Exact coherent states in channel flow

2020 Fiscal Year Final Research Report

• Project/Area Number: 18K03951
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 19010:Fluid engineering-related
• Research Institution: Kyushu University
• Principal Investigator: Wall Darren 九州大学, 工学研究院, 准教授 (30534309)
• Project Period (FY): 2018-04-01 – 2021-03-31
• Keywords: Navier-Stokes equations / Rotating Couette Flow / Tilted vortex / Plane Poiseuille Flow / Exact coherent states

Outline of Final Research Achievements

This study considers transition and turbulence of channel flows in plane Poiseuille and Couette configurations. In particular, we consider whether the families of flows that bifurcate successively from the laminar Poiseuille flow are relevant to the turbulent flow, as suggested by previous research. The present study computes a number of families of such flows, but finds
all exist above a value around three times the size of Reynolds number at which transition is first observed. The previous results of Ehrenstein & Koch (JFM, 1991), which differ from the present results, are shown to be numerical artefacts due to the low truncation level used in their study.
We have also considered rotating plane Couette flow, finding the unexpected result that the 2D roll-cell flow that was thought to explain the first transition from the basic state with increasing rotation rate is unstable from its inception, and the flow observed in experiments is likely to be a newly discovered tilted vortex flow.

Free Research Field

流体力学

Academic Significance and Societal Importance of the Research Achievements

乱流流れの無効化的ポンプ輸送は世界の電力の１０％を浪費することと思われている。この問題を取り組むために先に乱流のメカニズムを理解しなければならない。この基礎的な研究ではこの現象の従来の誤解を訂正し、新しい理解を導入する。乱流が急に発生する平面Poiseuille流れ（PPF)と遷移が相次いで行うが可能である回転させた平面Couette流れ（RPCF)という２つの流れ配置を検討する。特に（PPF)においての低いReynolds数に現れる乱流が層流から分岐する流れによって説明ができない。それから、RPCFは回転率の増加を伴って最初現れる流れはロールセールでなく、傾斜渦流れと思われる。