Experimental measurements of nonlinear waves

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Table of contents

Remerciements
Abstract
1 Introduction
1.1 Motivation
1.2 Surface wave theory
1.3 Expansion of surface wave equations
1.4 The step problem
1.5 Space-time resolved measurements for water waves
2 Multi-modal model of a nonlinear wave
2.1 Introduction
2.2 A toy model: One-dimensional nonlinear wave
2.2.1 First order problem
2.2.2 Second order problem
2.2.3 Numeric example
2.2.4 Concluding remarks about the one dimensional model
2.3 Analysis of the reflection and transmission of a nonlinear wave
2.3.1 Statement of the problem
2.3.2 First order problem
2.3.3 Second order problem
2.3.4 Surface elevation of free and bound waves
2.3.5 Numerical example
2.3.6 On the convergence of the second order problem
2.3.7 Convergence of the solution with the number of modes
2.4 Concluding remarks and perspectives
2.4.1 Third order problem
3 Experimental measurements of nonlinear waves
3.1 Introduction
3.2 Governing equations
3.2.1 The weakly nonlinear model
3.2.2 Surface tension in water waves
3.3 Experimental Set-up
3.4 Results
3.4.1 Waves celerity in the space-time plane
3.4.2 Analysis of the frequency-wavenumber spectra
3.4.3 Separation of free and bound waves
3.4.4 Beating length and the influence of the surface tension
3.4.5 Comparison between theoretical and experimental harmonic modulation
3.5 Concluding remarks
3.6 Supplementary results
3.6.1 Separation of left and right going waves
3.6.2 Complex fit of free and bound waves
3.6.3 Contribution of the terms added to the multi-modal model
4 Low-frequency modes in a tank with submerged step
4.1 Introduction
4.1.1 Governing equations
4.2 Experimental Set-up
4.3 Characterization of quasi-periodic and purely harmonic regimes
4.3.1 Space-time measurements
4.3.2 Experimental spectrum and phase plane
4.3.3 Transient signal
4.3.4 Low-frequency mode profile
4.4 Low-frequency resonance by varying the forcing frequency
4.5 Low-frequency resonance by forcing amplitude
4.6 Concluding remarks
5 Measurement of attenuation in shallow water
5.1 Introduction
5.2 Experimental set-up
5.2.1 Geometry and method of measurement
5.2.2 Forcing signal
5.3 Wave packet in multiple directions
5.3.1 Method of measurement of attenuation
5.4 Harmonic one-directional waves
5.5 Theoretical attenuation and comparison with experiments
5.6 Conclusion
6 Wetting properties in small scale experiments
6.1 Introduction
6.2 Influence of meniscus in an absorbing beach
6.2.1 Experimental measurement of the beach absorption
6.3 Influence of meniscus in a narrow channel
6.3.1 Decomposition in transverse modes
6.3.2 Cut-off frequency
6.3.3 Vertical displacement of a transverse profile
6.3.4 FTP measurement of a waveguide with and without mesh
6.4 Conclusion
7 Experimental measurements of perfect wave absorption
7.1 Introduction
7.1.1 The radiation damping
7.1.2 Wave absorption
7.1.3 Trapped modes resonance
7.2 Experimental set-up
7.3 Results analysis
7.3.1 Mono-modal propagation
7.3.2 Obtaining the absorption coefficient
7.3.3 Comparison of low and high absorption cases
7.3.4 Variation of resonator parameters
7.4 Conclusions and perspectives
8 Conclusion and perspectives
8.1 Conclusions of main results
8.2 Perspectives