Elucidation and control of subcritical transition to turbulence using homotopy to supercriticality

2020 Fiscal Year Final Research Report

• Project/Area Number: 18H01370
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Review Section: Basic Section 19010:Fluid engineering-related
• Research Institution: Osaka University
• Principal Investigator: Kawahara Genta 大阪大学, 基礎工学研究科, 理事 (50214672)
• Co-Investigator(Kenkyū-buntansha): 清水 雅樹 大阪大学, 基礎工学研究科, 助教 (20550304) ; 本木 慎吾 大阪大学, 基礎工学研究科, 助教 (70824134)
• Project Period (FY): 2018-04-01 – 2021-03-31
• Keywords: 亜臨界乱流遷移 / ホモトピー

Outline of Final Research Achievements

In this study, the origin of subcritical transition to turbulence was found through continuous deformation (homotopy) of dynamical systems for plane Poiseuille flow and rectangular duct flow. We change the control parameters representing external force or different boundary conditions in plane Poiseuille flow or rectangular duct flow. In the case of subcritical turbulent transition in plane Poiseuille flow, the origin of transition to turbulence was identified as the instability of a vortex street in the upstream part of the spatially localized turbulence called the turbulent band. If this part is stabilized, band structure with stable periodic fluctuations appears. On the other hand, the homotopy between planar Poiseuille flow and rectangular duct flow, where the aspect ratio is a control parameter, shows that the onset of the turbulent band can be attributed to the symmetry breaking of the turbulent puffs.

Free Research Field

熱流体工学

Academic Significance and Societal Importance of the Research Achievements

本研究によって，平面ポアズイユ流の亜臨界乱流遷移に現れる空間局在乱れ（乱流縞）の発生起源がその上流部分の渦列不安定と同定された．また，アスペクト比をパラメターとする平面ポアズイユ流と矩形ダクト流とのホモトピーでは，乱流縞の発生の起源を乱流パフの対称性の破れに帰着できることを示した．これらの知見から，乱流縞の上流部分を安定化することにより平面ポアズイユ流の亜臨界乱流遷移を遅延できる可能性が示唆された．一方，矩形ダクト流においては，そのアスペクト比を適切に設定することにより，乱流遷移の様相を制御できることが示唆された．