Vortex line representation for flows of ideal and viscous fluids
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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
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