#### Transcript slides

```Atmospheric Motion
SOEE1400: Lecture 7
Plan of lecture
1.
2.
3.
4.
5.
6.
7.
Forces on the air
Coriolis force
Geostrophic wind
Effects of curvature
Effects of friction
Upper level charts.
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Isobars at 4mb intervals
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• The air is subject to Newton’s second law
of motion: it accelerates when there is an
unbalanced force.
• When the forces are balanced, the airflow
• There are 3 forces which influence
horizontal airflow:
– Coriolis force
– Frictional drag
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main driving force for winds.
Pressure gradient force = - 1 dP
 dx
where P is pressure,  is air density,
and x is distance. The force is thus
inversely proportional to the spacing
of isobars (closer spacing  stronger
force), and is directed perpendicular
to them, from high pressure to low.
1000 mb
1004 mb
pressure
force
The pressure force acts to accelerate
the air towards the low pressure.
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The coriolis force is an apparent
force, introduced to account for the
apparent deflection of a moving
object observed from within a rotating
frame of reference – such as the
Earth.
Axis of spin
The coriolis force acts at right angles
to both the direction of motion and the
spin axis of the rotating reference
frame.
V
Coriolis Force
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Movies … see web page.
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Coriolis Force on a Flat Disk
Fc
V
1
2
3
4
5
6
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Earth is a sphere – more complex
than disk: horizontal and vertical
components to the coriolis force.
In the atmosphere, we are concerned
only with the horizontal component
of the coriolis force. It has a
magnitude (per unit mass) of:
2Ω V sin = f V
Ω = angular velocity of the earth
V = wind speed
 = latitude
f = 2Ω V sin = “Coriolis parameter”
This is a maximum at the poles and
zero at the equator, and results in a
deflection to the right in the northern
hemisphere, and to the left in the
southern hemisphere.
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Geostrophic Balance
FP
1000 mb
Vg
1004 mb
Fc
Steady flow tends to lie parallel to the isobars, so that the
pressure and coriolis forces balance. This is termed
geostrophic balance, and Vg is the geostrophic wind speed.
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Steady flow in the absence of
friction
Since the coriolis force balances
the pressure force we have:
Pressure gradient force = coriolis force
1 dP = 2Ω Vg sin
 dx
Geostrophic wind speed is directly
proportional to the pressure
on latitude.
 For a fixed pressure gradient,
the geostrophic wind speed
decreases towards the poles.
N.B. air density  changes very
little at a fixed altitude, and is
usually assumed constant, but
decreases significantly with
increasing altitude
 pressure gradient force for a
increases with altitude
 geostrophic wind speed
increases with altitude.
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Geostrophic wind scale (knots)
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Geostrophic flow is a close
approximation to observed winds
throughout most of the free
atmosphere, except near the
equator where the coriolis force
approaches zero.
Departures from geostrophic
balance arise due to:
– constant changes in the
pressure field
– curvature in the isobars
Significant departure from
geostrophic flow occurs near the
surface due to the effects of
friction.
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Centripetal Acceleration
Motion around a curved path requires
an acceleration towards the centre of
curvature: the centripetal
acceleration.
HIGH
Fc
V
LOW
FP
FP
V
Centripetal
acceleration
Centripetal
acceleration
Fc
The required centripetal acceleration
is provided by an imbalance between
the pressure and coriolis forces.
V is here called the gradient wind
For a low, the coriolis force is less
than the pressure force; for a high it is
greater than pressure force. This
results in:
LOW: V < geostrophic
(subgeostrophic)
HIGH: V > geostrophic
(supergeostrophic)
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Effect of friction
FP
FP
1000 mb
V
Fd
Vg
1004 mb
Fc
The direction of the drag force (Fd) is approximately opposite
to the wind direction.
The drag force exactly balances the coriolis and pressure
The wind speed is lower than the geostrophic wind.
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Effect of Friction
Geostrophic flow
away from surface
Friction at the surface slows the
wind. Turbulent mixing extends
effects of friction up to ~100 m to
~1.5 km above surface.
Lower wind speed results in a
smaller coriolis force, hence
reduced turning to right.
Wind vector describes a spiral:
the Ekman Spiral. Surface wind
lies to left of geostrophic wind
• 10-20 over ocean
Ekman Spiral • 25-35 over land
The wind speed a few metres
above the surface is ~70% of
geostrophic wind over the ocean,
even less over land (depending
Vg
on surface conditions)
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Surface winds cross
isobars at 10-35
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Upper-level charts
“Height of a pressure surface  Pressure on a height surface”
4000m
700 hPa
surface
3000m
2000m
1000m
Ground
level
Lower
pressure
850 hPa
surface
Higher
pressure
On a 2000 m chart, the
pressure here is lower
than to each side.
The height of the 850 hPa
surface is also low.
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Example
500 hPa height is
black contour).
500hPa winds
circulate around
the low.
Surface pressure is
the white lines.
500 hPa
geostrophic
wind
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Global Circulation
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For a non-rotating Earth,
convection could form simple
symmetric cells in each
hemisphere.
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Coriolis force turns the air
flow. Stable mean
circulation has 6 counterrotating cells – 3 in each
hemisphere.
Within each cell, coriolis
forces turn winds to east or
west. Exact boundaries
between cells varies with
season.
This is a grossly simplified
model, circulations are not
continuous in space or
time. Notably the Ferrel cell
is highly irregular in reality.
Polar Cell
Ferrel Cell
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Summary
• Balance of pressure and
coriolis forces results in
geostrophic flow parallel to
isobars
• Curvature of isobars around
centres of high and low
acceleration to turn the flow, so
– supergeostrophic around
HIGH
– subgeostrophic around
LOW
• Friction reduces wind speed
near surface
• Lower wind speed  reduced
coriolis turning, wind vector
describes an Ekman Spiral
between surface and level of
geostrophic flow
• Surface wind lies 10-35 to left
of geostrophic wind, crossing
isobars from high to low
pressure.
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• Difference in solar heating
between tropics and poles
requires a compensating flow
of heat
• Coriolis turning interacts with
large scale convective
circulation to form 3 cells in
each hemisphere
• This 6-cell model is a crude
over-simplification of reality,
but accounts for major features
of mean surface winds, and