Higher-Order Bragg Reflection of Gravity Waves by Arrays of Vertical Cylinders

Abstract An experimental study in a basin of the scattering of a gravity wave by an array of regularly spaced vertical cylinders evidenced a strong reflection of the wave in the opposite direction to the incident wave under Bragg resonance conditions, i.e., for a spacing between cylinders that is a multiple of the half-wavelength of the wave. Strong reflections in oblique directions, with amplitudes greater than that of the incident wave, were also observed when the distance between two cylinders is an odd multiple of a quarter of the wavelength, i.e., under phase quadrature conditions between two successive cylinders. Finally, due to the excitation of transverse modes, strong amplitudes are observed in the central part of the array in such resonant conditions, however, of less amplitude than predicted by a linear model based on integral matching method. It is probably due to incomplete stationary conditions and dissipation, particularly in the case of large trapped mode oscillations. Finally, regarding the wave separation technique, a minimisation method is used here to determine the amplitudes and the angles of the oblique waves in addition to the incident and reflected waves along the basin.