Energy equation for certain approximate models of long-wave hydrodynamics

Zinaida Fedotova (1) , Gayaz Khakimzyanov (1) , Denys Dutykh (2, 3, 4)

1 Institute of Computational Technologies
2 LAMA - Laboratoire de Mathématiques
3 INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques
4 USMB [Université de Savoie] [Université de Chambéry] - Université Savoie Mont Blanc

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.

Mots clés: nonlinear dispersion equations; ideal incompressible fluid; Conservative laws; ideal incompressible uid; surface waves

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Dynamique des Fluides [physics.flu-dyn]; Physique Atmosphérique et Océanique [physics.ao-ph]

Zinaida Fedotova, Gayaz Khakimzyanov, Denys Dutykh. Energy equation for certain approximate models of long-wave hydrodynamics. Russian Journal of Numerical Analysis and Mathematical Modelling, 2014, 29 (3), pp.167-178. ⟨10.1515/rnam-2014-0013⟩. ⟨hal-00998927⟩