Abstract:
An analytical description is given to the spherical partially invariant solution of the gas-dynamics equations in the case of additional symmetry – the homogeneous singular vortex. The solution was specified by a generalized potential – an auxiliary function satisfying the inhomogeneous Schwarz equation. It is proved that the part of the factor system of the homogeneous singular vortex in a Lagrangian representation that describes the kinematics of a gas particle is a system of linear equations with the potential defined by the solution of the Schwarz equation. For particular values of the adiabatic exponent equal to 1, 4/3, and 5/3, the solution of the Schwarz equation is written in terms of lower-order equations. The isothermal gas flow in the homogeneous singular vortex isdescribed. It is shown that a periodic geometrical trajectory configuration can exist but the gas density in this case has a singularity. A physically definite solution exists on time intervals that do not contain singularity points. Examples of motion obtained by implementation of analytical formulas on a computer are given.
Citation:
A. A. Cherevko, A. P. Chupakhin, “Homogeneous singular vortex”, Prikl. Mekh. Tekh. Fiz., 45:2 (2004), 75–89; J. Appl. Mech. Tech. Phys., 45:2 (2004), 209–221
This publication is cited in the following 8 articles:
A. A. Cherevko, A. P. Chupakhin, “Implicit differential equations of gas dynamics”, J Math Sci, 188:3 (2013), 322
Sergey V. Golovin, The IMA Volumes in Mathematics and its Applications, 144, Symmetries and Overdetermined Systems of Partial Differential Equations, 2008, 367
S. V. Golovin, “Ovsyannikov plane vortex: The equations of the submodel”, J. Appl. Mech. Tech. Phys., 49:5 (2008), 725–736
B. D. Annin, “New exact solutions of the spatial Tresca plasticity equations”, Dokl. Phys., 52:8 (2007), 422
Sergey V Golovin, “Generalization of the one-dimensional ideal plasma flow with spherical waves”, J. Phys. A: Math. Gen., 39:23 (2006), 7579
Sergey V Golovin, “Invariant solutions of the singular vortex in magnetohydrodynamics”, J. Phys. A: Math. Gen., 38:37 (2005), 8169
A. S. Pavlenko, “Projective submodel of the Ovsyannikov vortex”, J. Appl. Mech. Tech. Phys., 46:4 (2005), 459–470
Sergey V Golovin, “Singular vortex in magnetohydrodynamics”, J. Phys. A: Math. Gen., 38:20 (2005), 4501
Citation in format AMSBIB
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