Three-dimensional instability of the flow around a rotating circular cylinder

Abstract The two-dimensional stationary flow past a rotating cylinder is investigated for both two- and three-dimensional perturbations. The instability mechanisms are analysed using linear stability analysis and the complete neutral curve is presented. It is shown that the first bifurcation in the case of the rotating cylinder occurs for stationary three-dimensional perturbations, confirming recent experiments. Interestingly, the critical Reynolds number at high rotation rates is lower than that for the stationary circular cylinder. The spatial characteristics of the disturbance and a qualitative comparison with the results obtained for linear flows suggest that the stationary unstable three-dimensional mode could be of hyperbolic nature.

[1]  Structural Sensitivity of Linear and Nonlinear Global Modes , 2008 .

[2]  M. Thompson,et al.  Three-dimensionality in the wake of a rotating cylinder in a uniform flow , 2013, Journal of Fluid Mechanics.

[3]  F. Godeferd,et al.  An illustration of the link between ribs and hyperbolic instability , 1999 .

[4]  F. H. Barnes.  Vortex shedding in the wake of a rotating circular cylinder at low Reynolds numbers , 2000 .

[5]  S. Mittal.  Three-Dimensional Instabilities in Flow Past a Rotating Cylinder , 2004 .

[6]  P. Luchini,et al.  Structural sensitivity of the first instability of the cylinder wake , 2007, Journal of Fluid Mechanics.

[7]  F. Durst,et al.  On the new vortex shedding mode past a rotating circular cylinder , 2003 .

[8]  O. Probst,et al.  Flow past a rotationally oscillating cylinder , 2013, Journal of Fluid Mechanics.

[9]  J. Pralits,et al.  Instability and sensitivity of the flow around a rotating circular cylinder , 2010, Journal of Fluid Mechanics.

[10]  Yannick Hoarau,et al.  The three-dimensional transition in the flow around a rotating cylinder , 2008, Journal of Fluid Mechanics.

[11]  Sangmo Kang,et al.  Laminar flow past a rotating circular cylinder , 1999 .

[12]  M. Provansal,et al.  Bénard-von Kármán instability: transient and forced regimes , 1987, Journal of Fluid Mechanics.

[13]  R. Kerswell,et al.  The nonlinear development of three-dimensional disturbances at hyperbolic stagnation points: A model of the braid region in mixing layers , 2000 .

[14]  Franz Durst,et al.  Effect of high rotation rates on the laminar flow around a circular cylinder , 2002 .

[15]  C. Williamson.  Vortex Dynamics in the Cylinder Wake , 1996 .

[16]  Bernd R. Noack,et al.  A global stability analysis of the steady and periodic cylinder wake , 1994, Journal of Fluid Mechanics.

[17]  S. Friedlander,et al.  Instability criteria for the flow of an inviscid incompressible fluid. , 1991, Physical review letters.

[18]  R. Henderson,et al.  Three-dimensional Floquet stability analysis of the wake of a circular cylinder , 1996, Journal of Fluid Mechanics.

[19]  A. Lifschitz,et al.  Local stability conditions in fluid dynamics , 1991 .