Vortex line representation for flows of ideal and viscous fluids

E. A. Kuznetsov

    Research output: Contribution to journalArticlepeer-review

    13 Citations (Scopus)

    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.

    Original languageEnglish
    Pages (from-to)346-350
    Number of pages5
    JournalJETP Letters
    Volume76
    Issue number6
    DOIs
    Publication statusPublished - 25 Sep 2002

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