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**Chapter 16** 

© 2012 Uda et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

**BG Model Based on Bagnold's Concept and Its** 

**Application to Analysis of Elongation of Sand** 

The accurate prediction of three-dimensional (3D) beach changes on a coast with a large shoreline curvature, such as a coast with a sand spit, and a wave field that significantly changes in response to topographic changes, has been difficult to achieve in previous studies. As a result, regarding the beach changes around a sand spit, most previous studies have focused on the shoreline changes. Ashton et al. (2001) showed that when the incident angle of deep-water waves to the mean shoreline exceeds 45, shoreline instability occurs, resulting in the development of sand spits from a small perturbation of the shoreline. They successfully predicted the planar changes in a shoreline containing sand spits using infinitesimal meshes divided in the *x*- and *y*-directions. However in Ashton et al.'s model, only the longshore sand transport equation is employed as the sand transport equation instead of a two-dimensional (2D) sand transport equation in which both cross-shore and longshore sand transport are considered. Furthermore, in evaluating the wave field, wave conditions at the breaking point are transformed into deep-water values assuming a bathymetry with straight parallel contours and using Snell's law. Since the sand transport equation is expressed using these deep-water parameters, the effect of large 3D changes in topography on the wave field cannot be accurately evaluated. Furthermore, the finitedifference scheme used to evaluate the breaker angle and the method of calculating the wave field around the wave-shelter zone are altered depending on the calculation conditions, resulting in a complicated calculation method that requires special calculation techniques. Watanabe et al. (2004) developed a model for predicting the shoreline changes of a sand spit under the conditions that the sand spit significantly changes its configuration with changes in the wave field. They selected orthogonal curvilinear coordinates parallel and normal to the shoreline of the sand spit, and the seabed topography after various

**Spit and Shore – Normal Sand Bar** 

Takaaki Uda, Masumi Serizawa and Shiho Miyahara

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/48547

**1. Introduction** 
