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Bistable Resonance In Gravity‐driven Film Flows
Author(s) -
Heining C.,
Wierschem A.,
Aksel N.
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610263
Subject(s) - bistability , nonlinear system , perturbation (astronomy) , resonance (particle physics) , duffing equation , mechanics , mathematical analysis , nonlinear resonance , physics , inclined plane , ordinary differential equation , classical mechanics , mathematics , differential equation , quantum mechanics
We study the flow of a viscous liquid down an inclined plane with a sinusoidal bottom profile. Applying the integral boundarylayer method leads to a nonlinear ordinary differential equation for the film thickness. Linear resonance between the free surface and the bottom contour is observed via a regular perturbation approach. Considering nonlinear contributions, the resonance curve shows a foldover effect which is typical for nonlinear oscillators. In order to understand the origin of this bistable behaviour we derive a simple model equation and show an analogy to the Duffing oscillator. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)