Energy equation for certain approximate models of long-wave hydrodynamics

Abstract : A new derivation of completely nonlinear weakly-dispersive shallow water equations is given without assumption of flow potentiality. Boussinesq type equations are derived for weakly nonlinear waves above a moving bottom. It is established that the total energy balance condition holds for all nonlinear dispersion models obtained here.
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Zinaida Fedotova, Gayaz Khakimzyanov, Denys Dutykh. Energy equation for certain approximate models of long-wave hydrodynamics. Russian Journal of Numerical Analysis and Mathematical Modelling, De Gruyter, 2014, 29 (3), pp.167-178. ⟨10.1515/rnam-2014-0013⟩. ⟨hal-00998927⟩

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