Bragg scattering of surface waves over permeable rippled beds with current

In this study we develop a time-dependent wave equation for waves propagating with a current over permeable rippled beds. As well known, Bragg resonance occurs when the incident wavelength is twice the wavelength of the bottom ripple undulation and no current is present. However, the current in the near-shore region changes the resonance condition. A one-dimensional wave field is solved numerically based on the derived equation to study the effect of current on the Bragg resonance condition. Nonlinear wave-wave resonant interaction theory provides an explanation of the effect on Bragg resonance. Numerical results also indicate that the maximum reflection coefficient increases as current velocity increases from a negative to a positive value. Furthermore, the velocity of the current affects the position of the maximum reflection coefficient. (C) 2000 American Institute of Physics. [S1070-6631(00)02806-3].