GFD I
Frierson
Lecture 6: 1-18-08
Last time…
• Derivation of equations of motion in
rotating frame:
– Centrifugal force
– Coriolis force
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Rotating frames
• Kinematic results:
(The change in a rotating vector as
observed in a non-rotating frame)
Change in C in non-rotating frame =
Change in rotating frame + rotation term
Applied to velocities:
(Applying kinematic result to the position vector)
(Applying kinematic result to vR)
Left hand side is a mixed representation (it’s in terms
of both rotating and inertial frame) -- this needs to be
rewritten (we’ll replace vR using the top result)
2
Rewriting term…
(Just substituting
But this term can
be rewritten:
)
(constant rotation rate)
(substituting)
Final result:
This equation is all we need!
Everything is measured in rotating frame, except 2nd term,
which is the acceleration that appears in Newton’s Laws,
i.e.,
3
Momentum equation in
rotating frame
Coriolis acceleration
Centrifugal acceleration
Coriolis Force Explanation?
http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/fw/crls.rxml
Centrifugal force is also active here…
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