There is a gap between model- or theory-based research outputs, which suggest that the runup and amplification of nonbreaking waves generally increase as the sea bottom slopes decrease, and field observations, which indicate that tsunami damage has been rarely reported in places with vast continental shelfs. To resolve this contradiction, we propose a Lagrangian-like volume tracking paradigm to describe the energy, mass, and momentum of travelling nearshore tsunamis and apply the paradigm to analyse the tsunami damping mechanism at typical geophysical scales. The results support the following conclusions: (i) The suggested paradigm is consistent with field observations; continental shelfs with long and mild slopes can effectively diminish tsunami impacts. (ii) Potential energy becomes significant due to the energy transformation process on steeply sloped bathymetries. (iii) On mild-sloped bathymetries, tsunami potential and kinetic energies are conserved until breaking occurs. After breaking, undular bores attenuate tsunami energies effectively. (iv) For extended continental shelf bathymetries, more of the tsunami mass is reflected offshore.
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