Abstract
The Euler hydrodynamics describing the vortex flows of ideal fluids is shown to coincide with the equations of motion obtained for a charged compressible fluid moving under the effect of a self-consistent electromagnetic field. For the Euler equations, the passage to the Lagrange description in the new hydrodynamics is equivalent to a combined Lagrange-Euler description, i.e., to the vortex line representation [5]. Owing to the compressibility of the new hydrodynamics, the collapse of a vortex flow of an ideal fluid can be interpreted as a result of the breaking of vortex lines. The Navier-Stokes equation formulated in terms of the vortex line representation proves to be reduced to a diffusion-type equation for the Cauchy invariant with the diffusion tensor determined by the metric of this representation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. I. Arnold, Catastrophe Theory (Znanie, Moscow, 1981; Springer-Verlag, Berlin, 1986); V. I. Arnold, Mathematical Methods of Classical Mechanics (Nauka, Moscow, 1984; Springer-Verlag, Berlin, 1989).
E. A. Kuznetsov and V. P. Ruban, Zh. Éksp. Teor. Fiz. 118, 893 (2000) [JETP 91, 775 (2000)].
V. A. Zheligovsky, E. A. Kuznetsov, and O. N. Podvigina, Pis’ma Zh. Éksp. Teor. Fiz. 74, 402 (2001) [JETP Lett. 74, 367 (2001)].
E. A. Kuznetsov, O. N. Podvigina, and V. A. Zheligovsky, in Proceedings of IUTAH Symposium “Tubes, Sheets, and Singularities in Fluid Dynamics,” Zakopane, 2002 (in press).
E. A. Kuznetsov and V. P. Ruban, Pis’ma Zh. Éksp. Teor. Fiz. 67, 1015 (1998) [JETP Lett. 67, 1076 (1998)].
E. A. Kuznetsov and V. P. Ruban, Phys. Rev. E 61, 831 (2000).
E. I. Yakubovich and D. A. Zenkovich, in Proceedings of the International Conference “Progress in Nonlinear Science,” Nizhni Novgorod, Russia, 2001, Ed. by A. G. Litvak (Nizhni Novgorod, 2002), p. 282; physics/0110004.
V. E. Zakharov and E. A. Kuznetsov, Usp. Fiz. Nauk 137, 1137 (1977).
R. Salmon, Annu. Rev. Fluid Mech. 20, 225 (1988).
Author information
Authors and Affiliations
Additional information
__________
Translated from Pis’ma v Zhurnal Éksperimental’no\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) i Teoretichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Fiziki, Vol. 76, No. 6, 2002, pp. 406–410.
Original Russian Text Copyright © 2002 by Kuznetsov.