Resonant Reflection of Waves over Sinusoidally Varying Topographies
Keywords:Water waves, eigenfunction expansion method, Bragg reflection, evanescent modes, sinusoidally varying topography
The propagation of monochromatic waves over an arbitrarily varying topography is studied theoretically. The varying topography is first represented by a finite number of small steps. A theoretical model is then developed by formulating the diffraction of monochromatic waves by abrupt depth changes, through the eigenfunction expansion method. Not only the propagating mode but also the evanescent modes are included in the model. The model developed is applied to the study of the Bragg reflection of monochromatic waves caused by a singly-sinusoidally varying topography. The effects of the oblique incidence of waves are also investigated. The model solutions are compared with available experimental data. The model is also used to investigate the Bragg reflection of monochromatic waves over a doubly sinusoidally varying topography. The reflection coefficients calculated are compared with laboratory measurements and other numerical results. A reasonable agreement is observed.