Submitting Campus

Daytona Beach

Department

Mathematics

Document Type

Article

Publication/Presentation Date

8-11-2020

Abstract/Description

We present experimental evidence of formation and persistence of localized waves, breathers, and solitons, occurring in a random sea state and uniformly traveling over non-uniform bathymetry. Recent studies suggest connections between breather dynamics and irregular sea states and between extreme wave formation and breathers, random sea states, or non-uniform bathymetry individually. In this paper, we investigate the joint connection between these phenomena, and we found that breathers and deep-water solitons can persist in more complex environments. Three different sets of significant heights have been generated within a Joint North Sea Wave Observation Project wave spectrum, and the wave heights were recorded with gauges in a wave tank. Statistical analysis was applied to the experimental data, including the space and time distribution of kurtosis, skewness, Benjamin–Feir index, moving Fourier spectra, and probability distribution of wave heights. Stable wave packages formed out of the random wave field and traveling over shoals, valleys, and slopes were compared with exact solutions of the nonlinear Schrödinger equation with a good match, demonstrating that these localized waves have the same structure as deep-water breathers. We identify the formation of rogue waves at moments and over regions where the kurtosis and skewness have local maxima. These results provide insights for understanding of the robustness of Peregrine and higher-order Akhmediev breathers, Kuznetsov–Ma solitons, and rogue waves, and their occurrence in realistic oceanic conditions, and may motivate analogous studies in other fields of physics to identify limitations of exact weakly nonlinear models in non-homogeneous media.

Publication Title

Physics of Fluids

DOI

https://doi.org/10.1063/5.0016379

Publisher

AIP Publishing

Grant or Award Name

Natural Science Foundation of China Grant Nos. NSFC-51639003 and NSFC-51679037, National Key Research and Development Program of China (Grant Nos. 2019 YFC0312400 and 2017 YFE0132000), the National Natural Science Foundation of China (Grant Nos. 51975032 and 51939003), and the State Key Laboratory of Structural Analysis for Industrial Equipment (Grant No. S18408)

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