Re: Midterm Question - Sort of

[brian whatcott <inet@INTELLISYS.NET>]

At 13:27 7/8/99 -0700, James McLean wrote:
> ... My vague
> recollection is that the turbulent vortices leave the object pretty
> regularly, even if the object is immobile.  Does the frequency (and
> phase coherence) of the vortex departure really depend on the motion
> of the bridge? ...

> --James McLean

Arthur Bryson offers this for von Karman vortices:

At Reynolds number Re = 50 to 300, the eddies from bluff or cylindrical
 objects are periodic and regular - at higher numbers the wakes become
increasingly turbulent. At Re 10^3 to 10^5 the shedding frequency for
a circular cylinder is well modeled by f.d/U =0.21
for f frequency, d diameter, U stream speed in compatible units.

The ratio of transverse distance between contralateral vortices to
the distance between successive vortices on one side is about 1.7

 Roshko discovered a spanwise periodicity of vortex shedding from a
cylinder at Re = 80 of about 18 diameters
(i.e the line vortices are not quite parallel to the cylinder's axis)

(Condensed from McGraw-Hill Enc of Sci & Technology)

  This travelling wave action appears to detract from the aliquot
excitation which I associated with the term 'aeolian'.
 But I cannot recall whether the locus of greatest deflection of the
 Tocoma Narrows bridge in fact moved transversely or not.

Given enough torsional compliance for the lateral vortex shedding force
to rotate the road bed a little, it is easy to speculate that ordinary
aerodynamic lift could well reinforce the motion. At the wind speed
involved, a light aircraft wing of 8 sq meters can develop a tonne
or more of lift - using a wing angle of attack never more than
15 degrees.

I should also mention that this encyclopedia entry seems to favor the
 explanation that the periodicity of vortex shedding needs to approach
 a structural resonance in order to significantly damage power lines,
 chimneys, bridges etc.
brian whatcott <inet@intellisys.net>
Altus OK