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流体力学セミナー ２００８ No.6

日時： 10月29日（水）15:00から16:30

場所： 京都大学 数理解析研究所 ００９号室

講師： Alex Oron
　　　（Department of Mechanical Engineering,
　 Technion-Israel Institute of Technology,
　 Haifa 32000 ISRAEL）

題目： Nonlinear dynamics of externally forced
　　　 falling liquid films

概要： Nonlinear dynamics of externally forced falling
thin liquid films is discussed in the framework
of a first-order weighted-residual integral
boundary-layer equations. The problems of (i) a
vertical tangentially oscillating planar and of
a corrugated periodic vertical wall are considered.
Both of these dynamics are analyzed analytically
and numerically in the framework of these equations.

In problem (i) the set of evolution equations admits
a solution corresponding to a flat film with a temporally
periodic volumetric flow rate. Using Floquet theory
stability of this solution is investigated. In the
region of instability of time-periodic flow, forcing
of the traveling wave and non-stationary wave regimes
arising in the unmodulated system, results in the emergence
of quasiperiodic and apparently chaotic regimes, respectively.
The wave regimes of crest and depression types survive the
forcing imparted by plane oscillation. The existence of
regions of asymptotical stability of the flat film
with a temporally periodic flow rate provides the window
for reduction or even suppression of the waviness of the
film interface. Numerical investigation of the nonlinear
dynamics of the modulated film confirms the analytical
results arising from Floquet theory.

In problem (ii) steady-state flows are found in the case
of an asymptotically small wall corrugation and their
stability is investigated. It is found that steady flow
regimes arise in the case of a relatively small wall
wavelength for the Reynolds number below its critical value
corresponding to the flat-wall flow and for larger amplitudes
of the wall corrugation when the Reynolds number exceeds its
critical value. In the case of a larger wall wavelength,
the emerging flows are genuinely nonstationary or time-periodic.
The temporal period of the time-periodic flows increases with the
amplitude of the wall corrugation and decreases with the
Reynolds number. A possibility of the emergence of reverse flows
in both problems is also discussed.

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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：山田道夫 yamada@kurims.kyoto-u.ac.jp
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