Geodesic
On the shape of the free-surface problem of an ideal incompressible fluid flow with a singular sink at the top of a triangular ledge at the bottom
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 207-236

Voir la notice de l'article provenant de la source Math-Net.Ru

A two-dimensional stationary problem of a potential free-surface flow of an ideal incompressible fluid 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 field of the fluid. 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 $\pi/2$ everywhere except at the cusp point, where is it equal to $\pi/2$.
Keywords: ideal incompressible fluid, free surface, singular sink. 
@article{SEMR_2021_18_1_a25,
     author = {A. A. Titova},
     title = {On the shape of the free-surface problem of an ideal incompressible fluid flow with a singular sink at the top of a triangular ledge at the bottom},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {207--236},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a25/}
}
TY  - JOUR
AU  - A. A. Titova
TI  - On the shape of the free-surface problem of an ideal incompressible fluid flow with a singular sink at the top of a triangular ledge at the bottom
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2021
SP  - 207
EP  - 236
VL  - 18
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a25/
LA  - ru
ID  - SEMR_2021_18_1_a25
ER  - 
%0 Journal Article
%A A. A. Titova
%T On the shape of the free-surface problem of an ideal incompressible fluid flow with a singular sink at the top of a triangular ledge at the bottom
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2021
%P 207-236
%V 18
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a25/
%G ru
%F SEMR_2021_18_1_a25
A. A. Titova. On the shape of the free-surface problem of an ideal incompressible fluid flow with a singular sink at the top of a triangular ledge at the bottom. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 207-236. http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a25/