Nonlinear water wave models with vorticity

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Kluczek, Mateusz
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University College Cork
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The results presented in this thesis consider geophysical nonlinear water waves and small-amplitude gravity waves. New exact and explicit solutions in terms of Lagrangian variables are derived to model geophysical surface and internal water waves and an analysis of small-amplitude waves from the point of view of the dispersion relation is presented. The solutions are Gerstner-like or Pollard-like in their character and prescribe three-dimensional water waves propagating in the horizontal direction. The models presented in this thesis represent various complicated and intricate scenarios which build the dynamics of the ocean. We prove using a rigorous mathematical analysis the validity of these models. In each model a dispersion relation arises as a product of the analysis indicating how the relative wave speed of the wave varies with respect to various physical parameters introduced by a particular model.
Gerstner-like solution , Nonlinear water waves , Geophysical water waves , Exact and explicit solution
Kluczek, M. 2019. Nonlinear water wave models with vorticity. PhD Thesis, University College Cork.