Abstract
This paper treats travelling waves in a heterogeneous, inviscid, non-diffusive fluid bounded between two horizontal boundaries. The fluid has two incompressible components of different, but constant density and is acted on by gravity. The flow is steady when viewed in a moving reference frame and gives rise to a quasilinear elliptic problem with an eigenvalue parameter related to the wave speed. The small amplitude solutions are analyzed using a dynamical systems approach. A center manifold reduction in combination with a conserved quantity for the flow is used to parametrise all ‘small’ solutions of the full elliptic system in terms of solutions of an autonomous first order ordinary differential equation for a principal component of the wave amplitude. The result is a characterization of all small waves, irrotational in each fluid, near the critical speed for the system. They are: solitary waves; surges connecting distinct conjugate flows at extreme ends of the channel; conjugate flows; and periodic waves.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.