Journal of Experimental and Theoretical Physics

, Volume 91, Issue 4, pp 775–785 | Cite as

Collapse of vortex lines in hydrodynamics

  • E. A. Kuznetsov
  • V. P. Ruban
Fluids

Abstract

A new mechanism is proposed for collapse in hydrodynamics associated with the “breaking” of vortex lines. The collapse results in the formation of point singularities of the vorticity field, i.e., a generalized momentum curl. At the point of collapse the vorticity |Ω| increases as ((t0t)−1 and its spatial distribution for t → t0 approaches quasi-two-dimensional: in the “soft” direction contraction obeys the law l1 → (t0t)3/2 whereas in the other two “hard” directions it obeys l2 → (t0t)1/2. It has been shown that this collapse scenario takes place in the general case for three-dimensional integrable hydrodynamics with the Hamiltonian ℋ = ∫|Ω| dr.

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Copyright information

© MAIK "Nauka/Interperiodica" 2000

Authors and Affiliations

  • E. A. Kuznetsov
    • 1
  • V. P. Ruban
    • 1
  1. 1.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia

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