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.

Keywords

Bibliographic record

BibTeX Citation

@article{Fedotova2014energyequation,
  author = {Fedotova, Z.I. and Khakimzyanov, G.S. and Dutykh, D.},
  title = {Energy equation for certain approximate models of long-wave hydrodynamics},
  journal = {Russian Journal of Numerical Analysis and Mathematical Modelling},
  year = {2014},
  volume = {29},
  number = {3},
  pages = {167--178},
  doi = {10.1515/rnam-2014-0013},
  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.},
  keywords = {nonlinear dispersion equations, ideal incompressible fluid, Conservative laws, ideal incompressible uid, surface waves}
}