Abstract: A two-dimensional stationary problem of a potential freesurface ow of an ideal incompressible uid caused by a singular sink is considered. The sink is located at the top of a triangular ledge at the bottom. The problem is to determine the shape of the free boundary and the velocity eld of the uid. By employing a conformal map and the Levi-Civita technique, the problem is rewritten as an operator equation in a Hilbert space. It is proved that, for the Froude number greater than some particular value, there is a solution of the problem. It is established that the free boundary has a cusp at the point over the sink. It is shown that the inclination angle of the free surface is less than π/2 everywhere except at the cusp point, where is it equal to π/2.

Cite: Титова А.А.
О форме свободной границы течения идеальной несжимаемой жидкости с точечным стоком в вершине треугольного выступа на дне
Сибирские электронные математические известия / Siberian Electronic Mathematical Reports. 2021. Т.18. №1. С.207-236. DOI: 10.33048/semi.2021.18.016 WOS Scopus РИНЦ OpenAlex

Dates:

Submitted:	Jan 21, 2021
Published online:	Mar 16, 2021

Identifiers:

Web of science:	WOS:000641262000001
Scopus:	2-s2.0-85104833344
Elibrary:	46265208
OpenAlex:	W3201128582

Citing:

DB	Citing
Scopus	1
OpenAlex	1
Elibrary	2

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