announcements midterm exam #1 will be given back in class friday. first homework assignment due next...
DESCRIPTION
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.TRANSCRIPT
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 15Newton’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
rFr
VVdp
2
2
sin1 Force Total
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
(1) (2) (3) (4)FOCUS ON LAST TWO THIS TIME…FOCUS ON LAST TWO THIS TIME…
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
INITIALWIND
FASTERWIND
INITIALWIND
SLOWERWIND
MASS LOST MASS GAINED
AIR RISINGBELOW
AIR SINKING ABOVE
AIR RISINGABOVE
AIR SINKINGBELOW
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.
Centripetal Force =
tvva 12
Arises from a change in wind direction with a constant speed (v) due to the curvature of the flow around a radius (r)
Center of circle
V1
Initial velocity
V2
Final velocity
-V1
V2
Centripetal acceleration (a)(towards the center of circle)
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.
rV2
a
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.
CENTRIFUGAL FORCE
Centripetal Force
WINDS IN WINDS IN GEOSTROPIC GEOSTROPIC BALANCEBALANCE
CENTRIPETAL CENTRIPETAL ACCELERATION ACCELERATION NEEDED ACCOUNT FOR NEEDED ACCOUNT FOR THE CURVATURE OF THE CURVATURE OF THE FLOWTHE FLOW
Assume PGF constant size along entire channel
Height 1
Height 2
Flow around curved height iso-lines
LLHH
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.
Height 1
Height 2
Gradient Balance: Curved Flow
WIND AROUND LOW PRESSURE
Centripetal + PGF = Coriolis
WIND AROUND HIGH PRESSURE
Centripetal + Coriolis = PGF
PGF
PGF
Coriolis
CoriolisCent.
Cent.
PGF
Coriolis
WIND
WINDWIND
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
Centripetal + PGF = Coriolis
OR, better to think…
PGF = Coriolis – Centripetal
Effectively REDUCES the pressure gradient force
Wind slows down.
WIND AROUND HIGH PRESSURE
PGF = Centripetal + Coriolis
Effectively INCREASES the pressure gradient force,
Wind speeds up.
Height 1
Height 2
WIND AROUND LOW PRESSURE
Centripetal + PGF = Coriolis
WIND AROUND HIGH PRESSURE
Centripetal + Coriolis = PGF
PGF
PGF
Coriolis
CoriolisCent.
Cent.
SLOWESTWIND
FASTEST WIND
SLOWEST WIND AT THE BASE OF A TROUGH
FASTEST WIND AT THE TOP OF THE RIDGE
Height 1
Height 2PGF
PGF
Coriolis
CoriolisCent.
Cent.
SLOWESTWIND
FASTEST WIND
WIN
D INCREASES
WIN
D INCREASES WIND DECREASES
WIND DECREASES
Because of the effect of centripetal force, winds increase to the east of trough and decrease to the east of a ridge.
THERE MUST BE COMPENSATING VERTICAL MOTION DUE TO CHANGES IN WIND SPEED AHEAD OF THE TROUGH AN RIDGE.
MASS DIVERGENCE MASS CONVERGENCE
INITIALWIND
FASTERWIND
INITIALWIND
SLOWERWIND
MASS DIVERGENCE AND COVERGENCE AT UPPER LEVELS (DUE TO CURVATURE OF THE FLOW)
Stratosphere (acts as a lid) Stratosphere (acts as a lid)
AIR RISING
AIR SINKING
AHEAD OF A TROUGH AHEAD OF A RIDGE
Height 1
Height 2PGF
PGF
Coriolis
CoriolisCent.
Cent.
SLOWESTWIND
FASTEST WIND
WIN
D INCREASES
WIN
D INCREASES
MASS DIV
ERGENCE
MASS DIV
ERGENCE WIND DECREASES
WIND DECREASES
MASS CONVERGENCE
MASS CONVERGENCERISING MOTIONRISING MOTIONAHEAD OF AHEAD OF TROUGHTROUGH SINKING MOTIONSINKING MOTION
AHEAD OF AHEAD OF RIDGERIDGE
Relationship between upper level troughs and ridges and vertical motion
Relationship between upper level troughs and ridges and vertical motion
SINKING MOTION TYPICALLY STABLE
RISING MOTIONMAY BE CONDITIONALLY UNSTABLE
(if clouds form and air is saturated)
Surface Surface HighHigh Surface Surface
LowLow
UPPER LEVEL~300 mb
SURFACE
RISING MOTIONSINKING
MOTION
SINKING MOTION
TROUGHTROUGH
RIDGERIDGE
RISING MOTION
SURFACE LOW (in Colorado) IS LOCATED DIRECTLY AHEAD OF TROUGH AT 300-MB, BECAUSE AIR IS RISING AHEAD OF THE TROUGH
TROUGHTROUGH
UPPER LEVEL SURFACE
Gradient balance and flow around lows and highs (Northern Hemisphere)
Cent. forceCent. force
Cent. forceCent. force
Counterclockwise flow around lows
Clockwise flow Around highs
Flow around low pressure
Counterclockwise flow Clockwise flow(because Coriolis force reverses with respect to wind direction)
NORTHERN HEMISPHERE SOUTHERN HEMISPHERE
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
LLCentrifugal
force
Pressure gradient
force
Pressure gradient balances the centrifugal force.
Occurs where flow is on a small enough scale where the Coriolis force becomes negligible.
PGF + centripetal force = 0
OR
PGF = Centrifugal force
Important in (the really cool) meteorological phenomena that have really strong winds and tight pressure gradients!
Examples of Cyclostrophic Flow
HURRICANES
TORNADOES
And the flushing
toilet, too!!
The Great Mystery of the
Flushing Toilet Solved!
PGFPGF
Centrifugal Centrifugal forceforce
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.
Mass convergence andrising motion
Air curves outward away from surface high pressure
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, 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
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