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ISSN オンライン: 2642-0554

THE ROLE OF THE HAIRPIN VORTEX SOLUTION ON LAMINAR-TURBULENT TRANSITION OF PLANE COUETTE FLOW AT MODERATE REYNOLDS NUMBER

Tomoaki Itano
Department of Pure and Applied Physics Faculty of Engineering Science, Kansai University Osaka, 564-8680, Japan

Sotos C. Generalis
School of Engineering and Applied Sciences Division of Mathematics, Aston University Aston Street, Birmingham B4 7ET, UK

Takahiro Ninomiya
Department of Pure and Applied Physics Faculty of Engineering Science, Kansai University Osaka, 564-8680, Japan

Takeshi Akinaga
School of Engineering and Applied Sciences Division of Mathematics, Aston University Aston Street, Birmingham B4 7ET, UK

Masako Sugihara-Seki
Department of Pure and Applied Physics Faculty of Engineering Science, Kansai University Osaka, 564-8680, Japan

要約

The shooting method is employed to outline a structural aspect of phase space of plane Couette flow, associated with laminar-turbulent transition at moderate Reynolds numbers (Re ~ 104). The basin boundary separating the laminar and the turbulent attractors in the phase space is emerged out of trajectories starting from initial conditions constituted by superposition of three distinct exact steady solutions of PCF, including the Hairpin Vortex Solution (Itano & Generalis (2009); Gibson et al. (2009)) and the so-called Nagata's solution (Nagata (1990)). The result implies that HVS is on the basin boundary even at moderate Reynolds numbers, and that one of the unstable manifolds of HVS heads towards the NBW, which lies on the basin boundary.