Vortex Line Representation for Flows of Ideal and Viscous Fluids
Abstract
It is shown that the Euler hydrodynamics for vortical flows of an ideal fluid coincides with the equations of motion of a charged {\it compressible} fluid moving due to a selfconsistent electromagnetic field. Transition to the Lagrangian description in a new hydrodynamics is equivalent for the original Euler equations to the mixed LagrangianEulerian description  the vortex line representation (VLR). Due to compressibility of a "new" fluid the collapse of vortex lines can happen as the result of breaking (or overturning) of vortex lines. It is found that the NavierStokes equation in the vortex line representation can be reduced to the equation of the diffusive type for the Cauchy invariant with the diffusion tensor given by the metric of the VLR.
 Publication:

Soviet Journal of Experimental and Theoretical Physics Letters
 Pub Date:
 September 2002
 DOI:
 10.1134/1.1525034
 arXiv:
 arXiv:physics/0209047
 Bibcode:
 2002JETPL..76..346K
 Keywords:

 Physics  Fluid Dynamics;
 Physics  Atmospheric and Oceanic Physics;
 Physics  Plasma Physics
 EPrint:
 Pis'ma v ZhETF (JETP Letters), 76, no 6 (2002)