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Deep Water Waves from Oscillating Elliptic Source

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Abstract

Asymptotic solutions describing linear waves generated by oscillating elliptic source are constructed employing the recently developed “Reference Solution Approach” (RSA). The source is assumed to be in rest. The resulting wave pattern exhibits pronounced anisotropy of the solutions for elongated sources. The classic Kelvin angles of the ship wave patterns determine specific distinguished directions. The analytical results within the RSA are shown to agree remarkably well with the exact linear solutions of the problem.

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Acknowledgements

The authors are grateful to Prof. Victor Shrira for fruitful discussion and useful suggestions.

Funding

The work is supported by Russian Science Foundation Grant \(\sharp \)19-72-30028 (S.B.) and by Ministry of Science and Higher Education of the Russian Federation under the program FMWE-2021-0003 (V.G.).

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Author notes

  1. Vladimir Gnevyshev and Sergei Badulin have contributed equally to this work.

Authors and Affiliations

  1. Ocean Physics Division, Shirshov Institute of Oceanology, Russian Academy of Sciences, 36, Nakhimovskii pr., Moscow, Russia, 117997

    Vladimir Gnevyshev & Sergei Badulin

  2. Laboratory of Integrable Systems and Turbulence, Skolkovo Institute of Science and Technology, 30, bld. 1, Bolshoy Boulevard, Moscow, Russia, 121205

    Sergei Badulin

Authors
  1. Vladimir Gnevyshev
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  2. Sergei Badulin
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Contributions

Conceptualization, formal analysis, writing—original draft preparation: VG. Methodology, formal analysis, visualization, writing—review and editing: SB. All authors have read and agreed to the published version of the manuscript.

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Correspondence to Sergei Badulin.

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Gnevyshev, V., Badulin, S. Deep Water Waves from Oscillating Elliptic Source. Water Waves 5, 239–256 (2023). https://doi.org/10.1007/s42286-023-00080-0

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