Fourier Analysis of Transient Wave System

The problem of approximating a transient wave process by a series of steady-state sinusoidal wave trains is considered. This study consists of a comparison of a theoretical, transient wave solution obtained from linearized theory with simulated solutions obtained from Fourier analysis of the theoretical surface profile and individual sinusoidal wave approximations of the profile between zero-crossings. The surface profile was in the form of data points simulating data obtained from a fixed probe. The quantities of interest are the dynamic pressure and the energy flux. Results indicate that both the Fourier analysis and the zero-crossing techniques yield very good results. To further test this decomposition, the simulated series of sinusoidal waves are released and the surface profile is reconstructed downstream. Results indicate that close to the fixed probe the surface profile compares well but degenerates with increasing distance from the probe.