Transcript Class Slides - The University of Arizona Department of Atmospheric

Weather, Climate and Society
Newton’s Laws of Motion
Upper-Air Winds
Do Rocks
Today’s
Always
Question….
Roll Downhill?
PGF
Gedzelman, p 247
Newton’s Laws of Motion
• Newton’s 1st Law
An object at rest will remain at rest and
an object in motion will remain at a
constant velocity (same speed and same
direction) if the net force exerted on it is
zero
An external force is required to speed up,
slow down, or change the direction of air
Newton’s Laws of Motion
• Newton’s 2nd Law
The net force exerted on an object equals
its mass times its acceleration
Sum of All Forces = Mass x Acceleration
Acceleration = Velocity Change / Time
Acceleration = Change in Either Speed
or Direction
Velocity, Acceleration and
Force are Vectors
• Speed/Size Change
New
Velocity
Original New
Velocity Velocity
Original
Velocity
• Direction Change
New
Velocity
Original
Velocity
New
Velocity
Original
Velocity
Acceleration
and Force
Acceleration
and Force
Uniform, Circular Motion
Requires Acceleration
New
Velocity
Circular
Path
Original
Velocity
New
Velocity
Original
Velocity
Acceleration
directed toward
center of circle
Centripetal
Accelerated Frame of Reference
You are glued to car’s floor and drop an egg.
What happens if the car begins to accelerate?
time
(rest)
Inside the car, it looks a mystery force is
attracting the egg to the back of the car.
Your frame of reference is accelerating.
Splat!
Someone outside the car sees
that the egg is just accelerating
to the floor, you are accelerating
with the box car. A force is
accelerating the car. Their frame
of reference is not accelerating.
Life on a Rotating Platform
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
(left click picture for animation)
World Weather Project 2010
Courtesy of M. Ramamurthy
U of Illinois, Urbana-Champaign
• From perspective of
person not on merrygo-round, path of ball
is straight.
• From perspective of
person on merry-goround, path of ball
deflects to left. There
is an apparent force.
Merry Go Round Link
Earth’s Rotation
Gedzelman, p 240
If viewed from space, earth is like a carousel!
Northern Hemisphere rotates counterclockwise
Southern Hemisphere rotates clockwise
Refinements
Simple, right?
But there are a couple of nuances
We will consider both…
Coriolis “force” varies with wind speed.
The earth is a sphere, not flat like a carousel.
Ball Appears to Deflect to the
Right of the Observer
Deflection increases if:
Speed of ball increases
slow
fast
Gedzelman, p 242
Ball Appears to Go Straight
Gedzelman, p 242
If the ball is thrown parallel to the axis of rotation,
there is no apparent deflection
Deflection Depends on
Orientation of Axis of Rotation
and Velocity
Apparent
Deflection
No
Deflection
velocity
Gedzelman, p 242
Coriolis Force Varies with Latitude
Gedzelman, p 243
Airplane Link
Geostrophic Adjustment
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
(left click picture to animate)
World Weather Project 2010
Courtesy of M. Ramamurthy
U of Illinois, Urbana-Champaign
A. Parcel at rest initially
accelerates toward lower
pressure.
B. Coriolis Force rotates
parcel to right in NH.
C. As parcel speeds up,
Coriolis Force increases.
D. Eventually (about a day),
PGF equals CF and flow
is parallel to isobars.
Animate Picture
Geostrophic Balance
Pressure Gradient Force
5640 m
Geostrophic Wind
5700 m
Coriolis Force
Geostrophic Wind Arises from a Balance
Between the PGF and the Coriolis Force.
PGF + Coriolis Force = 0
(Technically, it can only exist for East-West
flow and for straight contours, but we will
ignore that technicality.)
Geostrophic Balance
Pressure Gradient Force
5640 m
Geostrophic Wind
5700 m
Coriolis Force
The Balance Leads to the Wind Blowing Parallel
to the Height Contours, with Lower Heights to the
Left of the Wind Direction in the NH.
Closer the Spacing Between the Height ContoursThe Faster the Geostrophic Wind Speed.
PGF
Cor
Geo
Today’s 500 mb Map
500 mb 1200 UTC CONUS
Take Home Points
• Rotation of Earth
Accelerated Frame of Reference
• Introduce Coriolis “Force”
Apparent Force to Account for Deflection
Depends on Rotation, Latitude, Wind Speed
• Geostrophic Balance and Wind
Balance Between PGF and Coriolis Force
Geostrophic Wind Blows Parallel to Contours
About One Day Required to Reach Balance
DoNot
Rocks
if the
Always
Hill isRoll
Big Downhill?
Enough!
PGF
Gedzelman, p 247