Bifurcation structure and boundary crisis in wall-bounded flows

2016 Fiscal Year Final Research Report

• Project/Area Number: 26820046
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Fluid engineering
• Research Institution: Osaka University
• Principal Investigator: Shimizu Masaki 大阪大学, 基礎工学研究科, 助教 (20550304)
• Research Collaborator: KAWAHARA Genta 大阪大学, 大学院基礎工学研究科, 教授 ; Manneville Paul Ecole Polytechnique ; Duguet Yohann CNRS
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 乱流 / 乱流遷移 / 力学系 / 機械学習

Outline of Final Research Achievements

In plane Couette flow, we performed numerical simulations of more than 100,000 cases with different Reynolds number and initial condition, and investigated the onset of initial chaos in detail. Because two different untrivial solutions exist in the same range of Reynolds number, we found the creation of the fractal basin boundaries and its crisis at several global bifurcation points. We calculated Lyapunov dimension of the chaotic attractor and found that the dimension is slightly higher than 2. So the chaotic attractor is considered to be homeomorphic to a one-dimensional map. In the case of the onset of chaos from Nagata steady solution, we constructed low-dimensional system, which reproduces Navier-Stokes equations very precisely, by using machine learning at least with five variables.

Free Research Field

流体工学