Cover Image


View/Hide Left Panel

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.


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.


[1] R.D.Blevins. Flow Induced Vibration. Van Nostrand Reinhold Company, New York, New York, 1977.

[2] J.K.Vandiver. Dimensionless parameters important to the prediction of vortex-induced vibrations of long, flexible cylinders in ocean currents. MIT Sea Grant Report, MITSG 91–93, 1991.

[3] S.E.Ramberg and O.M.Griffin. The effects of vortex coherence, spacing, and circulation on the flow-induced forces on vibrating cables and bluff structures . Naval Research Laboratory Report 7945, 1976.

[4] F.S.Hover, M.A.Grosenbaugh, and M.S. Triantafyllou. Calculation of dynamic motions and tensions in towed underwater cables . IEEE J. Oceanic Engineering, 19:449, 1994.

[5] D.R.Yoerger, M.A.Grosenbaugh, M.S.Triantafyllou, and J.J.Burgess. Drag forces and flow-induced vibrations of a long vertical tow cable —part 1: Steady-state towing conditions. J. Offshore Mechanics and Arctic Engineering, 113:117, 1991.

[6] R.D.Henderson and G.E.Karniadakis. Unstructured spectral element methods for simulation of turbulent flows. J. Computational Physics, 122:191, 1995.

[7] K.S.Ball, L.Sirovich, and L.R.Keefe. Dynamical eigenfunction decomposition of turbulent channel flow. Intl. J. Num. Meth. Fluids, 12:585, 1991.

[8] A.E.Deane, I.G.Kevrekidis, G.E.Karniadakis, and S.A.Orszag. Low-dimensional models for complex geometry flows: Application to grooved channels and circular cylinders. Physics of Fluids, 3(10):2337, 1991.

[9] G.H.Koopmann. The vortex wakes of vibrating cylinders at low reynolds numbers. J. Fluid Mechanics, 28:501–512, 1967.

[10] A.Ongoren and D.Rockwell. Flow structure from an oscillating cylinder—part 1: Mechanisms of phase shift and recovery in the near wake. J. Fluid Mechanics, 191:197–223, 1988.

[11] C.H.K.Williamson and A.Roshko. Vortex formation in the wake of an oscillating cylinder. J. Fluids and Structures, 2:355–381, 1988.

[12] D.J.Newman and G.E.Karniadakis. Simulations of flow past a freely vibrating cable. J. Fluid Mechanics, 1996. Submitted.

[13] D.J.Newman and G.E.Karniadakis. Simulations of flow over a flexible cable: A comparison of forced and flow-induced vibration. J. Fluids and Structures , 1996. Submitted.

[14] M.Hammache and M.Gharib. An experimental study of the parallel and oblique vortex shedding from circular cylinders. J. Fluid Mechanics, 232:567–590, 1991.

[15] C.H.K.Williamson. Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds numbers. Journal of Fluid Mechanics, 206:579–627, 1989.

The National Academies | 500 Fifth St. N.W. | Washington, D.C. 20001
Copyright © National Academy of Sciences. All rights reserved.
Terms of Use and Privacy Statement