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Stability of slender inverted flags and rods in uniform steady flow

Published online by Cambridge University Press:  21 November 2016

John E. Sader ,
Cecilia Huertas-Cerdeira  and
Morteza Gharib
John E. Sader*
Affiliation:
School of Mathematics and Statistics, The University of Melbourne, Victoria 3010, Australia Department of Physics, California Institute of Technology, Pasadena, CA 91125, USA
Cecilia Huertas-Cerdeira
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
Morteza Gharib
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
*
†Email address for correspondence: [email protected]
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Abstract

Cantilevered elastic sheets and rods immersed in a steady uniform flow are known to undergo instabilities that give rise to complex dynamics, including limit cycle behaviour and chaotic motion. Recent work has examined their stability in an inverted configuration where the flow impinges on the free end of the cantilever with its clamped edge downstream: this is commonly referred to as an ‘inverted flag’. Theory has thus far accurately captured the stability of wide inverted flags only, i.e. where the dimension of the clamped edge exceeds the cantilever length; the latter is aligned in the flow direction. Here, we theoretically examine the stability of slender inverted flags and rods under steady uniform flow. In contrast to wide inverted flags, we show that slender inverted flags are never globally unstable. Instead, they exhibit bifurcation from a state that is globally stable to multiple equilibria of varying stability, as flow speed increases. This theory is compared with new and existing measurements on slender inverted flags and rods, where excellent agreement is observed. The findings of this study have significant implications to investigations of biological phenomena such as the motion of leaves and hairs, which can naturally exhibit a slender geometry with an inverted configuration.

JFM classification

Aerodynamics: Aerodynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 809 , 25 December 2016 , pp. 873 - 894
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Copyright
© 2016 Cambridge University Press 

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Sader et al. supplementary material

Intermittent dynamics of a slender inverted flag at a wind speed just above bifurcation (κ' = 9.2). Data from figure 9(a) taken from this move.

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Sader et al. supplementary material

Intermittent dynamics of a slender inverted flag at a wind speed well above bifurcation (κ' = 14.3). Data from figure 9(b) taken from this move.

Download Sader et al. supplementary material(Video)
Video 976.1 KB