Dependence on aspect ratio of symmetry breaking for oscillating foils: implications for flapping flight
dc.contributor.author  Deng, Jian  en 
dc.contributor.author  Caulfield, Colmcille  en 
dc.date.accessioned  20151030T13:12:25Z  
dc.date.available  20151030T13:12:25Z  
dc.date.issued  20151207  en 
dc.identifier.citation  Journal of Fluid Mechanics 2016. 787: 1649. doi:10.1017/jfm.2015.661  en 
dc.identifier.issn  00221120  
dc.identifier.uri  https://www.repository.cam.ac.uk/handle/1810/252476  
dc.description.abstract  Using twodimensional direct numerical simulations, we investigate the flow in a fluid of kinematic viscosity ν and density ρ around elliptical foils of density ρ_s with major axis c and minor axis b for three different aspect ratios: AR = b/c = 1 (a circle); AR = 0.5; and AR = 0.1. The vertical location of these foils y_s(t) = A sin(2πf₀t) oscillates with amplitude A and frequency f₀ in two distinct ways: ‘pure’ oscillation, where the foils are constrained to remain in place; and ‘flying’ oscillation, where horizontal motion is allowed. We simulate the flow for a range of the two appropriate control parameters, the nondimensional amplitude or KeuleganCarpenter number KC = 2πA/c and the nondimensional frequency or Stokes number β = f₀c²/ν. We observe three distinct patterns of asymmetry, labelled ‘Stype’ for synchronous asymmetry, ‘QP_Htype’ and ‘QP_Ltype’ for quasiperiodic asymmetry at sufficiently high and sufficiently low (i.e. AR = 0.1) aspect ratios respectively. These patterns are separated at the critical locus in KC − β space by a ‘freezing point’ where the two incommensurate frequencies of the QPtype flows combine, and we show that this freezing point tends to occur at smaller values of KC as AR decreases. We find for the smallest aspect ratio case (AR = 0.1) that the transition to asymmetry, for all values of KC, occurs for a critical value of an ‘amplitude’ Stokes number βA = β(KC)² = 4π² f0A²/ν ≃ 3. The QP_Ltype asymmetry for AR = 0.1 is qualitatively different in physical and mathematical structure from the QP_Htype asymmetry at higher aspect ratio. The flow at the two ends of the ellipse become essentially decoupled from each other for the QP_L type asymmetry, the two frequencies in the horizontal force signature being close to the primary frequency, rather than twice the primary frequency as in the QP_Htype asymmetry. Furthermore, the associated coefficients arising from a Floquet stability analysis close to the critical threshold are profoundly different for low aspect ratio foils. Freedom to move slightly suppresses the transition to Stype asymmetry, and for certain parameters, if a purely oscillating foil subject to Stype asymmetry is released to move, flow symmetry is rapidly recovered due to the negative feedback of small horizontal foil motion. Conversely, for the ‘higher’ aspect ratios, the transition to QP_Htype asymmetry is encouraged when the foil is allowed to move, with strong positive feedback occurring between the shed vortices from successive oscillation cycles. For AR = 0.1, freedom to move significantly encourages the onset of asymmetry, but the newly observed ‘primary’ QP_Ltype asymmetry found for pure oscillation no longer occurs when the foil flies, with Stype asymmetry leading ultimately to locomotion at a constant speed occurring all along the transition boundary for all values of KC and β.  
dc.language  English  en 
dc.language.iso  en  en 
dc.publisher  Cambridge University Press  
dc.title  Dependence on aspect ratio of symmetry breaking for oscillating foils: implications for flapping flight  en 
dc.type  Article  
dc.description.version  This is the author accepted manuscript. The final version is available from Cambridge University Press via http://dx.doi.org/10.1017/jfm.2015.661  en 
prism.endingPage  49  
prism.publicationDate  2015  en 
prism.publicationName  Journal of Fluid Mechanics  en 
prism.startingPage  16  
prism.volume  787  en 
rioxxterms.versionofrecord  10.1017/jfm.2015.661  en 
rioxxterms.licenseref.uri  http://www.rioxx.net/licenses/allrightsreserved  en 
rioxxterms.licenseref.startdate  20151207  en 
dc.contributor.orcid  Caulfield, Colmcille [0000000231709480]  
dc.identifier.eissn  14697645  
rioxxterms.type  Journal Article/Review  en 
rioxxterms.freetoread.startdate  20160607 
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