Coexistence of multiple long-time solutions for two-dimensional laminar flow past a linearly sprung circular cylinder with a rotational nonlinear energy sink

Antoine B. Blanchard, Lawrence A. Bergman, Alexander F Vakakis, Arne J Pearlstein

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For two-dimensional flow past a linearly sprung circular cylinder to which has been attached an internal "nonlinear energy sink" consisting of a mass allowed to rotate about the cylinder axis and a viscous damper that linearly retards the rotational motion of that mass, we show, for a given set of parameters, that as many as three distinct unsteady long-time solutions (two periodic and one chaotic), in addition to one or more steady solutions, can coexist. For other combinations of the parameters, two unsteady solutions (both periodic, one periodic and one quasiperiodic, one periodic and one chaotic, one quasiperiodic and one chaotic, or both chaotic) can coexist with one or more steady solutions. These multiple solutions, all of which appear to be linearly stable, are found in a range of Reynolds number (15<Re<50) in which the flow is expected to be two dimensional. The discovery of this unprecedented degree of solution multiplicity establishes the potential of this system to serve, at low Re, as a test bed for detailed investigation of basins of attraction of the Navier-Stokes equations, and in studies of noise- and disturbance-induced transitions between different long-time solutions.

Original languageEnglish (US)
Article number054401
JournalPhysical Review Fluids
Issue number5
StatePublished - May 2019


ASJC Scopus subject areas

  • Computational Mechanics
  • Modeling and Simulation
  • Fluid Flow and Transfer Processes

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