TY - JOUR

T1 - Transition to chaos through period doublings of a forced oscillating cylinder in steady current

AU - Cheng, Liang

AU - Ju, Xiaoying

AU - Tong, Feifei

AU - An, Hongwei

PY - 2020

Y1 - 2020

N2 - Transition to chaos through a cascade of period doublings of the primary synchronization mode is discovered in steady approaching flow around a forced inline oscillating cylinder near a plane boundary at a Reynolds number of 175. The transition occurs well within the otherwise synchronized region (known as the Arnold tongue) in the frequency and amplitude space of the oscillating cylinder, creating two parameter strips of desynchronized flows within the Arnold tongue. Five orders of period doublings from mode to mode are revealed by progressively increasing the frequency resolution in the simulation. The ratio of frequency intervals of two successive period-doubling modes asymptotes towards the first Feigenbaum constant, reaching a value of 4.52 at mode of. Additional three-dimensional simulations demonstrate the existence of period doubling with a regular spanwise flow structure similar to regular mode B of steady flow around an isolated cylinder. Although transition to chaos through cascades of period doublings is primarily reported for the primary synchronization mode, it is also observed for other synchronization modes (Tang et al., J. Fluid Mech., vol. 832, 2017, pp. 146-169), where and are integers with a non-reducible , such as. The physical mechanisms responsible for the present period-doubling bifurcations and transition to chaos through cascades of period doublings are ascribed to the interaction of asymmetric vortex shedding from the cylinder (due to a geometric asymmetry) and the boundary layer developed on the plane boundary, through specifically designed numerical tests.

AB - Transition to chaos through a cascade of period doublings of the primary synchronization mode is discovered in steady approaching flow around a forced inline oscillating cylinder near a plane boundary at a Reynolds number of 175. The transition occurs well within the otherwise synchronized region (known as the Arnold tongue) in the frequency and amplitude space of the oscillating cylinder, creating two parameter strips of desynchronized flows within the Arnold tongue. Five orders of period doublings from mode to mode are revealed by progressively increasing the frequency resolution in the simulation. The ratio of frequency intervals of two successive period-doubling modes asymptotes towards the first Feigenbaum constant, reaching a value of 4.52 at mode of. Additional three-dimensional simulations demonstrate the existence of period doubling with a regular spanwise flow structure similar to regular mode B of steady flow around an isolated cylinder. Although transition to chaos through cascades of period doublings is primarily reported for the primary synchronization mode, it is also observed for other synchronization modes (Tang et al., J. Fluid Mech., vol. 832, 2017, pp. 146-169), where and are integers with a non-reducible , such as. The physical mechanisms responsible for the present period-doubling bifurcations and transition to chaos through cascades of period doublings are ascribed to the interaction of asymmetric vortex shedding from the cylinder (due to a geometric asymmetry) and the boundary layer developed on the plane boundary, through specifically designed numerical tests.

KW - bifurcation

KW - flow-structure interactions

KW - vortex dynamics

UR - http://www.scopus.com/inward/record.url?scp=85078525946&partnerID=8YFLogxK

U2 - 10.1017/jfm.2019.1057

DO - 10.1017/jfm.2019.1057

M3 - Article

AN - SCOPUS:85078525946

VL - 887

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

M1 - A51

ER -