Computing local crest phase speed in multi-directional sea states through the Spatial Hilbert Transform

The detection of wave breaking plays a fundamental role in the modelling of this complex physical phenomenon within nonlinear potential flow solvers . Recent studies have demonstrated that utilizing the ratio of fluid velocity to local wave crest phase speed enables accurate identification of individual breaking waves in a wave field. However, evaluating the local wave crest phase speed poses great challenges, especially for multi-directional sea states. Based on the multi-dimensional Hilbert transform in space, we correlated the local phase function and amplitude components to a mixed local amplitude (envelope) and phase function. Then, associated with these slow-varying assumptions of the local quantities, two methodologies, the linear spatial Hilbert transform method and the spatial Hilbert transform method, are proposed to compute the local wave crest phase speed in multi-directional sea states. These approaches are first compared to a classical crest-tracking method for short-crested waves and then investigated in detail by accounting for the existence of nonlinearity, directionality , and spectrum bandwidth. The present work shows that the proposed spatial Hilbert transform method allows for an efficient and accurate evaluation of the local wave crest phase speed in multi-directional sea states, particularly for strongly nonlinear configurations.