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The wave passage over a seamount without reflection: Analytical results using the generalized Carrier–Greenspan transform
Physics of Fluids. 2024. Vol. 36. No. 7. Article 076609.
A method for the transformation of linear shallow water equations based on a generalization of the Carrier–Greenspan transform, well known in the theory of wave rolling on a flat slope, is presented. Thanks to it, the initial equations for waves over arbitrary bathymetry are reduced to a wave equation, from which both the displacement of the free surface and the flow velocity can be obtained simultaneously. Exact solutions in the sum of traveling waves have been obtained for certain configurations of the seabed in the form of seamounts. It is shown that when moving from a more gentle slope to a sharper one, the waveform will integrate a certain number of times, and the maximum amplitude is not reached at the very top of the mountain.
Language:
English
Keywords: уравнения мелкой водыshallow water equationstraveling wavesбегущие волныCarrier-Greenspan transformEuler-Darboux-Poisson equationуравнение Эйлера-Дарбу-Пуассонаподводные горы
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