On the Analysis of Dispersion Relation of Spatially Shoaling Waves

As waves propagate into nearshore waters, the wave dispersive relation is significantly affected by the nonlinear dynamics of the shoaling process (Herbers et al. 2002). This could have important effects to the interpretation and application of remote sensing results of shallow water waves (Stockdon and Holman, 2000). Many field studies are carried out based on temporally measured wave data to examine and clarify the wave dispersion relation in shallow waters (Thornton and Guza, 1982; Herber et al. 2002). Recently, an airborne topographic mapper (ATM, an airborne scanning laser ranging system) has bee n deployed to acquire three-dimensional (3D) topography of ocean surface waves off the coast of Duck, North Carolina (Hwang et al. 2000). The ATM spatial wave data reveal the typical shoaling wave features of a decreasing wavelength and skewed wave profile with a shaper crest and flatter trough. These shoaling features occur within a short distance relative to wave length. Analyzing the dispersion relation of the spatially shoaling waves requires methods that can deal with these non-stationary and nonlinear features. In this study, we explore the application of the Fourier-based wavelet analysis to examine the dispersion relation.