Transcript Chapter 7 - Atmospheric and Oceanic Sciences

Chapter 7
Forces 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
• 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
Pressure
Gradient Force
(PGF)
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
Figure 7.4
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!
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 Iceland
From: 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
• 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 downward
Altitude
Instability and Turbulence
Slow
Ground
• 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?
Altitude
Shear Induced
Turbulence
Ground
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/bas
ic/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
AM  M *V * R
• 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
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 acceleration
F=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 subtropical 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 in
Chapter 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 in
the 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