Steady-State Flows of Ideal Incompressible Fluid with Velocity Pointwise Orthogonal to the Pressure Gradient Full article
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Arnold Mathematical Journal
ISSN: 2199-6792 , E-ISSN: 2199-6806 |
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| Output data | Year: 2024, Volume: 10, Number: 2, Pages: 223–256 Pages count : 34 DOI: 10.1007/s40598-023-00234-5 | ||||
| Tags | Euler equations · Ideal fluid · Gavrilov flow · Geodesic vector field | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0006 |
Abstract:
A new important relation between fluid mechanics and differential geometry is established. We study smooth steady solutions to the Euler equations with the additional property: the velocity vector is orthogonal to the gradient of the pressure at any point. Such solutions are called Gavrilov flows. We describe the local structure of Gavrilov flows in terms of the geometry of isobaric hypersurfaces. In the 3D case, we obtain a system of PDEs for axisymmetric Gavrilov flows and find consistency conditions for the system. Two numerical examples of axisymmetric Gavrilov flows are presented: with pressure function periodic in the axial direction, and with isobaric surfaces diffeomorphic to the torus.
Cite:
Rovenski V.
, Sharafutdinov V.A.
Steady-State Flows of Ideal Incompressible Fluid with Velocity Pointwise Orthogonal to the Pressure Gradient
Arnold Mathematical Journal. 2024. V.10. N2. P.223–256. DOI: 10.1007/s40598-023-00234-5 Scopus РИНЦ OpenAlex
Steady-State Flows of Ideal Incompressible Fluid with Velocity Pointwise Orthogonal to the Pressure Gradient
Arnold Mathematical Journal. 2024. V.10. N2. P.223–256. DOI: 10.1007/s40598-023-00234-5 Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Feb 16, 2023 |
| Accepted: | Jul 14, 2023 |
| Published online: | Aug 1, 2023 |
| Published print: | Mar 7, 2024 |
Identifiers:
| Scopus: | 2-s2.0-85166282951 |
| Elibrary: | 63421548 |
| OpenAlex: | W4385462764 |
Citing:
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