Geodesic
A discontinuous conically symmetric flow of an ideal incompressible fluid
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 88 (2024), pp. 149-163 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The Euler equations are considered in spherical coordinates to describe the steady flow of an ideal incompressible fluid. An exact conically symmetric solution based on the source/sink and strong conic discontinuity with an apex in zero of the coordinate system is obtained. The northern region of the flow is situated in the finite vicinity of the symmetry axis, i.e., within a discontinuity cone, where the solution is regular and vortex-free. On the other side of the discontinuity, the flow adjoins the permeable equator plane. In this region, the flow is vortex-like, and its properties are determined by a density jump. The fluid flowing through the discontinuity is governed by the increase of entropy principle. The thermal field corresponding to the flow is presented. It shows that the spatial heterogeneity of temperature results from the interaction between the azimuth vorticity component and the meridional velocity component. A strong discontinuity cone angle is revealed to be a significant parameter of the problem. A comparative analysis of the source and sink properties is performed. The considered flows qualitatively differ in terms of pressure and velocity behavior.
Keywords: hydrodynamic source and sink, strong flow discontinuity, density jump, entropy increase, vorticity rotor. 
@article{VTGU_2024_88_a11,
     author = {O. N. Shablovskiy},
     title = {A discontinuous conically symmetric flow of an ideal incompressible fluid},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {149--163},
     year = {2024},
     number = {88},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2024_88_a11/}
}
TY  - JOUR
AU  - O. N. Shablovskiy
TI  - A discontinuous conically symmetric flow of an ideal incompressible fluid
JO  - Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
PY  - 2024
SP  - 149
EP  - 163
IS  - 88
UR  - http://geodesic.mathdoc.fr/item/VTGU_2024_88_a11/
LA  - ru
ID  - VTGU_2024_88_a11
ER  - 
%0 Journal Article
%A O. N. Shablovskiy
%T A discontinuous conically symmetric flow of an ideal incompressible fluid
%J Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
%D 2024
%P 149-163
%N 88
%U http://geodesic.mathdoc.fr/item/VTGU_2024_88_a11/
%G ru
%F VTGU_2024_88_a11
O. N. Shablovskiy. A discontinuous conically symmetric flow of an ideal incompressible fluid. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 88 (2024), pp. 149-163. http://geodesic.mathdoc.fr/item/VTGU_2024_88_a11/

[1] Sedov L.I., Continuum mechanics, v. 1, Nauka, M., 1973

[2] Golovkin M.A., Golovkin V.A., Kalyavkin V.M., Issues of vortex hydromechanics], Fizmatlit, M., 2009

[3] Khatuntseva O.N., “Analysis of the reasons for an aerodynamic hysteresis in flight tests of the Soyuz reentry capsule at the hypersonic segment of its descent”, Journal of Applied Mechanics and Technical Physics, 52 (2011), 544–552 | DOI

[4] Guvernyuk S.V., Maksimov F.A., “Supersonic flow past a flat lattice of cylindrical rods”, Computational Mathematics and Mathematical Physics, 56 (2016), 1012–1019 | DOI | DOI

[5] Volkov V.F., Tarnavskiy G.A., “Symmetry breaking and hystere sis of stationary and quasi-stationary solutions of the Euler and Navier-Stokes equations”, Zhurnal vychislitel'noy matematiki i matematicheskoy fiziki – Computational Mathematics and Mathematical Physics, 41:11 (2001), 1742–1750

[6] Shtern V., Hussain F., “Collapse, symmetry breaking, and hysteresis in swirling flows”, Annual Review of Fluid Mechanics, 31 (1999), 537–566 | DOI

[7] Ogus G., Baelmans M., Vanierschot M., “On the flow structures and hysteresis of laminar swirling jets”, Physics of Fluids, 28 (2016), 123604-1–123604-16 | DOI

[8] Bogomolov B.A., “Motion of an ideal fluid of constant density in the presence of sinks”, Mekhanika zhidkosti i gaza – Fluid Dynamics, 1976, no. 4, 21–27

[9] Goldshtik M.A., Shtern V.N., Yavorskiy N.I., Viscous flows with paradoxical properties, Nauka, Novosibirsk, 1989

[10] Pukhnachev V.V., “Problem of a point source”, Journal of Applied Mechanics and Technical Physics, 60 (2019), 200–210 | DOI

[11] Bardos C., Titi E.S., “Euler equations for incompressible ideal fluids”, Russian Mathematical Surveys, 62:3 (2007), 409–451 | DOI | DOI

[12] Shablovskiy O.N., “Spherical flow of an ideal fluid in a spatially inhomogeneous force field”, Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and mechanics, 2020, no. 64, 146–155 | DOI