## Özet

In this study we consider the stability and transitions for the Poiseuille flow of a second grade fluid which is a model for non-Newtonian fluids. We restrict our attention to perturbation flows in an infinite pipe with circular cross section that are independent of the axial coordinate. We show that unlike the Newtonian (∈=0) case, in the second grade model (∈>0 case), the time independent base flow exhibits transitions as the Reynolds number R exceeds the critical threshold _{Rc}=8.505^{∈-1/2} where ∈ is a material constant measuring the relative strength of second order viscous effects compared to inertial effects. At R=_{Rc}, we find that the transition is either continuous or catastrophic and a small amplitude, time periodic flow with 3-fold azimuthal symmetry bifurcates. The time period of the bifurcated solution tends to infinity as R tends to _{Rc}. Our numerical calculations suggest that for low ∈ values, the system prefers a catastrophic transition where the bifurcation is subcritical. We also show that there is a Reynolds number _{RE} with _{RE}<_{Rc} such that for R<_{RE}, the base flow is globally stable and attracts any initial disturbance with at least exponential speed. We show that the gap between _{RE} and _{Rc} vanishes quickly as ∈ increases.

Orijinal dil | İngilizce |
---|---|

Sayfa (başlangıç-bitiş) | 71-80 |

Sayfa sayısı | 10 |

Dergi | Physica D: Nonlinear Phenomena |

Hacim | 331 |

DOI'lar | |

Yayın durumu | Yayınlandı - 15 Eyl 2016 |

### Bibliyografik not

Publisher Copyright:© 2016 Elsevier B.V.