atmospheric force balances. quiz ! newton’s laws of motion g 1. every object in a state of uniform...

Atmospheric Force Balances

Atmospheric Force Balances

QUIZ !QUIZ !

Newton’s Laws of motionNewton’s Laws of motion

1. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.

2. F = ma 3. For every action there is an

equal and opposite reaction.

1. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.

2. F = ma 3. For every action there is an

equal and opposite reaction.

Newton’s second lawNewton’s second law

F = maLets examine the termsWe know what mass means

F = maLets examine the termsWe know what mass means

AccelerationAcceleration

The rate of change of velocity with time Given one force an object must have an

acceleration in the same direction If more than one force: (F1 + F2 + …) = ma

- Remember no acceleration does not necessarily imply no movement (velocity)

The rate of change of velocity with time Given one force an object must have an

acceleration in the same direction If more than one force: (F1 + F2 + …) = ma

- Remember no acceleration does not necessarily imply no movement (velocity)

Main Atmospheric ForcesMain Atmospheric Forces

Lets name the important atmospheric forces…

Pressure Gradient Force (PGF) Coriolis Force (Apparent) Frictional Force Centrifugal Force (Apparent) Gravitational Force Buoyancy Force

Lets name the important atmospheric forces…

Pressure Gradient Force (PGF) Coriolis Force (Apparent) Frictional Force Centrifugal Force (Apparent) Gravitational Force Buoyancy Force

Buoyancy ForceBuoyancy Force

The larger the difference in Tparcel and Tenv , the larger the force and acceleration

(F = ma)

More buoyancy leads to stronger updrafts, up to 50 m/s

The larger the difference in Tparcel and Tenv , the larger the force and acceleration

(F = ma)

More buoyancy leads to stronger updrafts, up to 50 m/s

env

envparcelbuoyancy T

TTgF

−=

All we are is dust in the Wind

All we are is dust in the Wind

What is wind?Measures how air movesCan feel it but can not really see it

unless big enough particles are present (i.e. dust or bigger)

What is wind?Measures how air movesCan feel it but can not really see it

unless big enough particles are present (i.e. dust or bigger)

How is the air forced to move?

How is the air forced to move?

Our atmospheric forces conspire to move air

Sometimes air accelerates (changes speed OR direction) Sometimes it moves without

accelerating.Examples…Lets first look at the horizontal wind…

Our atmospheric forces conspire to move air

Sometimes air accelerates (changes speed OR direction) Sometimes it moves without

accelerating.Examples…Lets first look at the horizontal wind…

The first main force – PGFThe first main force – PGF

What is a gradient?Change in quantity over a distancePG – change in pressure over a

distance Gradient of X = (X2 –X1)/ D

What is a gradient?Change in quantity over a distancePG – change in pressure over a

distance Gradient of X = (X2 –X1)/ D

The Pressure Gradient Force (PGF)

This is analogous to the pressure gradient force!

The pressure gradient force is the atmosphere’s way to try and balance out the pressure field.

http://www.indiana.edu/~geog109/topics/10_Forces&Winds/pgf.html

Review: The Pressure Gradient Force (PGF)

PGF =The change in pressure

Distance

• Direction of the PGF: Always from HIGHHIGH to LOWLOW pressure

• Perpendicular to the isobars (lines of constant pressure)

• Magnitude of the PGF: Related to how closely packed the isobars are.

• With isobars very close together, the numerator in the PGF equation is large (a very large change in pressure), so the pressure gradient is large, and thus, the PGF is very strong.

Hydrostatic BalanceHydrostatic Balance

Vertical PGF = Gravitational ForceWill discuss more next week and

the important conclusions that can be drawn from this balance

Vertical PGF = Gravitational ForceWill discuss more next week and

the important conclusions that can be drawn from this balance


Example of the pressure gradient force around an area of low pressure.

Notice how the PGF arrows (“vectors”) are approximately perpendicular to the isobars.


An example of how the pressure gradient force is much stronger where the isobars are closely packed together. The “closeness” of the isobars represents the magnitude of the PGF.

The Coriolis Force

The Coriolis force is an apparent force that results from the constant rotation of the Earth.

In the northern hemisphere, it always acts exactly 90o to the right of the object in movement (such as the wind)

Wind

Coriolis Force

The Coriolis Force cont.

Axis of rotation

R2

R1

What does the Earth’s rotation have to do with the Coriolis force?

As a parcel of air moves from one latitude to another, its distance from the axis of rotation changes.

The speed of a stationary parcel changes, because the speed of the Earth is different for different latitudes

The Coriolis Force cont.

Remember: Since angular momentum is conserved, the path of a parcel changes as it moves north/south!

Angular momentum = Angular momentum = constantconstant = V = Vradialradial + V + Vrelativerelative

A northward moving object will thus be deflected to the right (east) in the northern hemisphere! (opposite for S.H.) This is because as an object moves north, Vradial decreases (the distance from the axis of rotation decreases), so Vrelative must increase!

Example: Ice Skater – why is skater able to spin so fast when not moving initially with a great initial speed and no outside force acting upon skater

Review: The Coriolis ForceExamples of the Coriolis force at work in the

northern hemisphere:

Review: The Coriolis Force

The Coriolis force has much a greater effect farther away from the equator (closer to the poles)

The Coriolis force only acts on an object in movement. It can’t help start the movement of air, only deflect it in a certain direction once it’s in movement.

Geostrophic Balance

The balance that exists between the two forces we’ve talked about:

1. Pressure Gradient Force

2. Coriolis Force

The “geostrophic windgeostrophic wind” is a wind that occurs as a result of this balance. The wind can be approximated as “geostrophic” in the absence of friction: Generally high above the ground, or over oceans.

Geostrophic Balance

996 mb

1000 mb

1004 mb

L

H

x

Geostrophic Balance

996 mb

1000 mb

1004 mb

L

H

Coriolis Force

Pressure Gradient Force

Geostrophic Balance

996 mb

1000 mb

1004 mb

L

H

Coriolis Force


Geostrophic Wind

What if an Object is Initially Not in Geostrophic BalanceWhat if an Object is Initially Not in Geostrophic Balance

http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/fw/gifs/geo.mov






Geostrophic BalanceThe geostrophic wind is . . .

•……alwaysalways parallel to the isobars

• …stronger if there is a stronger pressure gradient

• …weaker if there is a weaker pressure gradient

The wind can be approximated as nearly geostrophic in the upper levels of the troposphere.

Geostrophic Balance

http://www.spc.noaa.gov

Winds at 300 mb are nearly geostrophic:

Geostrophic Balance

http://www.spc.noaa.gov

Winds at 850 mb are generally NOTNOT geostrophic, they often flow across the isobars:

The Frictional Force

The reason that geostrophic balance doesn’t hold close to the surface of the Earth is due to frictionfriction.

The frictional force alwaysalways acts in the opposite direction of the wind.

The Frictional Force• Certain terrain is especially rough, like cities or forests.

• Generally, friction is much less over oceans or large seas and lakes.

• This is why it is much windier over large bodies of water. The wind has very little counteractive force over water!

http://slamonline.com/online/wp-content/uploads/2006/07/PacificOcean.jpeg http://www.ccauthority.com/images/minneapolis.jpg

Small frictional force Large frictional force


Height above the surfaceThe further away from the surface, the less frictionFor instance, the winds at 300 mb experience less friction than the winds at the surface

Wind speedThe stronger the wind, the more friction will oppose the motionTherefore, slower winds experience less friction than fast winds

Surface TypeThe rougher the surface, the greater the frictionFor example, the friction over an open body of water is weaker than that over a mountainous terrain

More factors that affect the frictional force:


Since friction acts in the opposite direction of the wind, it slows the wind

Change in speed change in magnitude of the Coriolis force

Friction + Coriolis force ~ PGF no longer geostrophic balance and winds can cross the isobars

How does friction affect geostrophic balance?

996 mb

1000 mb

1004 mb

L

H

x

Atmospheric Force Balancing with the Frictional Force

996 mb

1000 mb

1004 mb

L

H




996 mb

1000 mb

1004 mb

L

H


Frictional ForceCoriolis Force


996 mb

1000 mb

1004 mb

L

H


Frictional ForceCoriolis Force

Wind

Notice that, with the presence of friction…

• …the wind blows ACROSS isobars! Thus, the flow can not be geostrophic

• …the wind is slightly weaker than it would be without friction

• …the frictional force is always in the exact opposite direction of the wind

• …the Coriolis force, however, is still always 90o to the right of the wind (in the northern hemisphere)

This kind of atmospheric flow is common at the surface of the Earth.


Surface winds around cyclones (L) and anticyclones (H) in the northern hemisphere.



http://ww2010.atmos.uiuc.edu/guides/mtr/fw/gifs/fric1.gif

Due to the frictional force, surface winds converge around areas of low pressure!

This results in the lifting of air parcels around low pressure centers.

Centripetal and Centrifugal Forces

Centripetal and Centrifugal Forces

When flow is curved, it is changing direction

To change direction, must accelerate!

To accelerate, need a force!

Centripetal force is what is pulling in toward the center of the circle

Centrifugal force is apparent force

When flow is curved, it is changing direction

To change direction, must accelerate!

To accelerate, need a force!

Centripetal force is what is pulling in toward the center of the circle

Centrifugal force is apparent force

Centripetal directed towardCenter of circle wind is blowingaround

Centripetal and Centrifugal Continued

Centripetal and Centrifugal Continued

A tighter curve requires a greater change of direction --> needs bigger force

Centrifugal force (inertial pull) greater when winds are more curved or moving faster (change of direction must occur in shorter time)

A tighter curve requires a greater change of direction --> needs bigger force

Centrifugal force (inertial pull) greater when winds are more curved or moving faster (change of direction must occur in shorter time)

Centripetal and Centrifugal cont.Centripetal and Centrifugal cont.

Centrifugal and centripetal forces are greater when speed is greater

Both are greater when radius of the curve is smaller

Centripetal = V2 / R

Centrifugal and centripetal forces are greater when speed is greater

Both are greater when radius of the curve is smaller

Centripetal = V2 / R

Couple Other Force Balances to think of…

Couple Other Force Balances to think of…

1. Gradient Wind Balance- Balance between PGF, Centrifugal Force (a result

of centripetal acceleration inward if curvature present), and Coriolis

- http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/fw/grad.rxml

2. Cyclostrophic Balance- Balance between PGF and the Centrifugal Force- In a small area and short time span the Coriolis

force is not that important- Example: tornadoes can spin both ways- http://profhorn.aos.wisc.edu/wxwise/AckermanKn

ox/chap6/cyclostrophic.html#fig

1. Gradient Wind Balance- Balance between PGF, Centrifugal Force (a result

of centripetal acceleration inward if curvature present), and Coriolis

- http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/fw/grad.rxml

2. Cyclostrophic Balance- Balance between PGF and the Centrifugal Force- In a small area and short time span the Coriolis

force is not that important- Example: tornadoes can spin both ways- http://profhorn.aos.wisc.edu/wxwise/AckermanKn

ox/chap6/cyclostrophic.html#fig

http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/fw/grad.rxml


http://profhorn.aos.wisc.edu/wxwise/AckermanKnox/chap6/cyclostrophic.html#fig






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