期刊
INTERNATIONAL JOURNAL OF MULTIPHASE FLOW
卷 35, 期 1, 页码 78-90出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijmultiphaseflow.2008.07.005
关键词
Resonance; Capillary-gravity waves; Free-surface flow; Bottom undulation
类别
We study nonlinear resonance in viscous gravity-driven films flowing over undulated substrates. Numerical solution of the full, steady Navier-Stokes equations is used to follow the emergence of the first few free-surface harmonics with increasing wall amplitude, and to study their parametric dependence on film thickness, inertia and capillarity. Bistable resonance is computed for steep enough bottom undulations. As an analytic approach, we apply the integral boundary-layer method and derive an asymptotic equation valid for rather thin films. The analysis recovers the key numerical findings and provides qualitative understanding. It shows that higher harmonics are generated by a nonlinear coupling of the wall with lower-order harmonics of the free surface. It also accounts for bistable resonance, and produces a minimum model whose solution is similar to that of the Duffing oscillator. All rights reserved (C) 2008 Elsevier Ltd..
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