Pattern formation of parametrically driven surface waves induced by vibration

Perez de Gracia Delgado, Jose Miguel (2016). Pattern formation of parametrically driven surface waves induced by vibration. Thesis (Doctoral), E.T.S.I. Aeronáuticos (UPM). https://doi.org/10.20868/UPM.thesis.39081.

Description

Title: Pattern formation of parametrically driven surface waves induced by vibration
Author/s:
  • Perez de Gracia Delgado, Jose Miguel
Contributor/s:
  • Vega de Prada, José Manuel
  • Varas Merida, Fernando
Item Type: Thesis (Doctoral)
Date: 8 January 2016
Subjects:
Faculty: E.T.S.I. Aeronáuticos (UPM)
Department: Matemática Aplicada a la Ingeniería Aeroespacial
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

Esta tesis se centra en la generación de ondas superficiales subarmónicas en fluidos sometidos a vibración forzada en el régimen gravitatorio capilar con líquidos de baja viscosidad. Tres problemas diferentes han sido estudiados: un contenedor rectangular con vibración horizontal, la misma geometría pero con una combinación de vibración vertical y horizontal y un obstáculo completamente sumergido vibrado verticalmente en un contenedor grande. Se deriva una ecuación de amplitud desde primeros principios para describir las ondas subarmónicas con forzamiento parámetrico inducido por la vibración. La ecuación es bidimensional mientras que el problema original es tridimensional y admite un forzamiento espacial no uniforme. Usando esta ecuación los tres sistemas han sido analizados, centrándose en calcular la amplitud crítica, la orientación de los patrones y el carácter temporal de los patrones espaciotemporales, que pueden ser estrictamente subarmónicos o cuasiperiodicos con una frecuencia de modulación temporal. La dependencia con los parámetros adimensionales también se considera. La teoría será comparada con los experimentos disponibles en la literatura. Abstract This thesis focus on the generation of subharmonic surface waves on fluids subject to forced vibration in the gravity-capillary regime with liquids of small viscosity. Three different problems have been considered: a rectangular container under horizontal vibration; the same geometry but under a combination of horizontal and vertical vibration; and a fully submerged vertically vibrated obstacle in a large container. An amplitude equation is derived from first principles that fairly precisely describes the subharmonic surfaces waves parametrically driven by vibration. That equation is two dimensional while the underlying problem is three-dimensional and permits spatially nonuniform forcing. Using this equation, the three systems have been analyzed, focusing on the calculation of the threshold amplitude, the pattern orientation, and the temporal character of the spatio-temporal patterns, which can be either strictly subharmonic or quasi-periodic, showing an additional modulation frequency. Dependence on the non-dimensional parameters is also considered. The theory is compared with the experiments available in the literature.

Funding Projects

TypeCodeAcronymLeaderTitle
Government of SpainTRA2010-18054UnspecifiedMinisterio de EducaciónUnspecified

More information

Item ID: 39081
DC Identifier: http://oa.upm.es/39081/
OAI Identifier: oai:oa.upm.es:39081
DOI: 10.20868/UPM.thesis.39081
Deposited by: Archivo Digital UPM 2
Deposited on: 26 Jan 2016 10:13
Last Modified: 20 Jul 2016 22:30
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