Obstacle-induced dissipation of tsunami waves: linking solitary-wave and N-wave formulations

Tsunami waves are long gravity waves that propagate nearly conservatively in deep water, but may undergo significant energy dissipation during nearshore propagation due to coastal vegetation, roughness, and man-made structures. Quantifying this obstacle-induced attenuation in a physically consistent and transferable way remains a key challenge for the assessment of tsunami hazard. This study presents a comparative theoretical and experimental framework for the attenuation of tsunami-like long-wave pulses in vegetated or obstructed environments. Energy-based formulations are developed for both solitary waves and tsunami-like N-waves, demonstrating that they share the same hyperbolic amplitude-decay structure, with differences arising solely from waveform geometry through a shape-dependent coefficient. Within a common shallow-water setting, the analysis explicitly separates waveform representation from the adopted damping closure. These formulations are contrasted with linearized depth-averaged resistance models commonly used for long waves, considering both a constant-rate exponential attenuation and a pulse-consistent variant. Laboratory experiments involving solitary waves propagating through rigid stem arrays are used to calibrate bulk drag coefficients and provide a physically grounded benchmark. The calibrated resistance parameters are then applied, without re-fitting and without introducing new experimental data for tsunami waves, to predict the attenuation of tsunami-like pulses using alternative waveform representations and resistance closures. The results show that, for identical obstacle properties, predicted wave damping depends primarily on the adopted attenuation closure. In particular, constant-rate exponential formulations systematically overestimate attenuation for finite pulses, highlighting the importance of energy-consistent, pulse-based models for tsunami propagation in vegetated regions.