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SUMMARY:Fluid dynamics of flapping wings associated with change of domain 
 topology - Kolomenskiy\, D\, Moffatt\, HK\, Farge\, M (CERFACS\, Toulouse\
 ; Univ. DAMPT\, Cambridge\; Paris ENS\; Aix-Marseille U)
DTSTART:20120724T141000Z
DTEND:20120724T143000Z
UID:TALK39025@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We re-examine the clap-fling-sweep mechanism employed by some 
 insects to increase lift. As argued by Lighthill (J Fluid Mech 60(1):1-17\
 , 1973)\, this mechanism can create a circulatory motion even in a totally
  inviscid fluid\, due to a topological change of the solid boundary that r
 epresents the wings surfaces. During the stroke\, the wings first clap tog
 ether behind the insect's back\, then open in a fling motion around the `h
 inge' formed by the two trailing edges\, and finally separate at the hinge
  and sweep apart. \n\nIn a two-dimensional approximation\, we use two diff
 erent conformal mappings in simply and doubly connected domains\, respecti
 vely\, to calculate the complex potential at all stages of the process. Th
 e results indicate that circulation (equal in magnitude and opposite round
  the two wings) can be generated in an inviscid fluid\, and that this circ
 ulation appears when a solid body immersed in the fluid breaks into two pi
 eces (when fling gives way to sweep). Bound vortex sheets produced during 
 fling are still carried by the just-separated wings. This is accompanied b
 y a continuous time evolution of the velocity everywhere in the fluid\, al
 though the pressure field jumps instantaneously at the moment of wing sepa
 ration. \n\nIn a viscous fluid\, the flow during the break is essentially 
 different because\, locally\, the Reynolds number is very low near the hin
 ge point. We describe it by local similarity solutions to the Stokes equat
 ion (J Fluid Mech 676:572-606\, 2011). \n\nThree-dimensional effects are p
 resent in the flow. We study them by performing numerical simulations of t
 he Navier-Stokes equations using a Fourier spectral method with volume pen
 alization. The flow before the break is found to be in a good agreement wi
 th the two-dimensional approximation. After the wings move farther than on
 e chord length apart\, the three-dimensional nature of the flow becomes es
 sential (J Fluids Struct 27(5-6):784-791\, 2011).\n
LOCATION:Seminar Room 1\, Newton Institute
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