Wake-mediated synchronization and drafting in coupled flags

A recent experiment has shown ‘inverted drafting’ in flags: the drag force on one flag is increased by excitation from the wake of another. Here we use vortex sheet simulations to show that inverted drafting occurs when the flag wakes add coherently to form strong vortices. By contrast, normal drafting occurs for higher frequency oscillations, when the vortex wake becomes more complex and mixed on the scale of the flag. The types of drafting and dynamics (synchronization and erratic flapping) depend on the separation distance between the flags. For both tandem and side-by-side flags in synchronized flapping, the phase difference depends nearly monotonically on separation distance.

[1]  J. Videler Fish Swimming , 1993, Springer Netherlands.

[2]  C. Peskin,et al.  Interaction of two flapping filaments in a flowing soap film , 2003 .

[3]  H. Weimerskirch,et al.  Energy saving in flight formation , 2001, Nature.

[4]  Jun Zhang,et al.  Anomalous hydrodynamic drafting of interacting flapping flags. , 2008, Physical review letters.

[5]  Michael P. Païdoussis,et al.  The coupled dynamics of two cantilevered flexible plates in axial flow , 2009 .

[6]  Bogdan I. Epureanu,et al.  Coherent structures and their influence on the dynamics of aeroelastic panels , 2004 .

[7]  Christophe Eloy,et al.  Aeroelastic instability of a flexible plate in a uniform flow , 2008 .

[8]  P. Lissaman,et al.  Formation Flight of Birds , 1970, Science.

[9]  E. G. Drucker,et al.  Locomotor function of the dorsal fin in teleost fishes: experimental analysis of wake forces in sunfish. , 2001, The Journal of experimental biology.

[10]  Martin Goland,et al.  Principles of aeroelasticity , 1975 .

[11]  C. Eloy,et al.  Aeroelastic instability of cantilevered flexible plates in uniform flow , 2008, Journal of Fluid Mechanics.

[12]  Djj Farnell,et al.  Coupled States of Flapping Flags , 2003 .

[13]  L. Mahadevan,et al.  Fluid-flow-induced flutter of a flag. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[14]  Jun Zhang,et al.  Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind , 2000, Nature.

[15]  C. Peskin,et al.  Simulation of a Flapping Flexible Filament in a Flowing Soap Film by the Immersed Boundary Method , 2002 .

[16]  Jun Zhang,et al.  Heavy flags undergo spontaneous oscillations in flowing water. , 2005, Physical review letters.

[17]  S. Alben,et al.  Flapping states of a flag in an inviscid fluid: bistability and the transition to chaos. , 2008, Physical review letters.

[18]  Silas Alben,et al.  Simulating the dynamics of flexible bodies and vortex sheets , 2009, J. Comput. Phys..

[19]  Fang Li,et al.  Coupling modes between two flapping filaments , 2007, Journal of Fluid Mechanics.

[20]  G. Batchelor,et al.  An Introduction to Fluid Dynamics , 1968 .

[21]  M. Sugihara,et al.  AN EXPERIMENTAL STUDY OF PAPER FLUTTER , 2002 .

[22]  Nicholas P. Jones,et al.  COUPLED FLUTTER AND BUFFETING ANALYSIS OF LONG-SPAN BRIDGES , 1996 .

[23]  R. Krasny Desingularization of periodic vortex sheet roll-up , 1986 .

[24]  Silas Alben,et al.  The flapping-flag instability as a nonlinear eigenvalue problem , 2008 .