Experimental study of interfacial solitary waves

Abstract

A small-scale experiment was conducted (in a 3 m long flume) to study interfacial long-waves in a two-immiscible-fluid system (water and petrol were used). Experiments and nonlinear theories are compared in terms of wave profiles, phase velocity and mainly frequency–amplitude relationships. As expected, the KdV solitary waves match the experiments for small-amplitude waves for all layer thickness ratios. The characteristics of ‘large’-amplitude waves (that is when the crest is close to the critical level – approximately located at mid-depth) asymptotically tend to be predicted by a ‘KdV-mKdV’ equation containing both quadratic and cubic nonlinear terms. In addition a numerical solution of the complete Euler equations, based on Fourier series expansions, is devised to describe solitary waves of intermediate amplitude. In all cases, solitary interfacial waves in this numerical theory tally with the experimental data. When the layer thicknesses are almost equal (ratio of lower layer to total depth equal to 0.4 or 0.63) both the KdV-mKdV and the numerical solutions match the experimental points.