At 06:58 PM 12/8/00 -0600, brian whatcott summarized various good and bad
explanations of Galloping Gertie. Some "explanations" mentioned vortex
shedding, and some mentioned aerodynamic effects such as lift.
1) There is a law of physics that essentially says you cannot have
aerodynamic lift without vortices. Any change in lift must be accompanied
by a change in circulation, i.e. "shedding" of some vorticity.
Therefore a correct "lift"-based explanation is equivalent to a correct
"vortex"-based explanation. But we have to be careful; obviously it is
possible to say wrong things about lift and/or wrong things about vorticity.
2a) For well-behaved aerodynamic structures such as airplane wings in
normal flight, the amount of circulation is controlled by the angle of
attack. If you want to change the amount of lift, you need to re-orient
something.
2b) For other structures, such as a cylinder under certain conditions, the
amount of circulation fluctuates. You will get a fluctuating amount of
lift, even if none of the boundary conditions is changing. This will
result in the shedding of a von Karman vortex street.
3) Although item (2b) is an amusing piece of physics, there is no reason to
believe it significantly contributed to the TN bridge story. Although the
bridge was certainly not a well-behaved aerodynamic structure, it would be
a better approximation to think of its lift as being controlled by angle of
attack than to think of it as being independent of angle of attack.
4) The role of the bridge's torsional modes is obvious from the
film. There are however other modes that should be considered, notably the
overall up/down mode.
4a) Aerodynamic lift, properly speaking, couples directly to the up/down
mode. The amount of lift depends sensitively on angle of attack.
4b) There is another aerodynamic quantity, the pitching moment, which is a
torque that couples directly to the torsional mode. It, too, depends
sensitively on angle of attack.
4c) There is yet another aerodynamic quantity, drag, which is horizontal,
transverse to the length of the bridge, i.e. in the same direction as the
wind. The drag depends on angle of attack (but less sensitively; there are
also contributions to drag independent of AoA).
4d) There will be coupling between the various modes, as in a Wilberforce
pendulum, so energy that goes "directly" into one mode may eventually find
its way to another mode.