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New Trends in the Analytical Theory of Long Sea Wave Runup

In: Applied Wave Mathematics

Author

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  • Ira Didenkulova

    (Institute of Cybernetics at Tallinn University of Technology
    Institute of Applied Physics)

Abstract

A modern view on the analytical theory of the long sea wave runup on a plane beach is presented. This theory is based on rigorous solutions of nonlinear shallow-water equations. The dynamics of the moving shoreline is studied in detail. It is demonstrated that extreme characteristics of the runup process (runup and rundown amplitudes, extreme values of on- and off-shore velocities, and critical amplitude of the breaking wave) can be found using the solution of the linear shallow-water theory, meanwhile the description of the time series of the wave field requires the nonlinear theory. The key and novel results presented here are: i) parameterization of basic formulas for extreme runup characteristics for bell-shape waves, showing that they weakly depend on the initial wave shape, which is usually unknown in real sea conditions; ii) runup analysis of periodic asymmetric waves with a steep front, as such waves are penetrating inland over larger distances and with greater velocities than symmetric waves.

Suggested Citation

  • Ira Didenkulova, 2009. "New Trends in the Analytical Theory of Long Sea Wave Runup," Springer Books, in: Ewald Quak & Tarmo Soomere (ed.), Applied Wave Mathematics, pages 265-296, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-00585-5_14
    DOI: 10.1007/978-3-642-00585-5_14
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