The stability, sound and forced motion of a flag

A. Manela, MIT, USA

Wednesday, March 25
at 16.15, HG E 1.2

The dynamics of a flag in a uniform stream is a fundamental fluid-structure interaction that has been studied extensively in recent years. The relative simplicity and richness of behaviour of this problem make it relevant for a wide range of natural bio-fluid phenomena, including the flapping motion of birds and fish and flow over crop fields; bio-acoustic problems, such as snoring in humans; and industrial applications, including paper flutter in commercial printing machines and studies of energy harvesting processes.

The prevailing view in existing studies of the flag motion is that the onset of flapping is caused by linear instability of the initial planar state. The effect of any external flow inhomogeneities is always disregarded. We re-examine this view by considering the forced motion of a flag subject to vortex shedding from its cylindrical pole. Our results show that forced motion is possible when the unforced flag is still temporally stable. This suggests that the forced-motion mechanism should be taken into account in future experimental and numerical studies. In addition, we develop a linear theory for the calculation of sound production by the flag motion. The significance of the results obtained for understanding related fluid-structure coupling phenomena and improving active control of flapping motion is discussed.