dorsal/arxiv
View SchemaForcing function control of Faraday wave instabilities in viscous shallow fluids
| Authors | Cristian Huepe, Yu Ding, Paul Umbanhowar, Mary Silber |
|---|---|
| Categories | |
| ArXiv ID | physics/0509087 |
| URL | https://arxiv.org/abs/physics/0509087 |
| DOI | 10.1103/PhysRevE.73.016310 |
Abstract
We investigate the relationship between the linear surface wave instabilities of a shallow viscous fluid layer and the shape of the periodic, parametric-forcing function (describing the vertical acceleration of the fluid container) that excites them. We find numerically that the envelope of the resonance tongues can only develop multiple minima when the forcing function has more than two local extrema per cycle. With this insight, we construct a multi-frequency forcing function that generates at onset a non-trivial harmonic instability which is distinct from a subharmonic response to any of its frequency components. We measure the corresponding surface patterns experimentally and verify that small changes in the forcing waveform cause a transition, through a bicritical point, from the predicted harmonic short-wavelength pattern to a much larger standard subharmonic pattern. Using a formulation valid in the lubrication regime (thin viscous fluid layer) and a WKB method to find its analytic solutions, we explore the origin of the observed relation between the forcing function shape and the resonance tongue structure. In particular, we show that for square and triangular forcing functions the envelope of these tongues has only one minimum, as in the usual sinusoidal case.
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"abstract": "We investigate the relationship between the linear surface wave instabilities\nof a shallow viscous fluid layer and the shape of the periodic,\nparametric-forcing function (describing the vertical acceleration of the fluid\ncontainer) that excites them. We find numerically that the envelope of the\nresonance tongues can only develop multiple minima when the forcing function\nhas more than two local extrema per cycle. With this insight, we construct a\nmulti-frequency forcing function that generates at onset a non-trivial harmonic\ninstability which is distinct from a subharmonic response to any of its\nfrequency components. We measure the corresponding surface patterns\nexperimentally and verify that small changes in the forcing waveform cause a\ntransition, through a bicritical point, from the predicted harmonic\nshort-wavelength pattern to a much larger standard subharmonic pattern. Using a\nformulation valid in the lubrication regime (thin viscous fluid layer) and a\nWKB method to find its analytic solutions, we explore the origin of the\nobserved relation between the forcing function shape and the resonance tongue\nstructure. In particular, we show that for square and triangular forcing\nfunctions the envelope of these tongues has only one minimum, as in the usual\nsinusoidal case.",
"arxiv_id": "physics/0509087",
"authors": [
"Cristian Huepe",
"Yu Ding",
"Paul Umbanhowar",
"Mary Silber"
],
"categories": [
"physics.flu-dyn"
],
"doi": "10.1103/PhysRevE.73.016310",
"title": "Forcing function control of Faraday wave instabilities in viscous shallow fluids",
"url": "https://arxiv.org/abs/physics/0509087"
},
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