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流体力学セミナー ２０１０

＃今回は木曜日の開催となっています．ご注意ください．

＃数理解析研究所の建物耐震改修工事のため，場所が京大理学部の
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日時： 2月18日（木） 15:00 から 16:30

場所： 京大 理学研究科5号館（物理学教室）413号室

講師： Prof. Sadruddin Benkadda
(International Institute for fusion Science-Universite
de Provence, Marseille France)

題目: Patterns, Intermittent Transport and Universality
in Convective Turbulence in Magnetic Fusion Plasmas

概要：Buoyancy-driven flows such as thermal convection are of great
importance for a wide range of phenomena in geophysical,
astrophysical and fusion plasmas [1,2,3]. We consider here
intermittent aspects of convective turbulence and transport in
magnetized plasma of magnetic fusion machines such as tokamaks or
stelerators. These investigations use Direct Numerical Simulation
(DNS) of Ion Temperature Gradient instability (ITG) which is
identical to the Rayleigh-Benard thermal convection problem in
neutral fluids [4,5,6]. Rayleigh-Benard convection in particular
is a fundamental paradigm for nonlinear dynamics including
instabilities and bifurcations, pattern formation, chaotic
dynamics and developed turbulence.

Using a weakly non-linear analysis, we show that the back-reaction
on the mean profile is the natural mechanism for saturation and
suggest that it will stay the main non-linear coupling mechanism
in the turbulent state. We also will review some basic aspects of
the interaction between convective cells and a mean flow [7,8]. In
particular and still along the line of the “defreezing” assumption
we study the behavior of a model for shear flow instability :
transient bursts of vorticity flux are generated in this model. We
briefly discuss the advantage of this kind of formulation compared
to the “non-normal” operator approach where the mean velocity is
also assumed frozen .

An extension of Herring model is derived. It takes into account
the self-consistent generation of a mean flow. It is shown that
our model has substantially richer dynamics than the one of
Herring. In particular the interaction between the convective
modes and the mean flow leads in the turbulent state to a
transition in the statistical properties of the transport. This
bifurcation is analogous the so-called soft to hard turbulence
transition in convection. In the strongly turbulent state,
intermittent bursts of thermal transport are observed in both
cases. For the latter regime, the reduced model as well as DNS
show that the Nusselt number Nu (normalized heat flux) scales with
the normalized ion pressure gradient Ki as Nu ‾ Ki1/3[6]. Since
the Rayleigh number for ITG turbulence is proportional to Ki, the
Nusselt number scaling for ITG turbulence is thus similar to the
classical Globe & Dropkin scaling for Rayleigh-Benard convection
in neutral fluids.

References:
[1]S. Benkadda, P. Beyer, N. Bian et al, Nuclear Fusion 41, 997
(2001)
[2] P. Beyer, S. Benkadda, X. Garbet and P.H. Diamond, Phys. Rev
Letters 85, 4892 (2000).
[3] Amita Das, Abhijit Sen, and Predhiman Kaw, S. Benkadda and
Peter Beyer, Physics of Plasmas 12, 032302 (2005)
[4] K. Takeda, S. Benkadda, S. Hamaguchi and M. Wakatani, Physics
of Plasmas 11, 3561-3571 (2004)
[5] K. Takeda, S. Benkadda, S. Hamaguchi and M. Wakatani, J.
Plasma Fusion Res 6 570 (2004)
[6] K. Takeda, S. Benkadda, S. Hamaguchi, M. Wakatani, Physics of
Plasmas 12, 052309 (2005)
[7] N. Bian, S. Benkadda, X. Garbet, O. Garcia, J. Paulsen, Physics
of Plasmas, 10, 1382, (2003)
[8] O. Garcia, N. Bian, J. Paulsen , S. Benkadda and K. Rypdal,
Plasma Physics and Controlled Fusion 45, 919-932, (2003)

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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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