Transcript slides

Atmospheric Motion
ENVI 1400: Lecture 3
Isobars at 4mb intervals
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The PressureGradient Force
Horizontal pressure gradients are the
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
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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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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:
2 V sin
 = angular velocity of the earth
V = wind speed
 = latitude
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
A pressure gradient imposed on
a stationary air mass will start to
accelerate it towards the region
of low pressure
1000 mb
The pressure force
continues to accelerate the
flow, and the coriolis force
continues to turn it
FP
FP
FP
1004 mb
FP
Vg
V
V
V
Fc
Fc
The coriolis force acts to
turn the flow to the right (in
the northern hemisphere)
Fc
Fc
Eventually the flow becomes
parallel to the isobars, and
the pressure and coriolis
forces balance. This is
termed geostrophic balance,
and Vg the geostrophic wind
speed.
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Since the coriolis force balances
the pressure force we have:
Pressure gradient force = coriolis force
1 dP = 2 Vg sin
 dx
Geostrophic wind speed is directly
proportional to the pressure
gradient, and inversely dependent
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
given pressure gradient
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
– vertical wind shear
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
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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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.
Polar Cell
Ferrel Cell
N.B. This is a simplified model,
circulations are not continuous in
space or time.
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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
pressure requires centripetal
acceleration to turn flow,
resulting gradient wind is:
– 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
• 6 cell model is an oversimplification of reality, but
accounts for major features of
mean surface winds
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