Horizontal circulation and jumps in Hamiltonian water wave models

bore-soliton-splash The paper “Horizonatal circulation and jumps in Hamiltonian wave models“, co-authored by E. Gagarina, J. van der Vegt, and O. Bokhove, has been published in Nonlin. Processes Geophysics. Any model that aims to predict the onset of wave breaking at the breaker line needs to capture both the nonlinearity of the wave and its dispersion. The paper formulates the Hamiltonian dynamics of a new water wave model, incorporating both the shallow water and pure potential flow water wave models as limiting systems. It is based on a Hamiltonian reformulation of the variational principle derived by Cotter and Bokhove (2010) by using more convenient variables. The new model has a three-dimensional velocity field consisting of the full three-dimensional potential velocity field plus extra horizontal velocity components. This implies that only the vertical vorticity component is nonzero. Variational Boussinesq models and Green–Naghdi equations, and extensions thereof, follow directly from the new Hamiltonian formulation after using simplifications of the vertical flow profile. The paper explores a variational approach to derive jump conditions for the new model and its Boussinesq simplifications. A link to the paper is here.

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