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Anomalous Waves Triggered by Abrupt Depth Changes: Laboratory Experiments and Truncated KdV Statistical Mechanics

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Recent laboratory experiments of Bolles et al. (Phys Rev Fluids 4(1):011801, 2019) demonstrate that an abrupt change in bottom topography can trigger anomalous statistics in randomized surface waves. Motivated by these observations, Majda et al. (Proc Natl Acad Sci 116(10):3982–3987, 2019) developed a theoretical framework, based on deterministic and statistical analysis of the truncated Korteweg-de Vries (TKdV) system that successfully captures key qualitative features of the experiments including the robust emergence of anomalous statistics and heightened skewness in the outgoing wavefield. Here, we extend these parallel experimental and modeling efforts with several new findings that have resulted from a synergetic interaction between the two. By precisely relating model parameters to physical ones, we calibrate the model inverse temperature to the specific conditions present in the experiments, thereby permitting a quantitative comparison. We find theoretically predicted distributions of surface displacement to match the experimental measurements with surprising detail. Prompted by the presence of surface slope in the TKdV Hamiltonian, we present new experimental measurements on surface slope statistics and compare them to model predictions. Analysis of some deterministic trajectories of TKdV elucidates the experimental length and time scales required for the statistical transition to a skewed state. Finally, the theory predicts a peculiar relationship between the outgoing displacement skewness and the change in slope variance, specifically how their ratio depends on the wave amplitude and depth ratio. New experimental measurements provide convincing evidence for this prediction.

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Acknowledgements

C.T.B. acknowledges support from the IDEA grant at Florida State University, as well as from the Geophysical Fluid Dynamics Institute. M.N.J.M. acknowledges support from the Simons Foundation, Award 524259. This research of A.J.M. is partially supported by the Office of Naval Research ONR N00014-19-1-2286. D.Q. is supported as a postdoctoral fellow on the grant.

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Authors and Affiliations

  1. United States Naval Academy, Annapolis, MD, USA

    Nicholas J. Moore

  2. University of Michigan, Ann Arbor, MI, USA

    C. Tyler Bolles

  3. Courant Institute of Mathematical Sciences, New York, NY, USA

    Andrew J. Majda & Di Qi

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  1. Nicholas J. Moore
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  2. C. Tyler Bolles
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  3. Andrew J. Majda
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  4. Di Qi
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Correspondence to Nicholas J. Moore.

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Communicated by Leslie Smith.

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Moore, N.J., Bolles, C.T., Majda, A.J. et al. Anomalous Waves Triggered by Abrupt Depth Changes: Laboratory Experiments and Truncated KdV Statistical Mechanics. J Nonlinear Sci 30, 3235–3263 (2020). https://doi.org/10.1007/s00332-020-09649-2

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