Resonant Triad Interactions of Acoustic and Gravity Waves in Water of Finite Depth

The interaction between acoustic and surface-gravity waves is typically disregarded in classical wave theory due to their distinct propagation speeds. However, nonlinear dynamics enable energy exchange through resonant triad interactions, facilitating significant coupling between these wave types. This study investigates the resonant interaction involving two acoustic modes and one gravity wave in water of finite and deep depths. Using the method of multiple scales, nonlinear amplitude equations are derived to characterise the system’s spatio-temporal behaviour.

The analysis reveals that energy transfer efficiency depends strongly on water depth. While deeper water hinders energy transfer, shallower regimes enhance interaction, particularly when higher acoustic modes are involved. Numerical simulations identify parameter ranges where gravity wave amplitudes can be amplified or reduced, contingent on factors such as initial acoustic amplitudes and wave packet widths.

These findings have implications for tsunami mitigation, offering a potential mechanism to reduce wave amplitudes before reaching shorelines. Furthermore, the insights contribute to renewable energy harnessing from surface gravity waves by leveraging resonant acoustic-gravity interactions. This work advances the theoretical framework for understanding acoustic-gravity wave dynamics, highlighting opportunities for practical applications in environmental and energy contexts.