Subcritical Dynamics of Axisymmetric Rotor-Stator Flow

  • Gesla, Artur (Sorbonne Université)
  • Martin Witkowski, Laurent (Univ Claude Bernard Lyon 1)
  • Duguet, Yohann (LISN-CNRS)
  • Le Quéré, Patrick (LISN-CNRS)

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Rotor-stator flows have been studied extensively in the past. There have been many experimental ob- servations of coexistence of both circular rolls and spiral arms (Schouveiler et al., 1998; Gauthier et al., 1999). The origin of the latter is well understood (Gelfgat, 2015) while that of the former is not. Such rolls display chaotic and sometimes transient dynamics (Lopez et al., 2009). Linear stability analysis performed by (Daube and Le Quéré, 2002) for an height/radius ratio of 0.1 revealed a Hopf bifurcation around Re = 3000, a value much higher than found experimentally, and the existence of a subcritical branch. We revisit this transitional flow using numerical simulation and dynamical systems tools. Additional results concerning the first axisymmetric Hopf bifurcation will be presented. For lower values of Re, at least three flow regimes are identified - base flow, turbulent state and an edge state separating the two. Contrarily to expectations, this edge state features several incommensurate frequencies, involves inertial waves, and does not originate directly from the Hopf bifurcation point. The turbulent solutions (top branch in figure 1a) are also investigated. Evidence will be shown that lifetime distributions are exponential above some value of Re. We will review the analogies in the subcritical transition process between this flow and more common three-dimensional open shear flows such as pipe, channels and Taylor-Couette flows.