Abstract
We consider the linear formulation of the 3-dimensional problem of a stationary flow with a free surface over a rough bottom of an irrotational capillary heavy ideal incompressible fluid. For fast near-critical flows we derive an approximate equation for the free surface elevation. We express a fundamental solution to the problem in terms of contour integrals and establish its asymptotic behavior at large distances from the origin.
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References
Landau L. D. and Lifshits E. M., Hydrodynamics [in Russian], Nauka, Moscow (1988).
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Original Russian Text Copyright © 2010 Nalimov V. I.
Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 4, pp. 871–882, July–August, 2010.
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Nalimov, V.I. Linear stationary surface waves over a rough bottom. Sib Math J 51, 696–705 (2010). https://doi.org/10.1007/s11202-010-0070-z
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DOI: https://doi.org/10.1007/s11202-010-0070-z