## Abstract

The bifurcation structure of the two-dimensional pressure-driven flow through a curved rotating duct is studied. In this study we add to the rich literature that already exists on this problem [J. Fluid Mech. 262, 353 (1994)], revealing even more intricate details of the solution structure. The problem depends on the Reynolds number, Re=Ub/v, the Rotation number, R_{Ω}=bΩ/U, the aspect ratio, γ=b/h, and the radius ratio (or curvature ratio), η=r_{i}/r_{0}; here U is the velocity scale, b is the duct width in the spanwise direction, Ω is the rotational speed, (r_{i} ,r_{0}) are the inner and outer radii of the duct, h=r_{0}-r_{i} and v is the kinematic viscosity of the fluid. For a curvature ratio η=0.960 784, continuation on Re is used to trace the bifurcation diagram for zero rotation (R_{Ω}=0). Then, for Re=800, continuation on K_{Ω} is used from the solutions at zero rotation (R_{Ω}=0) to generate bifurcation diagrams for positive and negative rotational number for the purpose of studying the effect of rotation. Extended systems are used to solve for limit points and symmetry breaking points. These points are then traced as functions of the Reynolds number. Eigenvalue systems are solved to determine the stability properties of the multiple solutions to two-dimensional perturbations. Bifurcation diagrams reveal more intricate solution structures than those found in earlier studies, raising the question whether it is ever possible to construct a complete bifurcation diagram. New solution branches are found even for the well-studied case of a system with no rotation.

Original language | English |
---|---|

Pages (from-to) | 2030-2043 |

Number of pages | 14 |

Journal | Physics of Fluids |

Volume | 11 |

Issue number | 8 |

DOIs | |

State | Published - Aug 1999 |

Externally published | Yes |