Symmetry of vortices in transition of plane Couette flow at moderate Reynolds number

Tomoaki Itano; Sotos C. Generalis; Takahiro Ninomiya; Takeshi Akinaga; Sugihara-Seki

Symmetry of vortices in transition of plane Couette flow at moderate Reynolds number

Tomoaki Itano
, Sotos C. Generalis
, Takahiro Ninomiya
, Takeshi Akinaga
, Sugihara-Seki

College of Engineering and Physical Sciences

Kansai University

Research output: Unpublished contribution to conference › Unpublished Conference Paper › peer-review

Abstract

The shooting method, which was established originally as a tool to find out an unstable steady solution of subcritical shear flows (cf. J. Phys. Soc. Jpn. 70, 703 [1]), is applied to outline a structural aspect of laminar-turbulent transition of minimal plane Couette flow at the moderate Reynolds number. By adopt as initial conditions the points on the plane in phase space spanned by three distinct exact steady solutions, including the Hairpin Vortex Solution (HVS, cf. Phys.Rev.Lett.102,114501 (2009)), a plenty of trial calculations based on the method are carried out. The result implies that HVS is on the boundary separating the laminar and the turbulent attractors of the plane Couette flow, and that one of the unstable manifolds of HVS constitutes the boundary. Moreover, the asymptotic behaviour of HVS at higher Reynolds number is investigated, which enables us to quantify the role of HVS in the laminar-turbulent transition of Plane Couette flow at the moderate Reynolds number.

Original language	English
Publication status	Published - 1 Jan 2013
Event	14th European Turbulence Conference, ETC 2013 - Lyon, France Duration: 1 Sept 2013 → 4 Sept 2013

Conference

Conference	14th European Turbulence Conference, ETC 2013
Country/Territory	France
City	Lyon
Period	1/09/13 → 4/09/13

Funding

We would like to dedicate the paper to our families, whose continued support enabled us to research in the eld of canonical shear ows. In particular we are grateful to our fathers who over the years installed on us the enthusiasm to pursue vigorously the unknown in order to establish the truth. T.I. is grateful for the nancial support received from Aston University under the Visiting Scholars Fund Scheme and EPSRC (GR/S70593/01), which allowed him to spend time in the United Kingdom, while working on this project. T.A. was supported by the European Union FP7 people Marie Curie International Incoming Fellowship grant: T2T-VDG F7-PEOPLE-2011-IIF 298891 . This work has been also supported in partly by KAKENHI (23760164) and partly by the Kansai University Special Research Fund, 2010-2011.

Cite this

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title = "Symmetry of vortices in transition of plane Couette flow at moderate Reynolds number",

abstract = "The shooting method, which was established originally as a tool to find out an unstable steady solution of subcritical shear flows (cf. J. Phys. Soc. Jpn. 70, 703 [1]), is applied to outline a structural aspect of laminar-turbulent transition of minimal plane Couette flow at the moderate Reynolds number. By adopt as initial conditions the points on the plane in phase space spanned by three distinct exact steady solutions, including the Hairpin Vortex Solution (HVS, cf. Phys.Rev.Lett.102,114501 (2009)), a plenty of trial calculations based on the method are carried out. The result implies that HVS is on the boundary separating the laminar and the turbulent attractors of the plane Couette flow, and that one of the unstable manifolds of HVS constitutes the boundary. Moreover, the asymptotic behaviour of HVS at higher Reynolds number is investigated, which enables us to quantify the role of HVS in the laminar-turbulent transition of Plane Couette flow at the moderate Reynolds number.",

author = "Tomoaki Itano and Generalis, \{Sotos C.\} and Takahiro Ninomiya and Takeshi Akinaga and Sugihara-Seki",

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language = "English",

note = "14th European Turbulence Conference, ETC 2013 ; Conference date: 01-09-2013 Through 04-09-2013",

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TY - CONF

T1 - Symmetry of vortices in transition of plane Couette flow at moderate Reynolds number

AU - Itano, Tomoaki

AU - Generalis, Sotos C.

AU - Ninomiya, Takahiro

AU - Akinaga, Takeshi

AU - Sugihara-Seki,

PY - 2013/1/1

Y1 - 2013/1/1

N2 - The shooting method, which was established originally as a tool to find out an unstable steady solution of subcritical shear flows (cf. J. Phys. Soc. Jpn. 70, 703 [1]), is applied to outline a structural aspect of laminar-turbulent transition of minimal plane Couette flow at the moderate Reynolds number. By adopt as initial conditions the points on the plane in phase space spanned by three distinct exact steady solutions, including the Hairpin Vortex Solution (HVS, cf. Phys.Rev.Lett.102,114501 (2009)), a plenty of trial calculations based on the method are carried out. The result implies that HVS is on the boundary separating the laminar and the turbulent attractors of the plane Couette flow, and that one of the unstable manifolds of HVS constitutes the boundary. Moreover, the asymptotic behaviour of HVS at higher Reynolds number is investigated, which enables us to quantify the role of HVS in the laminar-turbulent transition of Plane Couette flow at the moderate Reynolds number.

AB - The shooting method, which was established originally as a tool to find out an unstable steady solution of subcritical shear flows (cf. J. Phys. Soc. Jpn. 70, 703 [1]), is applied to outline a structural aspect of laminar-turbulent transition of minimal plane Couette flow at the moderate Reynolds number. By adopt as initial conditions the points on the plane in phase space spanned by three distinct exact steady solutions, including the Hairpin Vortex Solution (HVS, cf. Phys.Rev.Lett.102,114501 (2009)), a plenty of trial calculations based on the method are carried out. The result implies that HVS is on the boundary separating the laminar and the turbulent attractors of the plane Couette flow, and that one of the unstable manifolds of HVS constitutes the boundary. Moreover, the asymptotic behaviour of HVS at higher Reynolds number is investigated, which enables us to quantify the role of HVS in the laminar-turbulent transition of Plane Couette flow at the moderate Reynolds number.

UR - https://www.scopus.com/pages/publications/85081084923

M3 - Unpublished Conference Paper

T2 - 14th European Turbulence Conference, ETC 2013

Y2 - 1 September 2013 through 4 September 2013

ER -

Symmetry of vortices in transition of plane Couette flow at moderate Reynolds number

Abstract

Conference

Funding

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