Breaking the symmetry of a wavy channel alters the route to chaotic flow

Doranehgard, Mohammad Hossein, Karimi, Nader, Borazjani, Iman and Li, Larry K.B. (2024) Breaking the symmetry of a wavy channel alters the route to chaotic flow. Physical Review E, 109, [045103]. (doi:10.1103/physreve.109.045103).

Abstract

We numerically explore the two-dimensional, incompressible, isothermal flow through a wavy channel, with a focus on how the channel geometry affects the routes to chaos at Reynolds numbers between 150 and 1000. We find that (i) the period-doubling route arises in a symmetric channel, (ii) the Ruelle-Takens-Newhouse route arises in an asymmetric channel, and (iii) the type-II intermittency route arises in both asymmetric and semiwavy channels. We also find that the flow through the semiwavy channel evolves from a quasiperiodic torus to an unstable invariant set (chaotic saddle), before eventually settling on a period-1 limit-cycle attractor. This study reveals that laminar channel flow at elevated Reynolds numbers can exhibit a variety of nonlinear dynamics. Specifically, it highlights how breaking the symmetry of a wavy channel can not only influence the critical Reynolds number at which chaos emerges, but also diversify the types of bifurcation encountered en route to chaos itself.

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Contributors

Author: Nader Karimi

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