Chapter 7

Chapter 7Forces and Force Balances

“What goes up, must come down”.

Weather

• Why do we have storms? Why do we have weather?

• In the atmosphere, we experience forces that lead to the movement of air

• Today’s lecture will discuss the four forces that lead to air movement

From www.noaa.gov

Fundamental Forces

• What are these four fundamental forces?

• You probably already have experience with some of them!

• What causes an apple to fall on your head if you are sitting under a tree (Isaac Newton)?– Gravity!

www.cartoonstock.com

Fundamental Forces• Remember the bouncy castle

analogy from Chapter 6?• Feed kids sugar, and put them in a

castle• Parents try to hold up the castle

on the outside?• This was related to what

property?– Pressure

• This is a way to explain something called the pressure gradient force

Fundamental Forces

• What happens when you rub your hands together?– They kind of stick, right?

• What happens when you slam the brakes on your car really hard?– Your tires squeal and you leave marks on the road

• What is this force called?– Friction!

Atmospheric Forces

• The previous three are called “fundamental forces”

• They occur on Earth even if the Earth was not rotating

• There is a fourth force that only occurs because the Earth is rotating

• This is called the Coriolis Force

www.rps.psu.edu

Pressure Gradient Force

• Let’s assume that we have a wall with people pushing on both sides of the wall

• How do we make the wall move to the right?

Pressure Gradient Force• Imagine that you are sitting

in a cubicle at work, while a friend sits on the other side of the wall

• If you and your friend push on either side of the cubicle wall, what do you need to happen for you to move the wall closer to them?– Push harder than your friend

Pressure Gradient Force

• Let’s say you and your friend are pushing with the same force

• Your boss shows up and helps you push the wall– This is another way to move the wall toward your

friend

Pressure Gradient Force (PGF)

• What we just learned about is the pressure gradient force!

• Imagine you have an invisible wall, with a certain number of molecules on either side of the wall– There are two ways to

accelerate the wall in one direction. What are they?

– Increase the force that the molecules are hitting the sides of the wall

– Increase the number of molecules on one side of the wall

How do we change the PGF?

• Increase the force the molecules are hitting the wall

• How do we do that?– Increase the temperature!

• How do we increase the number of molecules on either side of the wall?– Increase the density of the air!

Translate to the atmosphere• We have gotten rid of our wall

and now only have a single molecule

• Apply the same concepts• If the temperature or density is

increased on the left side of the molecule, it will accelerate to the right– Increased pressure

• What atmospheric property that we talked about does this represent? – Wind!!

Figure 7.2

Fundamental Force #1: PGF

• Congratulations! Now you understand one of the basic forces on Earth!

• On a broader scale, if we have a pressure gradient from one region to another, the air molecules will move from one place to another– Generates wind!

Interpreting maps

• In Chapter 3 we briefly mentioned that wind and pressure are related

• Which direction does the air move around the low pressure system?– Counter-clockwise

• The pressure gradient force is the first step to understanding how pressure and wind are related

Pressure Gradient

• The acceleration of the air from one place to another will depend on the pressure gradient– Do you think the wind will accelerate more or less

in a strong pressure gradient area?– More

• What are some weather situations where you think we might see a strong pressure gradient? Or, in other words, what are some weather situations where we see strong winds?

Strong Pressure Gradients

• Hurricanes• Tornadoes• Low pressure systems• High pressure systems• Mountain wind storms• Blizzards• Basically, any situation where you have strong

winds – you’ll have a strong pressure gradient!

Figure 7.4

Pressure Gradient Force Direction

• A force always has a magnitude and a direction

• We’ve discussed how to make molecules move one direction or another– If you push a cubicle wall with a stronger force on

one side than another, this will make the wall move away from the larger force

• Let’s apply this to real weather situations!

What direction is the PGF?

• Where is the force the greatest? High pressure or low pressure?

• Remember the definition of pressure

Note the size of the arrows! What does this mean??

Pressure Gradient Force

• Remember, the pressure gradient force is always directed from high to low!

• The intensity of the force depends on the gradient!

• The PGF is always perpendicular to isobars!

Calculating Pressure Gradient

• How would we calculate a pressure gradient?• What is a gradient?– Change in a property over a distance

• How would we translate this into calculating a pressure gradient?

980 mb 1000 mb

10 km

Pressure Variations

• In a hurricane, pressure can vary by 1 mb per km or more– Hurricane Andrew was 1.9 mb/km

• Low pressure systems can have pressure gradients of 0.1 mb per km

• Over the depth of the troposphere we know the pressure changes 900 mb over 16 km, or about 120 mb km in the lower atmosphere

Low pressure system near IcelandFrom: NASA

The atmosphere

• That’s a large pressure gradient in the vertical!• What direction is the pressure gradient

directed vertically?– How does pressure change with altitude?

• Why doesn’t the Earth’s atmosphere fly off into space?

• We need to have another force that is directed towards the surface

Gravity!

• What goes up, must come down

• We’ve all experienced gravity in many forms

• Gravity is what keeps us on Earth

How does the Gravity force work?

• Any two objects in the universe that have a mass are attracted to each other by a gravitational force

• How strong the gravitational force is will be dependent on the size of the object’s mass

• Gravity can considered to be constant on earth, despite some minor variations

Friction

• The last of our fundamental forces• What do you know about friction?– Tends to slow objects down

• Friction acts opposite the direction of air motion

Wind

Frictional Force

Turbulence

• Turbulence in the atmosphere is a result of friction– Mixing to the surface

• Mixing of air parcels at very different speeds• Turbulence is very important to us on Earth!– Wind gusts– Storms

• What do you think the speed of air at the Earth’s surface is?

Types of Turbulence

• The turbulent motions that lead to the mixing of air are called turbulent eddies

• There are three ways turbulence is generated in the atmosphere– Mechanical turbulence– Thermal turbulence– Shear-induced turbulence

• Each have different implications and different causes

Mechanical Turbulence

• What happens on windy days in Colorado when you walk between two buildings?– The eddies that you

encounter are due to mechanical turbulence

Figure 7.5a

Thermal Turbulence

• What happens when we heat the surface of the Earth?

• Convection also causes over-turning, and turbulence!– Instability– Slower moving surface air

mixed in with stronger winds aloft leads to a slowdown of upper-level winds

Figure 7.5b

Instability and Turbulence

• Changing the stability of the atmosphere causes mixing throughout the depth of the atmosphere– Slower moving air gets

mixed upward– Faster moving air gets

mixed downwardGround

Altit

ude

Slow

Shear Induced Turbulence

• Wind shear is what exists when we have a change in wind over a distance– What is another term that we have

used to describe a change in an atmospheric property over a distance?

• Shear induced turbulence occurs when wind changes rapidly with distance– Height

• Which one(s) of these types of turbulence impact you in an airplane?

Ground

Altit

ude

Figure 7.5c

Boundary Layer• The boundary layer is the

depth of the atmosphere that is impacted by friction– What layer of the

atmosphere would encompass the boundary layer?

• What are some things that the depth of the boundary layer would depend on?

From NASA’s Glenn Research Center

Boundary Layer Height

• One thing the height of the boundary layer depends on is the stability of the atmosphere– Would the depth of the boundary layer be larger

or smaller for a stable atmosphere? For an unstable atmosphere?

– What time of day are we more likely to see a stable atmosphere? An unstable atmosphere?

Coriolis Force

• The only force we are discussing that is not a fundamental force

• Apparent force due to the rotation of the earth

• Due to angular momentum and the centrifugal force

• Dependent on frame of reference

• View from rest• View from merry-go-round

Figure 7.6

The Coriolis Force

• Merry-go-round• http://

www.hurricanescience.org/science/basic/coriolis/

Angular Momentum

• To understand Coriolis Force on Earth, we need to understand angular momentum

• Easiest explanation is from a figure skater– Brings arms in, moves faster– Conservation of angular momentum

• Angular momentum is defined as the product of its mass (M), rotational velocity (V), and radius from the center axis of rotation (R)

AM M *V *R

Angular Momentum

• Momentum describes the tendency for an object to continue to move in a straight line without any outside force exerted on it

• Angular momentum is the same idea, but rotating– Its tendency to continue to spin

• It depends on the object’s mass, velocity, and distance from the point the object is spinning around

Conservation of Angular Momentum

• Without a torque being applied, we can assume our air parcel’s angular momentum is conserved– Can be transferred, but not created or destroyed– What does angular momentum depend on?

• Therefore, since we can’t get rid of the angular momentum, and if its mass doesn’t change, if we change the distance to the axis of rotation we must change its rotation rate

Axis of Rotation

• Let’s say you have an air parcel initially at rest with respect to the Earth’s surface– What is the rotation rate of the air parcel?

• The rotation rate of the Earth depends on where you are on Earth– How far away from the axis of rotation you are– What will happen to your air parcel’s angular

momentum if it is pushed toward the poles? – What will happen to its rotation rate?

Angular Momentum• As the air parcel moves closer to the poles, its rotational

velocity will speed up, since its mass does not change and angular momentum is conserved

• Like the figure skater• His arms are pulled in closer to the

axis of rotation (his body)– Mass doesn’t change, but the distance

to the axis center does so must rotate faster

AM M *V *R

Recap Thus Far• Have an air parcel sitting at

the equator• Its rotational velocity is the

same as the rotation rate of the Earth– Moves with the same speed

as the Earth– It has some sort of angular

momentum associated with it that is constant

– Some tendency to want to spin on its own without an outside torque applied

Recap Thus Far• Now we take that air parcel

and move it toward the pole at some speed

• The distance to the axis of rotation gets smaller

• So the air parcel will rotate faster because its tendency to want to spin will remain the same but its mass doesn’t change

• Because it is rotating faster will move to the right (in the NH)

Centrifugal Force

• Consider the force that pushes you against a car door when you turn a corner

• The air on earth also wants to get pushed out into space• What force holds it on earth?• When our air parcel moves faster than the Earth’s

rotation rate, it also wants to be thrown outward• If we are heading north to the equator, it wants to be

thrown to the right, or east• Will keep our air parcel from continuously moving to the

east

How do we apply this to the atmosphere?

• Let’s take our fictional air parcel

• This air parcel becomes part of a weather system that has a rotation rate due to the Earth

• When the parcels move on earth, they are deflected

• This has an impact on low pressure systems, hurricanes, and jetstreams

Important Facts About the Coriolis Force

• Causes objects to deflect to the right in the Northern Hemisphere and the left in the Southern Hemisphere– Why is this different?

• Has no impact on the speed of an object; only changes direction

• Strongest for faster moving objects– Does not effect stationary objects

• Is zero at the equator and a maximum at the poles• Only matters over large distances and is small for short

distances

In Class Exercise

• Exercise 7.2

Newton’s Laws of Motion

• Does anyone know Newton’s first law of motion?– An object at rest will remain at rest– An object in motion will remain in motion

traveling at a constant speed in a straight line assuming there is no force exerted on the object

• What would happen if we threw a ball in a world with no friction or gravity? What happens to that ball in the real-world?

Newton’s Second Law of Motion• What is his second law of motion?– The force exerted on an object equals its mass times its

accelerationF=m*a

– An object experiences an acceleration anytime it changes speed or direction

• Always consider forces per unit mass• Newton’s second law leads us to understand force

balances which act on the air on Earth• Look at Table 7.1 in the book to understand these force

balances

Force Balances

• If we never had a torque applied to the air, our atmosphere would be in exact balance– What are some things that might cause the

disruption of air flow?• Not actually true, but we can think of the

atmosphere as being in balance (at least for now)– No acceleration of the flow– This simplified model can tell us a lot about weather

on Earth

Hydrostatic Balance• We have said that the pressure on Earth changes

more in the vertical than in the horizontal– What force is this referring to?– What force keeps our atmosphere from flying off

into space?• When exactly in

balance, this is called the hydrostatic balance

Hydrostatic Balance

• We are almost always in hydrostatic balance across the Earth because these two forces balance

• This leads to us not having strong vertical motion all the time on Earth

• However, sometimes we are not in hydrostatic balance. When?

Geostrophic Balance

• Acceleration of air parcel at points A-D• Once at E the forces are in balance and the air parcel no

longer accelerates

Geostrophic Balance• The balance that is achieved when the PGF

and CF (Coriolis Force) are in balance is called geostrophic balance

• The wind that we see at point E is called the geostrophic wind

Geostrophic Wind

• The geostrophic wind flows parallel to isobars• Strength is related to the pressure gradient• In the northern hemisphere, higher pressures

are to the right of the geostrophic wind

Where in the world is geostrophic balance?• 500 mb

chart with height contours and geostrophic wind

• Can we ever be in geostrophic balance near the surface? Why or why not?

Summary of Force Balances

• Review Table 7.2 in the book

Geostrophic Balance and the Jet Stream

• What is the jet stream?– Strong winds– Wave-like pattern– Maximum near

tropopause• Can have a polar jet

stream and a sub-tropical jet stream

• Jet streaks are regions of strong winds

Why do jetstreams exist?

• Due to being in both hydrostatic and geostrophic balance in the presence of a temperature gradient

• We learned that pressures slope from warm air to cold air inChapter 3

• Above the surface, in the warmer air column, our pressure is greater below the 500 mb surface, and lower just above the 500 mb surface

Why do jetstreams exist?• What happens if we have a

strong temperature gradient?– The pressure gradient will then

increase– Our pressure lines will get

steeper• What will happen to the

pressure gradient force?• On this figure, which direction

will the PGF be directed? Toward or away from the poles?

• How will this impact our geostrophic wind?

Why do jetstreams exist?• Same idea if we consider

between the tropics and the poles

• Pressure surfaces slope more steeply with altitude– Steeper slope at 5 km

than at 1 km• Geostrophic winds are then

increasing with height in the troposphere

• Slopes are steepest inthe mid-latitudes

Jetstream• If we have a steep temperature

gradient at the surface, like what exists from the tropics to the poles, we will have a steep pressure gradient that gets steeper with altitude

• This will increase our PGF, which is directed poleward

• Because we are away from the surface, we can assume geostrophic balance

• This is why we have prevailing westerly winds, and thus, a jet stream

Fronts and jetstreams• We can see from this slide that

pressures slope in areas overlying temperature gradients

• Pressures slope downward toward cold air

• Jetstreams are found above fronts at the surface

• If you can find a jetstream on a map, you can find a temperature gradient at the surface– In other words, a frontal boundary