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Shallow water equations for equatorial tsunami waves.

Anna Geyer1, Ronald Quirchmayr2

  • 1Delft University of Technology, Delft Institute of Applied Mathematics, Faculty Electrical Engineering, Mathematics and Computer Science, Mekelweg 4, 2628 CD Delft, The Netherlands ronaldq@kth.se.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|December 13, 2017
PubMed
Summary

This study derives shallow water model equations, including Korteweg-de Vries and Boussinesq types, for equatorial tsunami waves using the f-plane approximation. It also evaluates the applicability of these nonlinear water wave models.

Keywords:
-plane approximationequatorial shallow water equationstsunami modelling

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Area of Science:

  • Fluid dynamics
  • Oceanography
  • Applied mathematics

Background:

  • Tsunami wave dynamics are complex and require accurate mathematical models for prediction and analysis.
  • Shallow water theory provides a framework for understanding wave propagation in reduced dimensions.
  • Equatorial regions present unique characteristics for wave behavior due to specific geophysical conditions.

Purpose of the Study:

  • To derive and present shallow water model equations of Korteweg-de Vries (KdV) and Boussinesq types.
  • To apply these models specifically to the phenomenon of equatorial tsunami waves.
  • To analyze and discuss the applicability and limitations of the derived models in the f-plane approximation.

Main Methods:

  • Derivation of nonlinear shallow water equations.
  • Application of the f-plane approximation to model equatorial dynamics.
  • Analysis of Korteweg-de Vries and Boussinesq type equations for tsunami waves.

Main Results:

  • Successful derivation of KdV and Boussinesq type shallow water equations tailored for equatorial tsunami waves.
  • Demonstration of the f-plane approximation's role in simplifying equatorial wave dynamics.
  • Initial discussion on the conditions under which these models are applicable.

Conclusions:

  • The derived Korteweg-de Vries and Boussinesq type equations offer valuable tools for studying equatorial tsunamis.
  • The f-plane approximation is a useful simplification for analyzing these waves in specific regions.
  • Further research is needed to fully validate the applicability of these models across diverse scenarios.