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Random focusing of tsunami waves

Nature Physics volume 12, pages 259–262 (2016)Cite this article

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Abstract

Tsunamis exhibit surprisingly strong height fluctuations. An in-depth understanding of the mechanisms that lead to these variations in wave height is a prerequisite for reliable tsunami forecasting. It is known, for example, that the presence of large underwater islands1 or the shape of the tsunami source2 can affect the wave heights. Here we show that the consecutive effect of even tiny fluctuations in the profile of the ocean floor (the bathymetry) can cause unexpectedly strong fluctuations in the wave height of tsunamis, with maxima several times higher than the average wave height. A novel approach combining stochastic caustic theory and shallow water wave dynamics allows us to determine the typical propagation distance at which the strongly focused waves appear. We demonstrate that owing to this mechanism the small errors present in bathymetry measurements can lead to drastic variations in predicted tsunami heights. Our results show that a precise knowledge of the ocean’s bathymetry is absolutely indispensable for reliable tsunami forecasts.

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Figure 1: Random focusing of a tsunami wave by the weakly fluctuating depth profile of the Indian Ocean.
Figure 2: Sensitivity of forecasts to errors in ocean topography.
Figure 3: Can we predict the mean distance to the strongest wave intensities?

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Acknowledgements

We thank E. Bodenschatz for fruitful discussions. This work has been supported by the DFG research group 760.

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Authors and Affiliations

  1. Max Planck Institute for Dynamics and Self-Organization (MPIDS), Am Fassberg 17, 37077 Göttingen, Germany

    Henri Degueldre, Jakob J. Metzger, Theo Geisel & Ragnar Fleischmann

  2. Department of Physics, Institute for Nonlinear Dynamics, University of Göttingen, 37077 Göttingen, Germany

    Henri Degueldre, Jakob J. Metzger & Theo Geisel

Authors
  1. Henri Degueldre
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  2. Jakob J. Metzger
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  3. Theo Geisel
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  4. Ragnar Fleischmann
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Contributions

The project was devised by J.J.M. and R.F., and developed jointly by all authors. All numerical work was performed by H.D. and J.J.M. The manuscript was written by all authors.

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Correspondence to Theo Geisel.

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The authors declare no competing financial interests.

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Degueldre, H., Metzger, J., Geisel, T. et al. Random focusing of tsunami waves. Nature Phys 12, 259–262 (2016). https://doi.org/10.1038/nphys3557

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