Universal lwas in laminar turbulence transition as a nonequilibrium phase transition

2018 Fiscal Year Final Research Report

• Project/Area Number: 16H02212
• Research Category: Grant-in-Aid for Scientific Research (A)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: The University of Tokyo
• Principal Investigator: Sano Masaki 東京大学, 大学院理学系研究科(理学部), 教授 (40150263)
• Project Period (FY): 2016-04-01 – 2019-03-31
• Keywords: 層流乱流転移 / 流れの安定性 / Directed Percolation / 非平衡統計力学 / 非平衡ゆらぎ

Outline of Final Research Achievements

Transition from laminar to turbulent flow drastically changes the mixing, transport, and drag properties of fluids, yet when and how turbulence emerges is elusive even for simple flow within pipes and rectangular channels. In this project, through extensive experimental investigation of channel flow, we identify a distinctive transition with critical behaviour. We identified 3 independent critical exponents and universal scaling relations which coincides with the theoretical predictions of (2+1)dimensional DP (Directed Percolation) transition. These results are not accidental, even if we consider the shortage in our system size and the existence of unstable solutions which grow slower than the observation time. We have also made experiments of turbulent liquid crystals under shear flow with an active wall and found that DP transition is robust against such conditions.
Phenomenological theory and simulation for DP transition with advetive flow and an active wall were also developed.

Free Research Field

非線形・非平衡物理学

Academic Significance and Societal Importance of the Research Achievements

流体の運動において、整った状態（層流）がいつどのようにして、乱れた状態（乱流）に遷移するのかは、世紀を超えて科学者が挑戦し続けている難問の一つである。20世紀終わりにカオスが発見され、閉鎖流における時間的乱れの発生機構が明らかになったが、パイプ流などの開放系のせん断流れにおいて、時空間的な乱れがどのような条件で発生するのかは、19世紀のレイノルズの実験以来、未解決であった。我々は、統計力学的な視点を導入し、粗視化した乱流構造が時空間全体に広がるかどうかに着目することで、非平衡相転移の一種であるDirected Percolationと呼ばれる普遍的な臨界現象と見做せることを明らかにした。