incorporate all the hydrodynamic wave-surf zone and sediment transport 

 knowledge that is available from laboratory and field studies. Numerical 

 modeling has the potential of providing accurate predictions of shoreline 

 response to various structural and nourishment alternatives. Additionally, 

 the possibility exists of employing numerical models and available field 

 measurements to learn more about sediment transport mechanisms. In this 

 latter mode, various candidate mechanisms or coefficients would be evaluated 

 by determining the best match between measured and predicted shorelines and 

 the bathymetry. Generally, this mode would require high-quality measurements 

 of the forcing function (waves and nonwave-related currents) and the 

 associated response (sediments) as well as the knowledge of appropriate 

 conditions at the boundaries of the model. 



The present report documents the development and application of an 

 n-line numerical model to investigate bathymetric response to time-varying 

 wave conditions and shoreline modification. The model includes both 

 longshore and onshore-offshore sediment transport. Based on laboratory 

 results, a new distribution of longshore sediment transport across the surf 

 zone is used. The wave climate is specified on the model boundaries which do 

 not need to extend to deep water. Efficient algorithms are employed for 

 representing wave refraction and diffraction. The equation of sediment 

 continuity and transport are solved by a completely implicit algorithm which 

 allows a large time-step. Specified sediment transport values or specified 

 contour positions can be accommodated at the model boundaries. The model is 

 suitable for investigating the shoreline response to a variety of 

 modifications such as one or more groins, terminal structures, structures 

 with variable permeability, and beach nourishment with or without terminal 

 structures. 



2. Study Objectives . 



The objectives of the present study include (a) the documentation of 

 state-of-the-art models, (b) the development and documentation of an improved 

 model which includes the capability to represent n-contour lines and (c) the 

 application of the model to several relevant coastal engineering problems. 



II. BACKGROUND 



This discussion describes significant contributions which either address 

 numerical modeling of shorelines directly or provide improved capability for 

 modeling. 



1. Wave Refraction (Noda. 1972) . 



Noda developed an algorithm for solving the following steady state 

 equation for wave refraction 



V X t = (1) 



in which v, the horizontal vector differential operator, and k, the wave 

 number, are defined in terms of their components as 



