Wave resonances and hydroelastic wave motion

Abstract

Three different types of resonances, i.e. blocking, trapping and Bragg resonance, associated with flexural gravity wave motion in the presence of current and permeable bottom are discussed. Also, using the different modes of wave propagation, the interconnection among all these resonances is analysed. An uneven pattern in the plate deflection is seen inside the blocking resonance zone. The uniform convergence of the infinite series associated with the trapped mode is proved. We have found that the trapped mode does not exist if the magnitude of the opposing current is higher or whenever we move the cylinder away from the platecovered surface. It is also observed that two propagating modes within the blocking frequencies create the environment for the occurrence of trapped waves. At the same time, all three modes have a remarkable contribution to Bragg resonance. The Bragg reflection increases in the blocking zone and decreases outside of it. We have seen that the amplitude of the Bragg reflection increases with the increase in current speed and porosity parameter. Also, the discontinuities in Bragg reflection coefficients are seen at blocking frequencies. The model is also carefully validated numerically for trapped and Bragg resonances against the results available in the existing literature.