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Integral Representations of Solution in the Problem on Skew Incidence of a Surface Wave on the Straight Shoreline Water Wedge
- Authors: Lyalinov M.A.1, Polyanskaya S.V.2
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Affiliations:
- Saint Petersburg State University
- North-Western Institute of Management of the RANEPA
- Issue: Vol 88, No 3 (2024)
- Pages: 406-421
- Section: Articles
- URL: https://journal-vniispk.ru/0032-8235/article/view/269260
- DOI: https://doi.org/10.31857/S0032823524030055
- EDN: https://elibrary.ru/ZAWQKP
- ID: 269260
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Abstract
In the linear approximation of the surface gravitational waves of small amplitude a classical model problem about the incursion of a surface wave under some angle on the shoreline is solved. The problem is formulated for the harmonic potential of velocity of the fluid in the 3D water wedge with the Robin-Steklov boundary condition on the free surface and with the no-flow condition along the normal on the bed of the water domain. Some critical comments about a known in the literature solution having a “non-physical” singularity of the logarithmic type on the coastal line are given. The asymptotics with respect to distance from the shoreline of the obtained solution, bounded on the edge, is constructed. The reflection coefficient of the wave reflected from the shoreline is calculated.
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About the authors
M. A. Lyalinov
Saint Petersburg State University
Author for correspondence.
Email: lyalinov@yandex.ru
Russian Federation, Saint Petersburg
S. V. Polyanskaya
North-Western Institute of Management of the RANEPA
Email: polyanskaya-sv@ranepa.ru
Russian Federation, Saint Petersburg
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