vorticity with time)
- Vorticity advection
- Divergence
vorticity advection is resembled by
Divergence is resembled by
Vorticity
Rotation of wind around vertical axis (cyclonic or anticyclonic) vertical or in a slope
vorticity equation:
what does the equation mean?
vorticity is changing due to vorticity advection and divergence
storm has …………. vorticity
large
the divergence term describe
the effects of divergence on the change of vorticity within a fluid.
When divergence occurs in a fluid, vorticity becomes more …………………
anticyclonic
When…………………… occurs in a fluid, vorticity becomes more anticyclonic
divergence
When convergence occurs in a fluid, vorticity becomes more ……………..
cyclonic
When ………………………..occurs in a fluid, vorticity becomes more cyclonic
convergence
When divergence occurs in a fluid, vorticity becomes more anticyclonic. Thus, …………………………spins up …………………………..vorticity
convergence, cyclonic
When ………………….occurs in a fluid, vorticity becomes more ……………………. Thus, convergence spins up cyclonic vorticity
divergence, anticyclonic
Surface low-pressure centers are characterized by ………………………….and thus tend to be foci for the production of low-level cyclonic vorticity.
convergence
Surface low-pressure centers are characterized by convergence and thus tend to be ……………………………………………………..
foci for the production of low-level cyclonic vorticity.
upper divergence results in vorticity….
anticyclonic
upper convergence results in……
cyclonic
vorticity cyclonic (+ve or -ve)
+ve vorticity
Term A
Vorticity minimum in the ridges
Term B
Min. vorticity advection
Term C
Maximum vorticity advection
Term D
Vorticity max in the trough
vorticity anticyclonic (+ve or -ve)
-ve vorticity
Upstream of the trough, the geostrophic wind is directed from the ……………………………towards the ……………………………
vorticity minimum, vorticity maximum
………………………………………., the geostrophic wind is directed from the vorticity minimum towards the vorticity maximum.
Upstream of the trough
Downstream of the trough, the geostrophic wind is directed from the …………………………………. towards the ……………………………
vorticity maximum, vorticity minimum
…………………………………………, the geostrophic wind is directed from the vorticity maximum towards the vorticity minimum.
Downstream of the trough,
Note that regions of maximum vorticity advection is collocated with regions of …………………………………….
divergence
Note that regions of …………………………………vorticity advection is collocated with regions of divergence
maximum
The most important application of QG theory is
the diagnosis of vertical motion
The fundamental equation of QG theory indicate that ………………….and ……………………………………are dynamically forced by two mechanisms:
–Vorticity advection
–Thermal advection
vertical motion 𝜔, geopotential height tendency 𝜒
The fundamental equation of QG theory indicate that vertical motion 𝜔 and geopotential height tendency 𝜒 are dynamically forced by two mechanisms:
- Vorticity advection
- Thermal advection
This parcel (the small circle) has some vorticity value as it enters the trough. Along its trajectory, it is encountering more and more
cyclonic vorticity values
This parcel (the small circle) has some vorticity value as it enters the trough. Along its trajectory, it is encountering more and more cyclonic vorticity values. If it is to stay in equilibrium with its environment, it must
increase its vorticity
This parcel (the small circle) has some vorticity value as it enters the trough. Along its trajectory, it is encountering more and more cyclonic vorticity values. If it is to stay in equilibrium with its environment, it must increase its vorticity through
horizontal convergence
By this reasoning, parcels entering the backside of the trough, in a region of
anticyclonic vorticity advection (negative vorticity advection (NVA))have to converge
By this reasoning, parcels entering the backside of the trough, in a region of anticyclonic vorticity advection (AVA) (that is, vorticity values are becoming more cyclonic along the flow) are having to converge. By the same argument, in the region of
cyclonic vorticity advection (CVA) on the other side of the trough axis, parcels are diverging.
in this way, PVA implies
divergence
NVA implies
convergence at any level in the atmosphere
generally speaking, PVA at 500 mb is
typically associated with PVA increasing with height
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