Flapping and Bending Bodies Interacting with Fluid Flows

The flapping or bending of a flexible planar structure in a surrounding fluid flow, which includes the flapping of flags and the self-streamlining of flexible bodies, constitutes a central problem in the field of fluid-body interactions. Herewe review recent, highly detailed experiments that reveal newnonlinear phenomena in these systems, as well advances in theoretical understanding, resulting in large part from the rapid development of new simulation methods that fully capture the mutual coupling of fluids and flexible solids. 449 Review in Advance first posted online on September 22, 2010. (Changes may still occur before final publication online and in print.) Changes may still occur before final publication online and in print. A nn u. R ev . F lu id M ec h. 2 01 1. 43 . D ow nl oa de d fr om w w w .a nn ua lr ev ie w s. or g by N E W Y O R K U N IV E R SI T Y B O B ST L IB R A R Y o n 12 /1 7/ 10 . F or p er so na l u se o nl y. FL43CH19-Shelley ARI 10 September 2010 19:30 1. BACKGROUND An archetype of fluid-structure interactions is the flapping of a flag in a steady wind, and the mutual motion of wind and fabric has long begged the question of the causal factors. For example, Figure 1 depicts the well-known and possibly apocryphal story that relates the contribution of the Chinese Buddhist master Hui-Neng (638–713) to an argument between two monks as they watched a temple flag flutter in the breeze. Listening as they argued back and forth, with one claiming “The flag flaps!” and the other replying “No, it is the wind that moves!”, Hui-Neng interrupted the argument to tell them that they were both wrong, and that instead “It is the mind that moves.” Although this might be so, it also diverted the framing of a fascinating scientific question that might be posed as whether the motions of the flag passively reflect the unseen dynamics of the fluid, or whether flag and wind are a coupled system with their motions jointly determined. The flapping of flags is a subset of a more general class of fluid-structure problems that concern the interaction of flexible sheets or bodies with high-speed fluid flows. Sails are a classical example, whereas understanding the flapping of flexible sheets is important to applications such as paper processing (Watanabe et al. 2002), as well as to possible approaches to energy harvesting (Allen & Smits 2001) and turbulence reduction (Shen et al. 2003). In the natural world, biological structures are found to bend, fold, twist, and wave in air and water flows, with these responses often allowing the organism to survive its wavey orwindy environment (Vogel 1994). Both the driven and intrinsic flapping of flexible structures are important to understanding the swimming of fish (Huber 2000, Liao et al. 2003, Muller 2003). Over the past decade there has been considerable research into the basic dynamics of flexible structures that separate high-speed flows, with some of that work coming out of our laboratory at New York University. Thus, this review selectively covers recent experimental, theoretical, and numerical work related to the flapping and bending of flexible sheets in high-speed flows, as well as discusses some interesting extensions. Not reviewed here is a related set of important