Experimental study of interfacial solitary waves

TLDR

The study aims to develop a numerical solution of the full Euler equations, using Fourier series, to model intermediate‑amplitude interfacial solitary waves. A 3‑m flume experiment with water and petrol was conducted, and the resulting wave profiles, phase velocities, and frequency–amplitude relationships were compared to nonlinear theories while a Fourier‑series Euler solver was also implemented. Experimental results show that KdV solitary waves agree with small‑amplitude data, KdV‑mKdV equations capture large‑amplitude behavior, and the numerical Euler solution matches the measurements, particularly when the layer thickness ratio is close to 0.4–0.63.

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.