Transcript lecture16

Announcements
Midterm exam #1 will be given back in class Friday.
First homework assignment due next Monday.
The Coriolis force:
A)Causes the wind to blow from high to low pressure
B)Causes the wind to blow perpendicular to lines of
constant pressure
C)Causes apparent deflection of a ball in a rotating
reference frame, like a merry-go-round.
D)All of the above
Survey question: If you flush a toilet in the southern
hemisphere:
A)The water will swirl counterclockwise.
B)The water will swirl clockwise.
C)The water can swirl either direction or may not even
swirl at all.
D) I don’t know.
Summary of Lecture 15
Newton’s 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.
Newton’s 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.
NATS 101
Section 4: Lecture 16
Why does the wind blow?
Part II
Last time we talked about two of the
force terms in the simplified equation
for horizontal air motion
Geostrophic Balance:
PRESSURE GRADIENT = CORIOLIS
Simplified equation of horizontal
atmospheric motion
1 p
V2
Total Force 
 2V sin 
 Fr
 d
r
TWO(4)
THIS TIME…
(1)FOCUS ON
(2) LAST(3)
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
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)
MASS DIVERGENCE
MASS CONVERGENCE
AIR RISING
ABOVE
AIR SINKING
ABOVE
INITIAL
WIND
FASTER
WIND
AIR RISING
BELOW
MASS LOST
INITIAL
WIND
SLOWER
WIND
AIR SINKING
BELOW
MASS GAINED
To begin a discussion of centripetal
force, let’s address the popular belief
about how water goes down the drain…
Popular belief: The way the toilet flushes
or the sink drains depends on which
hemisphere you’re in.
Bart vs. Australia Simpson’s episode: Bart calls an
Australian boy to see if his toilet really does flush
clockwise…We’ll see what the surprising answer is later.
V2
Centripetal Force =
r
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
V1
Initial velocity
a
v  v1
a 2
t
V2
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.
Centripetal Force
CENTRIFUGAL
FORCE
CENTRIPETAL
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 wheel—so you
stay put and don’t fall off even
when upside down.
CENTRIPETAL
ACCELERATION
NEEDED ACCOUNT FOR
THE CURVATURE OF
THE FLOW
WINDS IN
GEOSTROPIC
BALANCE
Flow around curved height iso-lines
Assume PGF constant size along
entire channel
Height 1
Height 2
L
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.
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
Coriolis
WIND AROUND
HIGH PRESSURE
Centripetal + Coriolis = PGF
The effect of curvature has curious—and
counter intuitive--implication for winds
around high and low pressure, if the
pressure gradient is constant
Changes in wind speed around highs and
lows due to gradient balance
WIND AROUND
LOW PRESSURE
WIND AROUND
HIGH PRESSURE
Centripetal + PGF = Coriolis
PGF = Centripetal + Coriolis
OR, better to think…
Effectively INCREASES the
pressure gradient force,
PGF = Coriolis – Centripetal
Wind speeds up.
Effectively REDUCES the
pressure gradient force
Wind slows down.
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
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.
Height 2
Coriolis
Cent.
SLOWEST
WIND
Coriolis
THERE MUST BE COMPENSATING VERTICAL MOTION DUE TO
CHANGES IN WIND SPEED AHEAD OF THE TROUGH AN RIDGE.
MASS DIVERGENCE AND COVERGENCE AT UPPER LEVELS
(DUE TO CURVATURE OF THE FLOW)
MASS DIVERGENCE
Stratosphere (acts as a lid)
INITIAL
WIND
FASTER
WIND
AIR
RISING
AHEAD OF A TROUGH
MASS CONVERGENCE
Stratosphere (acts as a lid)
INITIAL
WIND
SLOWER
WIND
AIR
SINKING
AHEAD OF A RIDGE
Relationship between upper level troughs
and ridges and vertical motion
PGF
FASTEST
WIND
Height 1
PGF
Height 2
Cent.
Cent.
Coriolis
SLOWEST RISING MOTION
WIND
AHEAD OF
TROUGH
Coriolis
SINKING MOTION
AHEAD OF
RIDGE
Relationship between upper level troughs
and ridges and vertical motion
UPPER LEVEL
~300 mb
Surface
High
SINKING MOTION
TYPICALLY STABLE
SURFACE
Surface
Low
RISING MOTION
MAY BE CONDITIONALLY UNSTABLE
(if clouds form and air is saturated)
RIDGE
SINKING
MOTION
RISING
MOTION
TROUGH
SINKING
MOTION
UPPER LEVEL
SURFACE
RISING
MOTION
TROUGH
SURFACE LOW (in Colorado) IS LOCATED DIRECTLY AHEAD OF
TROUGH AT 300-MB, BECAUSE AIR IS RISING AHEAD OF THE
TROUGH
Gradient balance and flow around lows
and highs (Northern Hemisphere)
Cent. force
Cent. force
Counterclockwise flow
around lows
Clockwise flow
Around highs
Flow around low pressure
NORTHERN HEMISPHERE
Counterclockwise flow
SOUTHERN HEMISPHERE
Clockwise flow
(because Coriolis force reverses
with respect to wind direction)
There is another force balance
possibility if the Coriolis
force is very small or zero,
so it’s negligible.
In that case, the pressure
gradient force would balance
the centripetal force.
Cyclostrophic Balance
PGF + centripetal force = 0
OR
PGF = Centrifugal force
L
Pressure
gradient
force
Centrifugal
force
Pressure gradient balances
the centrifugal force.
Occurs where flow is on a
small enough scale where
the Coriolis force becomes
negligible.
Important in (the really cool) meteorological phenomena that have
really strong winds and tight pressure gradients!
Examples of
Cyclostrophic Flow
TORNADOES
HURRICANES
And the
flushing
toilet, too!!
The Great Mystery
of the
Flushing Toilet
Solved!
PGF
Centrifugal
force
To Bart and Lisa: “A swirling, flushing toilet is in cyclostrophic
balance, so the way it flushes depends more on the shape of the
drain—and nothing to do with whether you’re in Australia or not!”
One last force to consider…
Friction
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.
Surface friction and flow around
surface highs and lows
Air curves inward toward
surface low pressure.
Air curves outward away
from surface high pressure
Mass convergence and
rising motion
Mass divergence and
sinking motion.
Zoom-in on
surface low in
Colorado
from earlier.
Summary of Force Balances:
Why 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,
Winds at upper levels
and centripetal (or centrifugal) 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
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