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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2002, Volume 43, Issue 3, Pages 66–75
(Mi pmtf2631)
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Exact solutions of equations of rotationally symmetric motion of an ideal incompressible liquid
E. Yu. Meshcheryakova Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk, 630090
Abstract:
A partially invariant solution of the Euler equations is considered, where the vertical component of velocity is a function of the vertical coordinate and time, whereas the remaining components of velocity and pressure are independent of the polar angle in a cylindrical coordinate system. Using the classification of equations obtained by analysis of an overdetermined system, we consider two hyperbolic systems: the first one describes the motion of a cylindrical layer of an ideal incompressible liquid under a punch, and the second system allows obtaining solutions in a half-cylinder with singularities at the axis of symmetry. A class of new exact solutions is obtained, which describe vortex motion of an ideal incompressible liquid, including the motion with singularities (sources of vortices) located along the axis of symmetry.
Received: 24.12.2001
Citation:
E. Yu. Meshcheryakova, “Exact solutions of equations of rotationally symmetric motion of an ideal incompressible liquid”, Prikl. Mekh. Tekh. Fiz., 43:3 (2002), 66–75; J. Appl. Mech. Tech. Phys., 43:3 (2002), 397–405
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https://www.mathnet.ru/eng/pmtf2631 https://www.mathnet.ru/eng/pmtf/v43/i3/p66
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Abstract page: | 29 | Full-text PDF : | 31 |
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