Small Internal Waves in Two-Fluid Systems
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 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 parameterize 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1988
- Accession Number
- ADA204100
Entities
People
- C. J. Amick
- Ross E. Turner
Organizations
- University of Wisconsin–Madison