Announcements

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Announcements
Midterm exam 1 will be given back in class
Friday. First homework assignment due next
Monday.
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• The Coriolis force
• Causes the wind to blow from high to low pressure
• Causes the wind to blow perpendicular to lines of
  constant pressure
• Causes apparent deflection of a ball in a
  rotating reference frame, like a merry-go-round.
• All of the above

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• Survey question If you flush a toilet in the
  southern hemisphere
• The water will swirl counterclockwise.
• The water will swirl clockwise.
• The water can swirl either direction or may not
  even swirl at all.
• I dont know.

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Summary of Lecture 15
Newtons first law of motion an object will
remain at rest and an object in motion will
maintain a constant velocity if the net force is
zero. Newtons second law of motion F ma.
Change acceleration by a change in speed or
direction. The simplified equation of horizontal
atmospheric motion has four force terms pressure
gradient force, Coriolis force, centripetal
force, and friction. The pressure gradient force
is due to the difference in pressure over a
distance. The Coriolis force is an apparent
force due to the rotation of the Earth, and
depends on speed (of the wind) and latitude. It
causes deflection from the reference point of an
observer in a rotating frame. Coriolis force
deflects the wind to the right or left depending
on which hemisphere. Geostrophic wind occurs
when the pressure gradient force balances the
Coriolis force and the wind is parallel to the
isobars. A good approximation for upper level
winds.
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NATS 101 Section 4 Lecture 16

• Why does the wind blow?
• Part II

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Last time we talked about two of the force terms
in the simplified equation for horizontal air
motion

• Geostrophic Balance
• PRESSURE GRADIENT CORIOLIS

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Simplified equation of horizontal atmospheric
motion
FOCUS ON LAST TWO THIS TIME
(1)
(2)
(3)
(4)
Term Force Cause
1 Pressure gradient force Spatial differences in pressure
2 Coriolis force Rotation of the Earth
3 Centripetal force Curvature of the flow
4 Friction force Acts against direction of motion due to interaction with surface
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The centripetal force and friction force are
typically much smaller, but they are very
important for two reasons

1. Cause mass divergence and convergence
2. Can be relatively large in special cases that are
   meteorologically important (i.e. cool)

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MASS DIVERGENCE
MASS CONVERGENCE
AIR RISING ABOVE
AIR SINKING ABOVE
INITIAL WIND
FASTER WIND
INITIAL WIND
SLOWER WIND
AIR SINKING BELOW
AIR RISING BELOW
MASS LOST
MASS GAINED
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To begin a discussion of centripetal force, lets
address the popular belief about how water goes
down the drain
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Popular belief The way the toilet flushes or the
sink drains depends on which hemisphere youre in.
Bart vs. Australia Simpsons episode Bart calls
an Australian boy to see if his toilet really
does flush clockwiseWell see what the
surprising answer is later.
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Centripetal Force
Arises from a change in wind direction with a
constant speed (v) due to the curvature of the
flow around a radius (r)
Centripetal acceleration (a) (towards the center
of circle)
Center of circle
-V1
V2 Final velocity
a
V2
V1 Initial velocity
The centripetal acceleration is always directed
toward the center of the axis of rotation.
Note to be physically correct, the expression
should have a negative sign, so V2/r is actually
the centrifugal acceleration.
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Centripetal Force
CENTRIFUGAL FORCE
You experience acceleration without a change in
speed, for example, on a tilt-a-whirl carnival
ride. The force is directed toward the center
of the wheel. An equal an opposite
(fictitious) centrifugal force is exerted by the
inertia of your body on the wheelso you stay put
and dont fall off even when upside down.
CENTRIPETAL FORCE
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CENTRIPETAL ACCELERATION NEEDED ACCOUNT FOR THE
CURVATURE OF THE FLOW
WINDS IN GEOSTROPIC BALANCE
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Flow around curved height iso-lines
Assume PGF constant size along entire channel
Height 1
L
Height 2
H
Centripetal acceleration (towards low pressure)
Centripetal acceleration (towards high pressure)
When wind curves, it must have an centripetal
acceleration towards the axis of rotation, so it
is NOT geostrophic.
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Gradient Balance Curved Flow
PGF
WIND AROUND LOW PRESSURE Centripetal PGF
Coriolis
WIND
PGF
WIND
Height 1
PGF
Cent.
Height 2
Coriolis
Cent.
Coriolis
WIND
WIND AROUND HIGH PRESSURE Centripetal
Coriolis PGF
Coriolis
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The effect of curvature has curiousand counter
intuitive--implication for winds around high and
low pressure, if the pressure gradient is constant
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Changes in wind speed around highs and lows due
to gradient balance
WIND AROUND HIGH PRESSURE PGF Centripetal
Coriolis Effectively INCREASES the pressure
gradient force, Wind speeds up.
WIND AROUND LOW PRESSURE Centripetal PGF
Coriolis OR, better to think PGF Coriolis
Centripetal Effectively REDUCES the pressure
gradient force Wind slows down.
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PGF
WIND AROUND LOW PRESSURE Centripetal PGF
Coriolis
FASTEST WIND
Height 1
PGF
Cent.
Height 2
Coriolis
Cent.
SLOWEST WIND
WIND AROUND HIGH PRESSURE Centripetal
Coriolis PGF
Coriolis
SLOWEST WIND AT THE BASE OF A TROUGH
FASTEST WIND AT THE TOP OF THE RIDGE
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Because of the effect of centripetal force, winds
increase to the east of trough and decrease to
the east of a ridge.
PGF
FASTEST WIND
Height 1
PGF
Cent.
WIND INCREASES
Height 2
Coriolis
WIND DECREASES
Cent.
SLOWEST WIND
Coriolis
THERE MUST BE COMPENSATING VERTICAL MOTION DUE TO
CHANGES IN WIND SPEED AHEAD OF THE TROUGH AN
RIDGE.
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MASS DIVERGENCE AND COVERGENCE AT UPPER LEVELS
(DUE TO CURVATURE OF THE FLOW)
MASS DIVERGENCE
MASS CONVERGENCE
Stratosphere (acts as a lid)
Stratosphere (acts as a lid)
INITIAL WIND
FASTER WIND
INITIAL WIND
SLOWER WIND
AIR RISING
AIR SINKING
AHEAD OF A TROUGH
AHEAD OF A RIDGE
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Relationship between upper level troughs and
ridges and vertical motion
PGF
FASTEST WIND
Height 1
PGF
WIND INCREASES MASS DIVERGENCE
Cent.
Height 2
Coriolis
Cent.
WIND DECREASES MASS CONVERGENCE
SLOWEST WIND
RISING MOTION AHEAD OF TROUGH
SINKING MOTION AHEAD OF RIDGE
Coriolis
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Relationship between upper level troughs and
ridges and vertical motion
UPPER LEVEL 300 mb
SURFACE
Surface High
Surface Low
RISING MOTION MAY BE CONDITIONALLY UNSTABLE (if
clouds form and air is saturated)
SINKING MOTION TYPICALLY STABLE
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RIDGE
SINKING MOTION
RISING MOTION
SINKING MOTION
TROUGH
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SURFACE
UPPER LEVEL
RISING MOTION
TROUGH
SURFACE LOW (in Colorado) IS LOCATED DIRECTLY
AHEAD OF TROUGH AT 300-MB, BECAUSE AIR IS RISING
AHEAD OF THE TROUGH
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Gradient balance and flow around lows and highs
(Northern Hemisphere)
Cent. force
Cent. force
Counterclockwise flow around lows
Clockwise flow Around highs
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Flow around low pressure
NORTHERN HEMISPHERE
SOUTHERN HEMISPHERE
Counterclockwise flow
Clockwise flow (because Coriolis force reverses
with respect to wind direction)
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There is another force balance possibility if the
Coriolis force is very small or zero, so its
negligible.

• In that case, the pressure gradient force would
  balance the centripetal force.

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Cyclostrophic Balance
PGF centripetal force 0 OR PGF
Centrifugal force
L
Pressure gradient balances the centrifugal
force. Occurs where flow is on a small enough
scale where the Coriolis force becomes negligible.
Pressure gradient force
Centrifugal force
Important in (the really cool) meteorological
phenomena that have really strong winds and tight
pressure gradients!
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Examples of Cyclostrophic Flow
TORNADOES
HURRICANES
And the flushing toilet, too!!
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The Great Mystery of the Flushing Toilet Solved!
Centrifugal force
PGF
To Bart and Lisa A swirling, flushing toilet is
in cyclostrophic balance, so the way it flushes
depends more on the shape of the drainand
nothing to do with whether youre in Australia or
not!
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One last force to consider

• Friction

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Effect of Friction Force (at the surface)
Friction acts to slow the wind at the
surface The slower wind decreases the magnitude
of the Coriolis force. Weaker Coriolis force no
longer balances the pressure gradient
force. Wind crosses the isobars, more toward the
pressure gradient.
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Surface friction and flow around surface highs
and lows
Air curves outward away from surface high
pressure Mass divergence and sinking motion.
Air curves inward toward surface low
pressure. Mass convergence and rising motion
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Zoom-in on surface low in Colorado from earlier.
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Summary of Force BalancesWhy the wind blows
Force Balance Forces Involved Where it happens
Geostrophic Pressure gradient and Coriolis Winds at upper levels (with no curvature)
Gradient Pressure gradient, Coriolis, and centripetal (or centrifugal) Winds at upper levels with curvature.
Cyclostrophic Pressure gradient and centrifugal Smaller-scale, tight rotations like tornadoes and hurricanes
Gradient Friction Pressure gradient, Coriolis, centripetal, and friction Surface winds
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Reading Assignment and Review Questions
Reading Chapter 9 Chapter 8 Questions Questions
for Review (8th ed.) 15,16,17,18,21,22
(9th ed.)
16,17,18,19,22,23 Questions for Thought
9,10,13,14,15