Irregular Wave Transformation Processes in Surf and Swash Zones

A frequency-domain model is developed for elucidating the nonlinear transformation processes of the Fourier amplitudes and phases of normally incident random waves in surf and swash zones. The vertically-integrated continuity and momentum equations which have been used to describe a turbulent bore on a beach are rearranged to derive the equations expressing the cross-shore variations of the Fourier components of normally incident random waves. The derived equations are solved numerically using forcing terms computed from a previously developed time-domain model. The frequency-domain model attempts to quantify the importance of the nonlinear forcing due to the cross-shore variations of instantaneous radiation stress and bottom shear stress as well as the seaward boundary condition related to incoming low frequency waves for generating two-dimensional surf beat in the surf and swash zones.