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

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.