What makes the free surface waves over topographies convex or concave? A study with Fourier analysis and particle tracking

• Published in: Physics of fluids (1994) Vol. 29; no. 9
• Main Authors: Dauth, Markus, Schörner, Mario, Aksel, Nuri
• Format: Journal Article
• Language: English
• Published: 01.09.2017
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.5003574

This article contributes to a better understanding of traveling waves over periodically undulated inclines. Therefore we used various measurement techniques to combine multiple information: (a) linear stability measurements, (b) measurement of the evolution of traveling free surface waves, and (c) single particle tracking. Thereby, we revealed two distinct wave shapes for different substrates, namely, convex and concave. Furthermore, we investigated the influence of the excitation amplitude and frequency on the flow’s linear stability and the evolution of nonlinear traveling waves. By varying the substrate shape and the wavelength to amplitude ratio, the dependence on the underlying flow field and the geometric constraints is examined. We report (a) an energy transfer from the excitation frequency to its higher harmonics, (b) a strongly varying strength of beat frequencies of the traveling wave and the substrate wave for different substrates, (c) similarities of the traveling wave for different substrate shapes but the same wavelength to amplitude ratio, and (d) a strong interaction between the traveling waves and the steady-state flow with even an eddy breakup for some substrates.