流体力学セミナー流体力学セミナー

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流体力学セミナー ２００９

日時： 11月 2日（月） 15:00-16:30

場所： 京大 理学部６号館 ２０３号室

講師： Prof. Abraham C.-L Chian
　　　 National Institute for Space Research (INPE), Brazil
　　　 RIMS, Kyoto Univ.
　　　
題目: Nonlinear dynamics of long waves: On-off spatiotemporal intermittency

概要：Long waves are relevant for shallow-water fluids and drift turbulence
in plasmas. We discuss the origin of on-off spatiotemporal intermittency in
high-dimensional models of nonlinear long waves governed by the
regularized long-wave equation (Benjamin-Bona-Mahony equation) and Kuramoto
-Sivashinky equation. First, we analyze the spatiotemporal dynamics and
structure of chaotic saddles before, at the onset, and after a crisis, at
the transition from temporal to sptatiotemporal chaos. The links between
chaotic saddles, crisis and spatiotemporal intermittency are elucidated.
Prior to the transition to spatiotemporal chaos, a spatiotemporally
chaotic saddle is responsible for chaotic transients that mimic the
dynamics of the post-transition attractor. At the onset of crisis, the
temporal chaotic attractor loses its stability and is converted to a
temporally chaotic saddle. After the onset of spatiotemporal chaos, we
identify temporally and spatiotemporally chaotic saddles which are
responsible for the laminar and bursty phases in the spatiotemporal
intermittency. In particular, we demonstrate that phase synchronization
due to multiscale interactions is the origin of on-off spatiotemporal
intermittency associated with laminar and bursty phases of wave energy
fluctuations in well-developed spatiotemporal chaos.

Chian ACL, Rempel EL, Macau EE, Rosa, RR, Christiansen, F.
High-dimensional interior crisis in the Kuramoto-Sivashinsky equation.
Phys. Rev. E 65 (Rapid Comm.), 035203, 2002.

He KF, Chian ACL. On-off collective imperfect phase synchronization and
bursts in wave energy in a turbulent state. Phys. Rev. Lett. 91, 034102,
2003.

He KF, Chian ACL. Critical dynamic events at the crisis of transition to
spatiotemporal chaos. Phys. Rev. E 69, 026207, 2004.

Rempel, EL, Chian ACL, Macau EEN, Rosa RR. Analysis of chaotic saddles in
high-dimensional dynamical systems: the Kuramoto-Sivashinsky equation.
CHAOS 14, 545, 2004.

Rempel EL, Chian ACL. Origin of transient and intermittent dynamics in
spatiotemporal chaotic systems. Phys. Rev. Lett. 98, 014101, 2007.

Rempel EL, Chian ACL, Miranda RA. Chaotic saddles at the onset of
intermittent spatiotemporal chaos. Phys. Rev. E 76, 056217, 2007.

Rempel EL, Miranda RA, Chian ACL. Spatiotemporal intermittency and chaotic
saddles in the regularized long-wave equation. Phys. Fluids 21, 074105,
2009.

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世話人：山田 道夫(京大数理研)， 藤 定義(京大)，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：山田道夫 yamada＠kurims.kyoto-u.ac.jp
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