Geodesic
Non-helical exact solutions to the Euler equations for swirling axisymmetric fluid flows
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 23 (2019) no. 4, pp. 764-770

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Swirling axisymmetric stationary flows of an ideal incompressible fluid are considered within the framework of the Euler equations. A number of new exact solutions to the Euler equations are presented, where, as distinct from the known Gromeka–Beltrami solutions, vorticity is noncollinear with velocity. One of the obtained solutions corresponds to the flow inside a closed volume, with the nonpermeability condition fulfilled at its boundary, the vector lines of vorticity being coiled on revolution surfaces homeomorphic to a torus.
Keywords: ideal incompressible fluid, swirling axisymmetric flows
Mots-clés : Euler equations, exact solutions. 
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     author = {E. Yu. Prosviryakov},
     title = {Non-helical exact solutions to the {Euler} equations for swirling axisymmetric fluid flows},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {764--770},
     publisher = {mathdoc},
     volume = {23},
     number = {4},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2019_23_4_a9/}
}
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E. Yu. Prosviryakov. Non-helical exact solutions to the Euler equations for swirling axisymmetric fluid flows. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 23 (2019) no. 4, pp. 764-770. http://geodesic.mathdoc.fr/item/VSGTU_2019_23_4_a9/