An analysis of extremal periodic water wave profile

Lie, S.L. (2007) An analysis of extremal periodic water wave profile.

Abstract:An investigation of Extremal water wave problem was initiated by Stokes in 1847. He found the so-called Stokes waves, the nonlinear variants of monochromatics waves. As one specific result he showed that for infinite depth water, the wave with largest amplitude which can travel at a certain speed without change of form will have 1200 angle at the crest position. Rainey and Longuet Higgins in 2005 approximated Stokes extreme wave by a simple function. A numerical simulation for a steady water wave problem is done by Rienecker and Fenton in 1979. The idea behind Rienecker and Fenton simulation is Fourier expansion in approximating potential function which satisfies Laplace equation and solving a system of non-linear equations by using Newton’s method. This thesis will give another contribution in the extremal water wave area by using a different approach of modeling. Using physical integral constraints, namely Momentum and Hamiltonian, the maximal high crest profile that satisfies such constraints will be determined. As a governing equation, this thesis considers the linearized KdV equation and the nonlinear AB-equation on deep water.
Item Type:Essay (Master)
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Subject:31 mathematics
Programme:Applied Mathematics MSc (60348)
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