Free Surface Waves And Interacting Bouncing Droplets: A Parametric Resonance Case Study

Handle URI:
http://hdl.handle.net/10754/296760
Title:
Free Surface Waves And Interacting Bouncing Droplets: A Parametric Resonance Case Study
Authors:
Borja, Francisco J.
Abstract:
Parametric resonance is a particular type of resonance in which a parameter in a system changes with time. A particularly interesting case is when the parameter changes in a periodic way, which can lead to very intricate behavior. This di↵ers from periodic forcing in that solutions are not necessarily periodic. A system in which parametric resonance is realized is when a fluid bath is shaken periodically, which leads to an e↵ective time dependent gravitational force. This system will be used to study the onset of surface waves in a bath with non-uniform topography. A linear model for the surface waves is derived from the Euler equations in the limit of shallow waves, which includes the geometry of the bottom and surface tension. Experiments are performed to compare with the proposed model and good qualitative agreement is found. Another experiment which relies on a shaking fluid bath is that of bouncing fluid droplets. In the case of two droplets the shaking allows for a larger bouncing droplet to attract a smaller moving droplet in a way that creates a bound system. This bound system is studied and shows some analogous properties to quantum systems, so a quantum mechanical model for a two dimensional atom is studied, as well as a proposed model for the droplet-wave system in terms of equations of fluid mechanics.
Advisors:
Kasimov, Aslan
Committee Member:
Ketcheson, David I. ( 0000-0002-1212-126X ) ; Thoroddsen, Sigurdur T.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Program:
Applied Mathematics and Computational Science
Issue Date:
Jul-2013
Type:
Thesis
Appears in Collections:
Applied Mathematics and Computational Science Program; Theses; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.advisorKasimov, Aslanen
dc.contributor.authorBorja, Francisco J.en
dc.date.accessioned2013-07-22T00:01:59Z-
dc.date.available2013-07-22T00:01:59Z-
dc.date.issued2013-07en
dc.identifier.urihttp://hdl.handle.net/10754/296760en
dc.description.abstractParametric resonance is a particular type of resonance in which a parameter in a system changes with time. A particularly interesting case is when the parameter changes in a periodic way, which can lead to very intricate behavior. This di↵ers from periodic forcing in that solutions are not necessarily periodic. A system in which parametric resonance is realized is when a fluid bath is shaken periodically, which leads to an e↵ective time dependent gravitational force. This system will be used to study the onset of surface waves in a bath with non-uniform topography. A linear model for the surface waves is derived from the Euler equations in the limit of shallow waves, which includes the geometry of the bottom and surface tension. Experiments are performed to compare with the proposed model and good qualitative agreement is found. Another experiment which relies on a shaking fluid bath is that of bouncing fluid droplets. In the case of two droplets the shaking allows for a larger bouncing droplet to attract a smaller moving droplet in a way that creates a bound system. This bound system is studied and shows some analogous properties to quantum systems, so a quantum mechanical model for a two dimensional atom is studied, as well as a proposed model for the droplet-wave system in terms of equations of fluid mechanics.en
dc.language.isoenen
dc.subjectWalking dropletsen
dc.subjectParametric Resonanceen
dc.subjectFree surfaceen
dc.subjectVariable Topographyen
dc.subjectFaraday Instabilityen
dc.titleFree Surface Waves And Interacting Bouncing Droplets: A Parametric Resonance Case Studyen
dc.typeThesisen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
thesis.degree.grantorKing Abdullah University of Science and Technologyen_GB
dc.contributor.committeememberKetcheson, David I.en
dc.contributor.committeememberThoroddsen, Sigurdur T.en
thesis.degree.disciplineApplied Mathematics and Computational Scienceen
thesis.degree.nameMaster of Scienceen
dc.person.id118358en
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