Application of a projection operator method to turbulence

• Project/Area Number: 21560067
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Engineering fundamentals
• Research Institution: Kyushu University
• Principal Investigator: OKAMURA Makoto 九州大学, 応用力学研究所, 准教授 (00185472)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000); Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 物理数学 / 乱流 / 射影演算子法

Research Abstract

We investigate the structure of the time correlation function for one-dimensional turbulence with a projection operator method. A closed model equation for the time correlation function is derived assuming the similarity between the time correlation function and the memory function. We obtain the following asymptotic forms of the time correlation functions both by solving the model equation and by carrying out the direct numerical simulation of the Kuramoto-Sivashinsky equation, which is a typical governing equation for one-dimensional turbulence : 1) the time correlation function indicates the algebraic form for the initial regime ; 2) the time correlation function decays exponentially with or without oscillation for the final regime depending on the wavenumber.

Research Products

• [Journal Article] Decay forms of the time correlation functions for turbulence and chaos. (2012)
  • Author(s): H. Mori and M. Okamura
  • Journal Title: Prog. Theor. Phys Volume: 127 Pages: 615-629
  • NAID: 110009444519
  • Peer Reviewed
• [Journal Article] Decay forms of the time correlation functions for turbulence and chaos (2012)
  • Author(s): H.Mori, M.Okamura
  • Journal Title: Progress of Theoretical Physics Volume: 127(掲載決定)
  • NAID: 110009444519
  • Peer Reviewed
• [Journal Article] Modal and total power spectra of Nikolaevskii turbulence (2010)
  • Author(s): D. Tanaka and M. Okamura
  • Journal Title: J. Phys. Soc. Jpn. Volume: 79 Pages: 124004-124004
  • NAID: 120006410499
  • Peer Reviewed
• [Journal Article] Modal and total power spectra of Nikolaevskii turbulence (2010)
  • Author(s): D.Tanaka, M.Okamura
  • Journal Title: Journal of the Physical Society of Japan Volume: 79 Pages: 124004-124004
  • NAID: 120006410499
  • Peer Reviewed
• [Journal Article] Almost limiting short-crested gravity waves in deep water (2010)
  • Author(s): 岡村誠
  • Journal Title: Journal of Fluid Mechanics 646 Pages: 481-503
  • NAID: 120006410500
  • Peer Reviewed
• [Journal Article] Dual structures of chaos and turbulence, and their dynamic scaling laws. (2009)
  • Author(s): H. Mori and M. Okamura
  • Journal Title: Rev. E Volume: 80 Pages: 51124-51124
  • NAID: 120006413989
  • Peer Reviewed
• [Journal Article] Time correlation functions in a similarity approximation for one-dimensional turbulence. (2009)
  • Author(s): M. Okamura and H. Mori
  • Journal Title: Phys. Rev. E,. Volume: 79 Pages: 56312-56312
  • NAID: 120006413990
  • Peer Reviewed
• [Journal Article] カオス・乱流の2重構造 (2009)
  • Author(s): 森肇, 岡村誠
  • Journal Title: 九州大学応用力学研究所研究集会報告集(2009) Pages: 143-151
• [Journal Article] Time correlation functions in a similarity approximation for one-dimensional turbulence (2009)
  • Author(s): M.Okamura, H.Mori
  • Journal Title: Physical Review E 79 Pages: 56312-56312
  • NAID: 120006413990
  • Peer Reviewed
• [Journal Article] Dual structures of chaos and turbulence, and their dynamic scaling laws (2009)
  • Author(s): H.Mori, M.Okamura
  • Journal Title: Physical Review E 80 Pages: 51124-51124
  • NAID: 120006413989
  • Peer Reviewed
• [Journal Article] 剥離点近傍の流れ (2009)
  • Author(s): 岡村誠
  • Journal Title: 日本流体力学会誌「ながれ」 28 Pages: 495-498
  • NAID: 110007539203
  • Peer Reviewed
• [Presentation] Nikolaevskii方程式のスケーリング指数 (2010)
  • Author(s): 岡村誠,田中ダン
  • Organizer: 第6回日本流体力学会中四国・九州支部講演会
  • Year and Date: 2010-12-11
• [Presentation] 乱流・カオスの二重構造とその相似性 (2010)
  • Author(s): 森肇,岡村誠
  • Organizer: 九州大学応用力学研究所研究集会「乱流現象及び非平衡系の多様性と普遍性」
  • Year and Date: 2010-11-12
• [Presentation] :Nikolaevskii乱流の時間相関関数とパワースペクトル (2010)
  • Author(s): 岡村誠,田中ダン
  • Organizer: 九州大学応用力学研究所研究集会「乱流現象及び非平衡系の多様性と普遍性」
  • Year and Date: 2010-11-11
• [Presentation] カオス・乱流の2重構造と動的スケーリング則 (2009)
  • Author(s): 森肇,岡村誠
  • Organizer: 九州大学応用力学研究所研究集会「乱流現象及び非平衡系の多様性と普遍性」
  • Year and Date: 2009-11-14
• [Presentation] Nikolaevskii乱流の時間相関関数とパワースペクトル (2009)
  • Author(s): 岡村誠, 田中ダン
  • Organizer: 九州大学応用力学研究所研究集会
  • Place of Presentation: 九州大学
  • Year and Date: 2009-11-11
• [Remarks] ホームページ:
  • URL: http://www.riam.kyushu-u.ac.jp/fluid/okamura/okamura.htm