Analytical and numerical models for tsunami run-up

  • Per A. Madsen
  • David R. Fuhrman


The classical analytical solution for the run-up of periodic long waves on an infinitely long slope is presented and discussed. This leads to simple expressions for the maximum run-up and the associated flow velocity in terms of the surf similarity parameter and the amplitude to depth ratio determined at some offshore location. We use these expressions to analyze the impact of tsunamis on beaches and relate the discussion to the recent Indian Ocean tsunami from December 26, 2004. An important conclusion is that the impact is very sensitive to the beach slope. Next, we present a numerical model based on a highly accurate Boussinesq-type formulation. This model incorporates nonlinear and dispersive effects, and is extended to include a moving shoreline. As a first step, the model is verified against the non-dispersive analytical run-up solution, demonstrating good quantitative accuracy. The model is then used to study an idealized three-dimensional nearshore-generated tsunami propagating over a hypothetical sound.


Wave Height Edge Wave Indian Ocean Tsunami Beach Slope Tidal Bore 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Per A. Madsen
    • 1
  • David R. Fuhrman
    • 1
  1. 1.Mechanical Engineering DepartmentTechnical University of DenmarkKgs. LyngbyDenmark

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