Characterization of local wave energy propagation

Understanding the local wave energy propagation is essential, especially for tracing the propagation of large energy. This paper focuses on characterizing the local wave energy propagation of slowly varying surface water waves. The wave is assumed to be unidirectional above flat bottom. We investigated the local features of waves such as wave energy, wave number, wave frequency, and local group velocity through complexification signal. From the analysis the local group velocity plays an important role as the double characteristic lines of the wave energy and the wave number. Therefore the local wave energy was successfully traced as energy trajectory by these characteristic lines. The energy trajectory was then numerically computed by finite difference scheme. In the application, we investigated the slowly varying waves; Gaussian waves, Trichromatic waves, and Peregrine soliton, in which the converging and diverging energy of these cases have been observed well from the energy trajectories.