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