Bistable Resonance In Gravity‐driven Film Flows | Zendy

Heining C. | Zendy; Wierschem A. | Zendy; Aksel N. | Zendy

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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)

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