On the reflection of a train of finite-amplitude internal waves from a uniform slope

The reflection of a train of two-dimensional finite-amplitude internal waves propagating at an angle β to the horizontal in an inviscid fluid of constant buoyancy frequency and incident on a uniform slope of inclination α is examined, specifically when β > α. Expressions for the stream function and density perturbation are derived to third order by a standard iterative process. Exact solutions of the equations of motion are chosen for the incident and reflected first-order waves. Whilst these individually generate no harmonics, their interaction does force additional components. In addition to the singularity at α = β when the reflected wave propagates in a direction parallel to the slope, singularities occur for values of α and β at which the incident-wave and reflected-wave components are in resonance; strong nonlinearity is found at adjacent values of α and β. When the waves are travelling in a vertical plane normal to the slope, resonance is possible at second order only for α In an Appendix some results of an experimental study of internal waves are described. The boundary layer on the slope is found to have a three-dimensional structure.