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scaling that is proportional to the frequency ratio ωf0. When the wake is not locked-in, the eigenmodes for the sub-lock-in case are quite different to the eigenmodes for the super-lock-in case. In the non-lock in cases, we need to retain three to four times as many modes to get the same accuracy as the locked-in cases. For example, to retain 99.9% of the flow energy, we would need about 10 eigenmodes to model a locked-in wake, and about 30 eigenmodes to model a non-locked-in wake. We see a similar effect with Reynolds number in the 3-d cases—for the Re=200 case we need to retain two to three times as many modes to get the same accuracy as the Re=100 cases. Here, to retain 99.9% of the flow energy, we would again need about 10 eigenmodes to model the Re=100 cases, and about 30 eigenmodes to model the Re=200 flow-induced vibration case.

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Acknowledgements

This work was supported by the Office of Naval Research, under the supervision of Dr. T.F.Swean. Computations were performed on the IBM-SP2s at the Cornell Theory Center and the Center for Fluid Mechanics at Brown University.

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