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A Theoretical and Numerical Analysis of the Faraday Wave Experiment

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thesis
posted on 06.08.2019, 00:00 by Marieme Ngom
This thesis focuses on the well-posedness and stability of the Water Wave Equation in the context of the Faraday wave experiment. We prove that the solutions to the viscous water wave equation formulated by Dias, Dyachenko and Zakharov (DDZ) and supplemented with viscosity, surface tension and small vertical forcing is well-posed. We then derive some numerical stability results in the case of larger forcing and solve these equations numerically by using High Order Perturbation of Surfaces (HOPS) methods. We validate our code by first testing it in the case of traveling waves where exact solutions can be derived and by testing our approach against methods present in the literature.

History

Advisor

Nicholls, David Peter

Chair

Nicholls, David Peter

Department

Mathematics, Statistics and Computer Science

Degree Grantor

University of Illinois at Chicago

Degree Level

Doctoral

Committee Member

Awanou, Gerard Dai, Mimi Nenciu, Irina Liang, Jie

Submitted date

May 2019

Issue date

12/04/2019