Announcements

Exam #1 will be handed back Wednesday or Friday.

First homework assignment due next Monday.

No class Wednesday before Thanksgiving.

Cloud drops grow rapidly into raindrops because of _________________:

A) The Bergeron process.

B) The fact they have a curved surface.

C) They collide and coalesce with each other.

D) They form on hygroscopic cloud condensation nuclei.

Summary of Lecture 14Reviewed the basic concepts of pressure from earlier in the course.

Ideal gas low relates pressure to density and temperature. Breaking this down (Boyles law, Charles law, etc.) we find:

•Pressure is proportional to density•Pressure is proportional to temperature•Temperature is inversely proportional to density

Heating (cooling) a column of air expands (contracts) it and decreases (increases) density. The pressure gradient will force air to go from high to low pressure.

The example of an Arctic high was used to illustrate these concepts. At the surface, high pressure is associated with very cold temperatures.

Upper air charts show the height of a pressure surface above the ground. In the Arctic high example, because the air is cold it had a relatively low height at 300-mb.

Station model sea-level pressure must be adjusted for altitude.

Air pressure can be measured using a mercury barometer and aneroid barometer.

NATS 101 Section 4: Lecture 15

Why does the wind blow?

Part I

To begin the answer to this question we first have to revisit

Sir Isaac Newton

Newton’s First Law of Motion

Sir Isaac Newton

An object at rest will remain at rest and an object in motion will remain at a constant velocity if the net force exerted on it is zero.

Constant velocity = same speed, same direction.

An external force is required to change either the direction or speed of an object (or air in the case of the atmosphere)

Newton’s Second Law of Motion

Sir Isaac Newton

The net force exerted on an object is equal to it’s mass times acceleration, or change in velocity over time.

FORCE = MASS X ACCELERATIONF = ma

SI Units: Newton (kg m s-2)

Velocity is a vector property of the object’s speed AND its direction, so to change it and cause acceleration either:

1. Change the speed of the object2. Change the direction of the object.

Two causes of acceleration

Change in speed (magnitude) over time (t).

V1

Change in direction over time (t) with no change in speed

t

vva 12

t

vva 12

V1 V2

V2

INITIAL VELOCITY

FINAL VELOCITY

ACCELERATION

INITIAL VELOCITYFINAL

VELOCITY

V1

V2

ACCELERATION

V1

V2

CENTRIPETAL CENTRIPETAL FORCEFORCE

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.

Important when considering curved flows, as well see later…

CENTRIFUGAL CENTRIFUGAL FORCEFORCE

Centripetal Force

Newton’s second law can be used to derive a governing equation for

atmospheric motion

The simplified form in the horizontal we’ll consider has four terms. By

understanding how each of these terms works, we’ll be able to explain

why the wind blows.

Simplified equation of horizontal atmospheric motion

rFr

VV

d

p

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 FIRST TWO TODAY…FOCUS ON FIRST TWO TODAY…

Force Balance

What we’re looking for in the equation of motion is the condition where the forces exactly balance—or the sum of the forces is equal to zero.

When this happens, there is no net acceleration and the wind speed is constant, by Newton’s first law.

rFr

VV

d

p

2

2

sin1

0

0 = Pressure gradient force + Coriolis force + Centripetal Force + Friction

0 = Pressure gradient force + Coriolis force Geostrophic Balance

Pressure gradient force

Definition: Force to a the difference in pressure (Δp) over a distance (d). (In the equation ρ is the density of air)

d

p1

The pressure gradient force is directed perpendicular to lines of constant pressure (isobars).

Strength of the pressure gradient force

How strong the pressure gradient force is depends on the distance between the areas of high and low pressure, or how close the lines of constant pressure are.

Strong pressure Strong pressure gradient: Isobars close gradient: Isobars close togethertogether

Weak pressure Weak pressure gradient: Isobars far gradient: Isobars far apart.apart.

WEAK WEAK PRESSURE PRESSURE GRADIENTGRADIENT

STRONG STRONG PRESSUREPRESSUREGRADIENTGRADIENT

HH LL

ALOFT

SURFACE

ALOFT

Cold column relatively less air above. LOW PRESSURE.

Warm column relatively more above. HIGH PRESSURE

Result: Air moves from warm column to cold column, changing the total amount of mass of air in each.

SURFACE

Cold column more mass above. HIGH PRESSURE

Warm column less mass above. LOW PRESSURE.

The pressure gradient force is why the wind blows, but you need the other

terms to complete the picture…

Upper Level Chart for Surface

Arctic High Example(300-mb)

PRESSURE PRESSURE GRADIENT AT GRADIENT AT

DENVERDENVER

LOWLOWHIGHHIGH

Observations for upper level winds:

Wind DOES NOT follow the pressure gradient.

Wind runs parallel to the lines of constant height (i.e. isobars).

Strength of the wind IS related to the closeness, or packing, of the isobars.

For example, compare the wind speed at Denver (105 knots) to some of the surrounding upper air observations, like Albuquerque.

NEED AT LEAST ONE OF THE OTHER THREE FACTORS TO ACCOUNT FOR WIND MOTION

DENVERDENVER105 knots105 knots

ALBUQUERQUEALBUQUERQUE90 knots90 knots

Coriolis Force sinV2

Definition: Apparent force due to rotation of the Earth (Ω). Depends on the speed (V) and the latitude (Φ).

Causes apparent deflection in reference from of an observer at a fixed point on Earth

Gaspard Coriolis

Coriolis force on a merry-go-round

From perspective of person NOT on merry-go-round, path of ball is straight.

From perspective of person on merry-go-round, path of ball deflects. This is an apparent (or fictitious force).

Merry-go-round example

Rotation of the Earth (from the polar perspective)

NORTHERN HEMISPHERE SOUTHERN HEMISPHERE

COUNTERCLOCKWISE ROTATIONDeflection to the right

CLOCKWISE ROTATIONDeflection to the left

(Getzelman)

SAME IDEA AS THE MERRY-GO-ROUND!

Coriolis Effect: An Apparent Force

Cannonball follows a straight path to an observer in space

Earth rotates counter-clockwise underneath cannonball (in Northern Hemisphere)

Cannonball appears to deflect to the right to an observer on earth

Coriolis Force and Latitude

All three airplanes travel in a straight line with respect to an outside observer (from space).

The largest deviation, or deflection to the right, with respect to an observer on Earth occurs for the one traveling closest to the pole.

The higher the latitude, the greater the Coriolis force. Accounted for by the sine term in the mathematical expression.

Zero at equator (sin 0° = 0)Maximum at poles (sin 90° = 1)

Coriolis force and speed

The Coriolis force is proportional to the wind speed.

The faster the speed (or velocity), the greater the amount of Coriolis force.

Note also the dependence on latitude here.

Coriolis Force vs. Wind Direction

NORTHERN HEMISPHERE SOUTHERN HEMISPHERE

WINDWIND

CORIOLIS FORCECORIOLIS FORCE(TO RIGHT)(TO RIGHT)

WIND

CORIOLIS FORCECORIOLIS FORCE(TO LEFT)(TO LEFT)

Coriolis forceCoriolis force acts perpendicular (at a right angle) to the wind directionwind direction, to the right or left depending on which hemisphere.

Geostrophic Wind

Positions 1 and 2:

Pressure gradient forcePressure gradient force accelerates the parcel towards the low pressure.

Coriolis forceCoriolis force acts to the right of the velocityvelocity of the parcelof the parcel, making it curve to the right.

PARCEL RELEASED

Geostrophic Wind

Positions 3 and 4:

Pressure gradient force continues to accelerate the parcel towards the low pressure.

As the velocity of the parcelvelocity of the parcel increases, the Coriolis forceCoriolis force increases, making the parcel continue to curve to the right.

Geostrophic Wind

Position 5: FINAL STATE

Pressure gradient forcePressure gradient force is balanced by the Coriolis forceCoriolis force.

Velocity of the parcelVelocity of the parcel is constant (no acceleration). Direction is parallel to the isobars.

FINAL STATE is called geostrophic balance.

Geostrophic Wind

Pressure gradient forcePressure gradient force is equally balanced by the Coriolis forceCoriolis force, so net force is zero.

Wind speed and direction (velocity)Wind speed and direction (velocity) is constant (no acceleration).

Direction of wind is parallel to the isobars, or lines of constant pressure.

WINDWIND

CORIOLIS FORCECORIOLIS FORCE

PRESSURE GRADIENTPRESSURE GRADIENTFORCEFORCE

Isobar 1

Isobar 2

WINDWIND

CORIOLIS FORCECORIOLIS FORCE

PRESSURE GRADIENTPRESSURE GRADIENTFORCEFORCE

Isobar 1

Isobar 2

WINDWIND

PRESSURE GRADIENTPRESSURE GRADIENTFORCEFORCE

Isobar 2

Isobar 1

WEAKGEOSTROPHIC

WIND

Isobars far apart

STRONGGEOSTROPHIC

WIND

Isobars close together

CORIOLIS FORCECORIOLIS FORCE

PRESSURE PRESSURE GRADIENT GRADIENT

FORCEFORCE

Geostrophic Wind and Upper Level Charts

CORIOLIS CORIOLIS FORCE FORCE

GEOSTROPHIC GEOSTROPHIC WIND WIND

Winds at upper levels are pretty close to being geostrophic:

Wind is parallel to isobars

Wind strength dependent on how

close together isobars are

Simplified equation of horizontal atmospheric motion

rFr

VV

d

p

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)

XGEOSTROPHY:

No centripetal force or friction

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.

Reading Assignment and Review Questions

Reading: remainder of Chapter 8.

Chapter 8 Questions

Questions for Review (8th ed.): 9,10,11,12,13

Questions for Review (9th ed.): 10,11,12,13,14

Questions for Thought: 8