Transfer matrix of linear water wave scattering over a stepwise bottom

For a two-dimensional linear wave scattering problem, a new transfer matrix incorporating evanescent modes is developed, from which the solution of a scattered wave field over a stepwise topography is directly obtained. The present method is shown to be capable of solving practical scattering problems with complicated bedforms, for which application of the conventional methods has been fairly limited. Highly accurate numerical solutions for sufficiently large systems are presented, and the computational efficiency of the present method is demonstrated. The interaction of bars in periodic beds is examined, and changes in the reflection coefficient with increasing number of bars are illustrated.