Study on Three-Dimensional Beach Deformation Model for Nonlinear Multi-Directional Random Waves

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The objective of the present study is to develop an accurate and practical numerical model for three-dimensional beach evolution under nonlinear multi-directional random waves. Nonlinear mild slope equations proposed by Isobe (1994) were adopted as a wave-current model and modified with respect to wave breaking by formulating a breaker-induced energy dissipation term, in which the breaking point can be automatically determined. For the breaking criterion on multi-directional random waves, a prototype of breaking index was proposed by introducing specific parameters for multi-directionality and frequency-wise irregularity. The nearshore boundary condition was also improved to include swash zone dynamics under multi-directional random waves.The extended Boussinesq-type equations derived by Nwogu (1993) were modified for applications to nearshore waves and currents including surf and swash zones. For a sand transport model, the sheet flow transport rate formula proposed by Dibajnia and Watanabe (1997) was used as a basis, which can determine the net sand transport rate using a set of asymmetric oscillatory flow velocities. The formula was extended to general horizontal plane problems where waves and currents were in the different directions. After predicting the net sand transport rate, the conservation equation of sediment mass was solved to determine the topographic change. The validity of the model was confirmed through comparisons with laboratory data on waves, currents and beach deformation around coastal structures under multi-directional irregular waves.