A variational formulation of a floating body [Elektronische Ressource] / vorgelegt von Magdalena Maria Roth

A Variational Formulationof a Floating BodyVon der Fakultat fur Mathematik, Informatik und Naturwissenschaften¨ ¨der RWTH Aachen Universityzur Erlangung des akademischen Grades einer Doktorin derNaturwissenschaften genehmigte Dissertationvorgelegt vonDiplom-Mathematikerin Magdalena Maria Rothaus OberhausenBerichter: AOR Priv.-Doz. Dr. Alfred WagnerUniv.-Prof. Dr. Heiko von der MoselProf. Dr. Boris BuffoniTag der mundlichen Prufung: 30. August 2010¨ ¨Diese Dissertation ist auf den Internetseitender Hochschulbibliothek online verfugba¨ r.AbstractIn this thesis we consider a two-dimensional motion with a floating bodyfrom a variational point of view. We consider an irrotational flow of an inviscid,homogeneous and incompressible liquid of finite depth acted on by gravity andsurface tension. We look for 2R-periodic waves which propagate steadily withphase velocityc from the left to the right without alteration of form. The rigidbody which will be a sphere throughout this thesis is assumed to move in thesame direction having the same speed. Since the wave profile of a steady waveandthevelocitypotentialarestationarywithrespecttoareferenceframeinuni-form horizontal motion we can restrict ourselves to the time-independent case.Moreover, a volume constraint is considered. We consider the energy functionaldepending on the velocity potential, the surface of the fluid and the position ofthe rigid body.