# Details of talk

Title | Nonlinear Exact Coherent Structures in pipe flow and their instabilities |
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Presenter | Ozge Ozcakir (Monash University) |

Author(s) | Ozge Ozcakir, Philip Hall and Saleh Tanveer |

Session | Dynamical Systems and Fluid Dynamics |

Time | 13:30:00 2017-09-26 |

Abstract | There is not much computational work on travelling wave computations in pipe flows at very large $R$ in existing literature apart from those reported in Ozcakir (2016). In this talk, we present results that extend reliable traveling wave computations through greater efficiency to a far greater Reynolds number (up to $R =5 \times 10^5$) regime than previously reported. Firstly, we confirm that travelling waves states which are referred to as C1 and C2 in Ozcakir (2016) are indeed finite $R$ realization of Nonlinear Viscous Core states because of much closer agreement of numerical results with asymptotics. The second part of the talk concerns determination of a new branch of solution (WK2) which connects to Wedin-Kerswell (WK) when continued to sufficiently large $R$ which ascertains that it is a finite $R$ realisation of asymptotic VWI states, with peak roll, wave, and stream amplitudes scaling as $R^{-1}$, $R^{-5/6}$ and $O(1)$ respectively. In the last part of the talk linear stability of traveling waves are discussed. We extend linear stability calculations to large enough $R$ so that asymptotics of unstable eigenvalues are apparent. These scalings are in agreement with the $R^{-1/2}$, $R^{-1}$ asymptotics for edge and meandering modes predicted by Deguchi \& Hall (2016) for uni-directional shear flow. We do not, however, find any $R^0$ unstable eigenvalue within the class of pressure-preserving two-fold azimuthally symmetric disturbances. |