Relaxed variational principles for water waves: beyond perturbations

clamond-eqnsDidier Clamond talked about using variational formulations to derive new model equations for water waves.  Motivated by related problems in quantum mechanics (e.g. lecture notes of Hitoshi Murayama) the concept of relaxed variational principles was introduced.  The starting point was Luke’s Lagrangian for water waves, but by introducing new velocity variables, new types of equations emerged.  In deep water a new generalized Klein Gordon equation was discovered.  A derivation and simulation using the latter equation can be found in the preprint Clamond, Dutykh & Chhay (2013) posted on the arXiv.  A second class of equations found is the “deep water Serre equations” which have an exact trochoidal solution.  The DWS equations have a free parameter, kappa, which can be used to optimize the equation.  New equations for shallow water were also introduced. A video of the talk is available here.

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