Vortex line representation for flows of ideal and viscous fluids
- 57 Downloads
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 . 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.
PACS numbers47.15.Ki 47.32.Cc
Unable to display preview. Download preview PDF.
- 1.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).Google Scholar
- 2.E. A. Kuznetsov and V. P. Ruban, Zh. Éksp. Teor. Fiz. 118, 893 (2000) [JETP 91, 775 (2000)].Google Scholar
- 3.V. A. Zheligovsky, E. A. Kuznetsov, and O. N. Podvigina, Pis’ma Zh. Éksp. Teor. Fiz. 74, 402 (2001) [JETP Lett. 74, 367 (2001)].Google Scholar
- 4.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).Google Scholar
- 5.E. A. Kuznetsov and V. P. Ruban, Pis’ma Zh. Éksp. Teor. Fiz. 67, 1015 (1998) [JETP Lett. 67, 1076 (1998)].Google Scholar
- 7.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.Google Scholar
- 8.V. E. Zakharov and E. A. Kuznetsov, Usp. Fiz. Nauk 137, 1137 (1977).Google Scholar