Transcript Coriolis Effect

Coriolis Effect
Going Down

On the Earth “down”
includes centrifugal effects.
• Objects at rest
• Assume effective gravity
• Local coordinates match
“down”

Select 3-axis opposite to
down.
• North in plane with w
• East as 1-axis
 



mr  F   mg eff  2mw  r


   
g eff  g  w  w  RE


g eff   g eff e3


 w  e3
e1 
w
  
e2  e3  e1

Local Velocity

w
e2

The angular velocity of the
Earth can be expressed in
local coordinates.

The local velocity is used to
get the Coriolis force.
e3





r  v1e1  v2e2  v3e3




w  0e1  w sin e2  w cos e3
Fcor


 2mw  r

 2mw[v2 cos   v3 sin  e1


 v1 cos e2  v1 sin e3 ]
Deflection







Velocity
North
South
East
West
Up
Down
Northern
Southern Hemisphere
East
West
West
East
South and Up
North and Up
North and Down
South and Down
West
West
East
East



Fcor  2mwv2 cos   v3 sin  e1  v1 cos e2  v1 sin e3 
Cyclone

L
• Straight line wind

L
In the absence of rotation air
would move from high to low
pressure.
The Coriolis force causes
wind to turn.
• Friction causes equilibrium
• Circular pattern
Global Flow

The general wind
circulation is a result of
Coriolis forces.

Equatorial warm air
rises and turns east.
• Replacing cold air
turns west
• Trade winds

Northbound air here
turns east – prevailing
wind.
Pendulum Swing

• Measure displacement from
equilibrium.
Fcor

Fcor

A pendulum has a local
velocity.
Coriolis force causes a
deflection.
• Select frame that rotates wF
with deflection.

 

 

 



mr  F   mg eff  2mw  r  mwF  w  r   2mwF  rF

 

r

r

w

r
F
F
F
 
 



  2mw  wF   r
mr  F   mg eff
Foucault Pendulum

The new rotation vector is up
in the local system.
• Related to colatitude

Select the local rotation to
cancel the Earth’s rotation.
• Pendulum moves in a
turning plane
• Turning represents
precession
w  wF   r  v2 w cos  wF e1


 v1 w cos   wF e2  v1 w sin  e3
wF  w cos
w  wF   r  v1 w sin  e3
2
2
1
1day
TF 


wF
w cos  cos 