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