流体物理学ゼミナール2008/02/20

数理研談話会をお知らせいたします.来聴歓迎.

このセミナーは,先にお知らせしました2月12日(火)のセミナーの翌日の
2月13日(水)に開催いたします.そのためやはり,セミナーの「曜日,時
間,場所」がすべて通常と異なります.ご注意ください.

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流体力学セミナー 2008 No. 3

日時: 2月13日(水)15:00から16:30

場所: 京都大学数理解析研究所1階115号室

講師: Dr. Paul Manneville
(Laboratoire d’Hydrodynamique, Ecole polytechnique, Palaiseau)

題目: Plane Couette flow at the laminar-turbulent transition

概要:
Though the mechanisms involved in the transition to turbulence in wall
flows are now better understood [1], statistical properties of the
transition itself are yet unsatisfactorily assessed. Poiseuille pipe
flow (Ppf) and plane Couette flow (pCf), both lacking linear
instability modes, have attracted considerable interest recently [2.6].
These flows become turbulent through the nucleation and growth or
decay of turbulent domains that, on the one hand, can be interpreted
within the framework of low dimensional dynamical systems theory as
transient chaotic states associated to stochastic repellors. On the
other hand, limitations due to finite observation times and/or system
size may play a role and correlative spatiotemporal processes cannot
be ruled out in the transitional regime. In the pCf case, the problem
has been explored via numerical simulations of a model focusing on the
in-plane (x, z) space dependence of a few velocity amplitudes with
reduced cross-stream (y) dependence [6]. The model is closer to Navier. Stokes
equations than previously considered coupled map reductions and
there is evidence that it is well suited to the low-R transitional
range. After a brief review of experimental results [5], I will
present my most recent findings, discuss them in view of those for Ppf
[2,4], and attempt to make a connection with the theory of first order
phase transitions [7], as suggested long ago by Y. Pomeau [8].

参考文献:
[1] T. Mullin, R. Kerswell, eds., IUTAM Symposium on Laminar-Turbulent
Transition and Finite Amplitude Solutions (Springer, 2005). [2] B. Hof et al.,
Nature 443 (2006) 59. [3] J. Peixinho, T. Mullin, Phys. Rev. Lett. 96 (2006)
094501. [4] A.P. Willis, R.R. Kerswell, Phys. Rev. Lett. 98 (2007) 014501. [5]
S. Bottin et al., Europhys. Lett. 43 (1998) 171. [6] M. Lagha, P. Manneville,
Eur. Phys. J. B 58 (2007) 433-447. [7] P. Manneville, “Understanding the
sub-critical transition to
turbulence in wall flows,” Pramana-Journal of Physics, to appear. [8] Y. Pomeau,
Physica D 23 (1986) 3-11.

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世話人:藤 定義(京大),山田 道夫(京大数理研),松本 剛(京大理)
アドバイザー:船越 満明(京大情報学)、水島 二郎(同志社大工)、
余田 成男(京大理)
連絡先:yamada@kurims.kyoto-u.ac.jp
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山田道夫
京都大学数理解析研究所
〒606-8502 京都市左京区北白川追分町
tel: 075-753-7221, fax: 075-753-7272
email: yamada@kurims.kyoto-u.ac.jp

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