Articles | Volume 9, issue 3/4
Nonlin. Processes Geophys., 9, 221–235, 2002
https://doi.org/10.5194/npg-9-221-2002
Nonlin. Processes Geophys., 9, 221–235, 2002
https://doi.org/10.5194/npg-9-221-2002

  31 Aug 2002

31 Aug 2002

Higher-order Korteweg-de Vries models for internal solitary waves in a stratified shear flow with a free surface

R. Grimshaw1, E. Pelinovsky2, and O. Poloukhina2 R. Grimshaw et al.
  • 1Department of Mathematical Sciences, Loughborough University, Loughborough, UK
  • 2Laboratory of Hydrophysics and Nonlinear Acoustics, Institute of Applied Physics and Department of Applied Mathematics, Nizhny Novgorod Technical University, Nizhny Novgorod, Russia

Abstract. A higher-order extension of the familiar Korteweg-de Vries equation is derived for internal solitary waves in a density- and current-stratified shear flow with a free surface. All coefficients of this extended Korteweg-de Vries equation are expressed in terms of integrals of the modal function for the linear long-wave theory. An illustrative example of a two-layer shear flow is considered, for which we discuss the parameter dependence of the coefficients in the extended Korteweg-de Vries equation.