The wave passage over a seamount without reflection: Analytical results using the generalized Carrier–Greenspan transform.

This article presents a generalized method based on the Carrier–Greenspan transform to obtain exact solutions of the linear shallow water equations over a broad family of non-monotonic bottom profiles, including seamounts. The approach reduces the original system to a single wave equation with variable coefficients, enabling simultaneous analytical determination of both free surface displacement and flow velocity without additional conditions. The study identifies an extensive set of non-reflective bathymetries where waves propagate without reflection, preserving energy even over steep slopes, and demonstrates that wave amplitude can increase beyond predictions by Green’s law, particularly for longer waves passing over underwater mountains. These findings suggest that seamounts may not mitigate tsunami wave impact and can, under certain shapes, amplify wave amplitudes.