Nonlinear Bragg resonance of focused wave groups by periodic seabed topography

Abstract

Bragg resonance induced by periodic bottoms has potential applications for coastal protection. Under extreme wave conditions, nonlinearity may play a critical role in the wave-topography interactions. It is important to understand the nonlinear effects in Bragg resonance of periodic bottoms subject to a nonlinear focused wave group, as a representation of an extreme transient event. An efficient fully nonlinear numerical model using the conformal mapping method is developed to simulate wave-topography interaction problems. Validation of this model is performed against theoretical predictions and experimental data in the literature. It is then employed to study Bragg reflection triggered by nonlinear focused wave groups. The nonlinear analysis finds that increased wave group amplitudes slightly weaken the Bragg reflection and shift the value of the corresponding relative wavelength 2S / LP , as a result of the free surface nonlinear effect. The three bottom configurations tested include ripples, rectified cosinoidal bars, and steps. A second order Bragg reflection is observed at 2S / LP = 2.0 , with reflection coefficients potentially exceeding the fundamental reflection coefficients by up to 20% at greater bar heights. This study provides new insights into the nonlinear Bragg Resonance of free surfaces and periodic seabed topography under extreme wave conditions.