Phase manipulation to analyse different types of non-linearity using water waves as a case study

Journal article

We develop a phase-based manipulation technique, which can be adopted for many physical problems that involve separating the slave harmonics from the free waves. This technique extends the existing literature by developing a general solution to the problem while enabling the incorporation of arbitrary numbers and combinations of phases for computation. We further extend our matrix formulation to phase-based reconstruction applications, where a missing phase can be predicted from other phase-shifted signals with all slave harmonics included. This allows a clean separation between weakly nonlinear effects from the strong nonlinear process such as the breaking of water waves. We examine the possible sources for the phase-based reconstruction error, including the bandwidth of the input signal, the nonlinear effects, different phase combinations and phase misalignment. We aim to provide a reference for the optimal choice of the number and combination of phases to be selected. We use surface gravity-driven water waves as a case study.

Authors: Liu, X; Tang, T; Mostert, W; Adcock, TAA

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Royal Society
• Journal: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
• Volume: 481
• Issue: 2313
• Article number: 20240831
• Publication date: 2025-05-14
• Acceptance date: 2025-04-11
• DOI: 10.1098/rspa.2024.0831
• EISSN: 1471-2946
• ISSN: 1364-5021
• Language: English
• Keywords: nonlinear; harmonics; signal separation; signal reconstruction; phase manipulation