Energy as a tool to study tsunami–bathymetry interaction
- College of Fisheries and Ocean Sciences, University of Alaska, Fairbanks, Alaska, USA;
* corresponding author
Highlights
- Tsunami propagation and its interaction with bathymetry.
- Energy imbalance arises as varying depth disrupts tsunami energy equilibrium.
- Magnitude of imbalance depends on depth contrast between shallow and deep regions.
- Energy imbalance serves as the basis for defining a new reflection coefficient.
- Reexamination of tsunami through regions of kinetic or potential energy dominance.
Abstract
This study introduces a new framework for investigating tsunami propagation and its interaction with bathymetry by decomposing total energy into kinetic and potential components. Unlike conventional approaches based on wave amplitude or energy flux, this decomposition reveals local energy imbalances that arise when a tsunami interacts with variable bathymetry. These imbalances provide a new diagnostic tool for quantifying reflection and for distinguishing regions dominated by velocity (kinetic energy) or sea-level displacement (potential energy). The method is first tested in an idealized channel with a depth discontinuity. In addition to the expected incident, reflected, and transmitted waves, an imbalance between kinetic and potential energy emerges, with its magnitude controlled by the depth contrast. This imbalance forms the basis for defining a new reflection coefficient. The approach is then applied to the 2011 Japan Tōhoku Tsunami. Results show that kinetic and potential energies remain in equilibrium during long-distance propagation but diverge near major bathymetric features such as Koko Guyot Seamount and Hess Rise, where the imbalance depends on the relative depth between the seafloor and the seamount summit. Finally, an elliptical seamount model illustrates the limitations of the method and clarifies the conditions under which energy imbalance is most relevant.
Keywords: Tsunami; Kinetic and potential energy; Energy equilibrium; Reflection at depth discontinuity; Japan tsunami 2011; Seamount tsunami interaction
Submitted: 10 April 2025; Revised: 20 January 2026; Accepted: 23 February 2026