Flow dynamics for coupled surface and internal deep-water waves

This article determines the fluid motion underlying coupled linear internal and surface waves in a deep-water two fluid-layer model (with the lower-layer being of infi nite depth). A detailed Eulerian description of the wave-fi eld kinematics for coupled linear travelling waves is achieved using phase-plane analysis. The qualitative motion of individual fluid particles is elucidated through analysis of the relevant nonlinear dynamical systems from the Lagrangian viewpoint.