記述言語：英語   掲載種別：研究論文（学術雑誌）  

Two new flows, a tilted-vortex flow and a periodic-vortex flow, are found numerically at the onset of instability in rotating plane Couette flow (RPCF). It has hitherto been believed that the first few bifurcation sequences from the laminar state are quite well understood, namely, that a streamwise-independent flow with a two-dimensional roll-cell (2dRC) structure bifurcates first, followed by the bifurcation of a wavy-vortex flow (WVF). The present study shows that the 2dRC is, in fact, unstable from its onset, and that the newly found tilted-vortex flow takes over in place of 2dRC. It is further found that the periodic-vortex flow takes part in the early stages of laminar–turbulent transition. The existence of the new flows can be verified by careful examinations of the experimental observations in Hiwatashi et al. (Phys. Fluids, vol. 19, 2007, 048103) and Kawata & Alfredsson (J. Fluid Mech., vol. 791, 2016, 191–213).

DOI： 10.1017/jfm.2021.283

リポジトリ公開URL： https://hdl.handle.net/2324/7236444

記述言語：英語   掲載種別：研究論文（学術雑誌）  

Three spatially extended travelling wave exact coherent states, together with one
spanwise-localised state, are presented for channel flow. Two of the extended flows
are derived by homotopy from solutions to the problem of channel flow subject
to a spanwise rotation investigated by Wall & Nagata (J. Fluid Mech., vol. 727,
2013, pp. 523–581). Both these flows are asymmetric with respect to the channel
centreplane, and feature streaky structures in streamwise velocity flanked by staggered
vortical structures. One of these flows features two streak/vortex systems per spanwise
wavelength, while the other features one such system. The former substantially
reduces the value of the lowest Reynolds number at which channel flow solutions
,other than the basic flow, are known to exist down to 665. The third flow has, in
contrast, half-turn rotational symmetry about a streamwise axis through a point on the
channel centreplane, and is found to be the flow from which one of the asymmetric
flows bifurcates in a symmetry-breaking bifurcation. This flow is found to exist on an
isolated bifurcation branch, whose upper and lower branches both lie on the boundary
basin separating initial conditions that lead to turbulent events, and those that directly
decay back to laminar flow. The structure of this flow, in which the disturbance to
the basic flow is concentrated in a core region in a spanwise period, allowed the
derivation of a corresponding spanwise-localised flow, which is also discussed.

DOI： 10.1017/jfm.2015.685

リポジトリ公開URL： https://hdl.handle.net/2324/7236476

開催年月日： 2020年6月

記述言語：英語   会議種別：口頭発表（一般）  

開催地：Torino   国名：イタリア共和国  

開催年月日： 2020年6月

記述言語：英語   会議種別：口頭発表（一般）  

開催地：Limerick   国名：アイルランド  

The problem of transition from laminar flow to turbulence in plane Couette flow subject to a span-wise system rotation is considered, where the fluid motion is governed by two non-dimensional parameters, R (shear-induced Reynolds number) and Ω (system rotation rate). This system has long been serving as a testing ground for comparing experimental and theoretical results towards understanding mechanisms of transition in fluid dynamics. It is believed that the basic laminar state first loses stability to stream-wise independent disturbances with increasing R and/or Ω, resulting in the onset of a secondary flow with a stream-wise independent roll-cell structure (TV1), followed by successive supercritical bifurcations originating from three-dimensional instabilities of TV1. In the present paper, we re-examine this seemingly well-known instability property of TV1, especially for small R, and find some unexpected result. We shall demonstrate that the solution branch for a three-dimensional tertiary flow with small stream-wise wavenumbers resulting from the afore-mentioned secondary instability connects with the so-called Ribbon flow, which is composed of two tilted vortex flows, elongated in the stream-wise direction with the same but opposite tilted angles. Similar to TV1 this Ribbon flow bifurcates from the laminar basic state, and we find the bifurcation point coincides with that of TV1 in the limit of vanishing stream-wise wavenumber. Thus, the stream-wise independent secondary flow, TV1, becomes unstable to disturbances with small stream-wise wavenumbers as soon as it bifurcates from the basic state, and so no stable stream-wise independent roll-cell structures can exist. We conclude that the roll-cells, which are observed in experiments as the secondary flow, might actually be a three-dimensional tilted vortex flow with long stream-wise wave lengths, which exists intrinsically, being independent of the different types of boundary condition at the sides in experiments.

開催年月日： 2020年6月

記述言語：英語   会議種別：口頭発表（一般）  

開催地：Imperial College, London   国名：グレートブリテン・北アイルランド連合王国(英国)  

開催年月日： 2019年9月

記述言語：英語  

開催地：Vienna   国名：オーストリア共和国  

開催年月日： 2018年8月

記述言語：英語  

開催地：Imperial College, London   国名：グレートブリテン・北アイルランド連合王国(英国)  

対象：社会人・一般,　学術団体,　企業,　市民団体,　行政機関

種別：セミナー・ワークショップ