# Atmospheric Force Balances

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Atmospheric Force Balances

QUIZ !

Newton’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.

Newton’s second law F = ma Lets examine the terms
We know what mass means

Acceleration 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 Forces
Lets name the important atmospheric forces… Pressure Gradient Force (PGF) Coriolis Force (Apparent) Frictional Force Centrifugal Force (Apparent) Gravitational Force Buoyancy Force

Buoyancy 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

All we are is dust in the Wind
What is wind? Measures how air moves Can 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?
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 – PGF
What is a gradient? Change in quantity over a distance PG – 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.

Review: The Pressure Gradient Force (PGF)
The change in pressure PGF = Distance Direction of the PGF: Always from HIGH to LOW 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 Balance Vertical PGF = Gravitational Force
Will discuss more next week and the important conclusions that can be drawn from this balance

Review: The Pressure Gradient Force (PGF)
Example of the pressure gradient force around an area of low pressure. Notice how the PGF arrows (“vectors”) are approximately perpendicular to the isobars.

Review: The Pressure Gradient Force (PGF)
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.
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 R2 R1 Axis of rotation

The Coriolis Force cont.
Remember: Since angular momentum is conserved, the path of a parcel changes as it moves north/south! Angular momentum = constant = Vradial + Vrelative 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 Force
Examples 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 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 L 996 mb x 1000 mb 1004 mb H

L H Geostrophic Balance Pressure Gradient Force Coriolis Force 996 mb

L H Geostrophic Balance Pressure Gradient Force Geostrophic Wind
996 mb Geostrophic Wind 1000 mb Coriolis Force 1004 mb H

What if an Object is Initially Not in Geostrophic Balance

Geostrophic Balance The geostrophic wind is . . .
…always 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.

Winds at 300 mb are nearly geostrophic:
Geostrophic Balance Winds at 300 mb are nearly geostrophic:

Geostrophic Balance Winds at 850 mb are generally NOT 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 friction. The frictional force always 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! Small frictional force Large frictional force

Height above the surface
The Frictional Force More factors that affect the frictional force: Height above the surface The further away from the surface, the less friction For instance, the winds at 300 mb experience less friction than the winds at the surface Wind speed The stronger the wind, the more friction will oppose the motion Therefore, slower winds experience less friction than fast winds Surface Type The rougher the surface, the greater the friction For example, the friction over an open body of water is weaker than that over a mountainous terrain

Change in speed  change in magnitude of the Coriolis force
The Frictional Force How does friction affect geostrophic balance? 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

Atmospheric Force Balancing with the Frictional Force
996 mb 1000 mb x 1004 mb H

Atmospheric Force Balancing with the Frictional Force
996 mb Pressure Gradient Force 1000 mb 1004 mb H

Atmospheric Force Balancing with the Frictional Force
996 mb Pressure Gradient Force 1000 mb Frictional Force Coriolis Force 1004 mb H

Atmospheric Force Balancing with the Frictional Force
996 mb Pressure Gradient Force Wind 1000 mb Frictional Force Coriolis Force 1004 mb H

Atmospheric Force Balancing with the Frictional Force
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.

Atmospheric Force Balancing with the Frictional Force
Surface winds around cyclones (L) and anticyclones (H) in the northern hemisphere.

Atmospheric Force Balancing with the Frictional Force
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
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 toward Center of circle wind is blowing around

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)

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

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 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