Download 02-12-2014 Forces and Wind

MIDTERM 1:
TOTAL POINTS = 45
AVERAGE = 33.5
HIGH SCORE = 44
APPROXIMATE GRADES
38.5 – 45.0 = A
30.0 – 38.0 = B
21.0 – 29.0 = C
< 21.0 NP
Newton’s Laws of Motion
1) 
2) 
Object at rest remains at rest;
Object in motion remains in motion;
As long as no NET force exerted on object.
F = m • a
Force = mass x acceleration
F, a are vectors (magnitude and direction)
Direction
of Motion
so, F is the NET force
F1
FNET
F2
Forces to consider:
1) Pressure Gradient Force
2) Coriolis Force
3) Centripetal Force
4) Friction Force
Force is a VECTOR!!
It has a magnitude AND a direction
Pressure Gradient Force (PGF)
pressure
change in pressure
=
gradient
distance
PGF is directed from HIGH pressure to LOW pressure
at right angles to isobars.
isobars
PGF
H
L
1008 mb
1004 mb
Clicker Question
Set Frequency to "AD"
At which location is the pressure gradient force (PGF) largest?
(A) A
(B) B
A
B
(C) Same PGF at A and B
isobars
(4mb interval)
Clicker Question
Set Frequency to "AD"
At which location is the pressure gradient force (PGF) largest?
(A) A
(B) B
A
B
(C) Same PGF at A and B
At "A", the distance between
isobars is smallest, so pressure
isobars
(4mb interval)
gradient is largest
PGF ~ ∆P / distance
Set Frequency to "AD"
Clicker Question
N
HIGH
San Diego
LOW
isobars
What would be the wind direction?
(A) to the north
(B) to the east
(C) to the west
(D) to the south
W
E
S
Set Frequency to "AD"
Clicker Question
N
HIGH
San Diego
LOW
isobars
What would be the wind direction?
(A) to the north
(B) to the east
(C) to the west
(D) to the south
W
E
S
MIT Coriolis Movie
Coriolis Force:
An "apparent" force we add to compensate for viewing
motion on a rotating reference frame
http://www.classzone.com/books/earth_science/terc/content/visualizations/es1904/es1904page01.cfm?chapter_no=visualization
http://www.fccj.info/gly1001/animations/Chapter18/Coriolis
Coriolis Force important when length-scale is large
(100-1000’s of km)
Coriolis Force (CF)
- Deflect objects to right in Northern Hemisphere
- Deflect objects to left in Southern Hemisphere
- Zero at equator
- Maximum at poles
- Proportional to speed of object
- Acts at right angles to direction of motion
If interested:
CF = 2 m Ω V sin(φ)
m = mass of object
Ω = rotation rate of Earth
V = Velocity of object
φ = latitude
What to know for
this class
Geostrophy:
Balance between Pressure Gradient force and Coriolis force
Consider straight isobars and ignore friction for now.
Low Pressure
High Pressure
Low Pressure
Initially, no motion, so
only force to start with
is the PGF
High Pressure
Low Pressure
PGF
Initially, no motion, so
only force to start with
is the PGF
High Pressure
At point 0
V0 = 0
Low Pressure
Air begins to move in direction of PGF.
PGF
V1
At point 1
V1 > 0
PGF
High Pressure
At point 0
V0 = 0
Low Pressure
Air begins to move in direction of PGF.
- PGF remains the same, but...
PGF
V1
At point 1
V1 > 0
PGF
High Pressure
At point 0
V0 = 0
Low Pressure
Air begins to move in direction of PGF.
- PGF remains the same, but...
- Now there is a Coriolis Force
PGF
V1
At point 1
CF1
V1 > 0
PGF
High Pressure
At point 0
V0 = 0
Low Pressure
PGF
V1
At point 1
NET
CF1
V1 > 0
Air begins to move in direction of PGF.
- PGF remains the same, but...
- Now there is a Coriolis Force
- Net force is combo of CF and PGF
PGF
High Pressure
At point 0
V0 = 0
Low Pressure
PGF
V1
At point 1
NET
CF1
V1 > 0
Air begins to move in direction of PGF.
- PGF remains the same, but...
- Now there is a Coriolis Force
- Net force is combo of CF and PGF
- Velocity increases and changes direction
PGF
High Pressure
At point 0
V0 = 0
Low Pressure
PGF
V2
Air moves in direction of NET force
At point 2
V 2 > V1
PGF
V1
At point 1
NET
CF1
V1 > 0
PGF
High Pressure
At point 0
V0 = 0
Low Pressure
PGF
V2
At point 2
V 2 > V1
CF2
PGF
V1
At point 1
Air moves in direction of NET force
- Coriolis perpendicular and proportional to velocity
NET
CF1
V1 > 0
PGF
High Pressure
At point 0
V0 = 0
Low Pressure
PGF
V2
NET
At point 2
V 2 > V1
CF2
PGF
V1
At point 1
Air moves in direction of NET force
- Coriolis perpendicular and proportional to velocity
- NET force adjusts and bends more
NET
CF1
V1 > 0
PGF
High Pressure
At point 0
V0 = 0
Low Pressure
PGF
V3
PGF
V2
NET
At point 2
V 2 > V1
CF2
PGF
V1
At point 1
As NET force bends, so does the velocity
NET
CF1
V1 > 0
PGF
High Pressure
At point 0
V0 = 0
Low Pressure
PGF
V3
PGF
V2
NET
At point 2
V 2 > V1
CF2
PGF
V1
At point 1
CF3
As NET force bends, so does the velocity
- Coriolis Force keeps changing direction as velocity change
NET
CF1
V1 > 0
PGF
High Pressure
At point 0
V0 = 0
Low Pressure
PGF
V3
PGF
NET
V2
NET
At point 2
V 2 > V1
CF2
PGF
V1
At point 1
CF3
NET
As NET force bends, so does the velocity
- Coriolis Force keeps changing direction as velocity change
- and NET force also adjusts
CF1
V1 > 0
PGF
High Pressure
At point 0
V0 = 0
Low Pressure
PGF
PGF
PGF
V3
PGF
NET
V2
NET
At point 2
At point 1
CF3
CF2
NET
CF1
V1 > 0
Finally, Coriolis force is equal and opposite of the PGF
- Now, no net force
- Velocity remains constant
- Velocity is parallel to the isobars
PGF
High Pressure
At point 0
CF
V 2 > V1
PGF
V1
V
V0 = 0
GEOSTROPHIC WIND
- Straight isobars; no friction
- Balance between Pressure Gradient Force and Coriolis Force
LOW
PGF
WIND
isobars
Coriolis Force
HIGH
GRADIENT WIND
isobars
WIND
LOW
PGF
V2/R
HIGH
Coriolis Force
PGF = CF + V2/R
(Flow around Low Pressure)