Influence of the bottom undulation on surface waves in thin film flow | Zendy

Heining Christian | Zendy; Wierschem Andreas | Zendy; Aksel Nuri | Zendy

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Influence of the bottom undulation on surface waves in thin film flow

Author(s) -

Heining Christian,

Wierschem Andreas,

Aksel Nuri

Publication year - 2007

Publication title -

pamm

Language(s) - English

Resource type - Journals

ISSN - 1617-7061

DOI - 10.1002/pamm.200700720

Subject(s) - flow (mathematics) , inclined plane , nonlinear system , plane (geometry) , mechanics , thin film , surface (topology) , boundary layer , volumetric flow rate , boundary (topology) , materials science , resonance (particle physics) , physics , mathematical analysis , mathematics , geometry , nanotechnology , atomic physics , quantum mechanics

We study gravity‐driven viscous thin films flowing down an undulated plane. Applying the integral boundary‐layer method we derive a set of two coupled PDEs for the film thickness and the flow rate. The steady state solution shows linear and nonlinear resonance. Based on this analytical solution we carry out a stability analysis with respect to surface waves and study wave generation and annihilation for time dependent flow. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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