Wave resonances in the presence of current and the frequency and time-domain interconnection

Abstract

The current work investigates the relationship between frequency and time domain problems associated with flexural gravity wave motion with oblique incidence and current. Different types of wave resonances such as buckling resonance, primary and secondary blocking resonance, Bragg resonance and interaction among them are discussed. Three propagating wave modes are observed between the primary and secondary blocking points, two of which are associated with positive group velocities and the third one is related to negative group velocities. Again, the Bragg resonance is analyzed for wave scattering problems. The complex porosity parameter is found to have a significant effect on the buckling and blocking resonance but does not affect Bragg resonance. The discontinuity of Bragg reflection is observed at primary and secondary blocking points and the peak values of Bragg reflection increase in the blocking zone. Again, we establish the interconnection between the frequency and time domain by deriving the time-domain solution from the frequency-domain solution and vice versa. The derivation of time-domain solutions using the dispersion relation and method of stationary phase is an intriguing finding. Wave energy and wave packets move faster in co-propagating waves than in counter-propagating waves and shallow water than in finite water depth. To validate the results, time-domain simulation and spectral methods are used.