On the Downshift of Wave Frequency for Bragg Resonance

• DOI: 10.1007/s13344-022-0006-y
• Publication Date: 2022-03-14T09:17:03Z
• Authors: Ji Peng; Ai-feng Tao; Jun Fan; Jin-hai Zheng; Yu-ming Liu
• Keywords: Free surface; Monochromatic color

For surface gravity waves propagating over a horizontal bottom that consists of patch sinusoidal ripples, strong wave reflection occurs under the Bragg resonance condition. The critical frequency, at which peak coefficient is obtained, has been observed in both physical experiments and direct numerical simulations to be downshifted from well-known theoretical prediction. It long speculated downshift may attributed higher-order rippled free-surface boundary effects, but intrinsic mechanism remains unclear. By regular perturbation analysis, we derive solution frequency due third-order nonlinear effects boundaries. found nonlinearity plays dominant role while actually causes upshift. downshift/upshift quadratic dependence bottom/free-surface steepness. Polychromatic leads larger relative monochromatic bottom. In addition, based on high-order spectral method are conducted validate present theory. compares well with available experimental data.