Transcript NATS 101 lecture - Department of Atmospheric Sciences

NATS 101
Lecture 16
Newton’s Laws of Motion
Upper-Air Winds
Supplemental References for
Today’s Lecture
Gedzelman, S. D., 1980: The Science and Wonders of the Atmosphere.
535 pp. John-Wiley & Sons. (ISBN 0-471-02972-6)
PGF
Wind
Do Rocks Always 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  Acceleration
Acceleration = Velocity Change / Time
Acceleration = Change in Either Speed
or Direction
Velocity, Acceleration and Force
are Vectors
• Size and Direction
Original New
Velocity Velocity
New
Velocity
Original
Velocity
Acceleration
and Force
New
Velocity
Original
Velocity
New
Velocity
Original
Velocity
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
(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
Ball Appears to Deflect to the
Right of the Observer
Deflection increases if:
Rotation rate increases
Speed of ball increases
Gedzelman, p 242
Ball Appears to Go Straight
Gedzelman, p 242
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
Geostrophic Adjustment
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, can exist only for East-West
flow and for straight contours.
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
DoNot
Rocks
if the
Always
Hill isRoll
TallDownhill?
Enough!
PGF
Gedzelman, p 247
Key Concepts for Today
• 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
Assignment for Next Lecture
• Topic – Centripetal force due to curved flow
Frictional force near the ground
• Reading - Ahrens pg 155-158
• Problems - 6.23, 24 (24,25)