Collapse of vortex lines in hydrodynamics |
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Authors: | E A Kuznetsov V P Ruban |
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Institution: | (1) Landau Institute for Theoretical Physics, Russian Academy of Sciences, Moscow, 117334, Russia |
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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 ((t 0 ? t)?1 and its spatial distribution for t → t 0 approaches quasi-two-dimensional: in the “soft” direction contraction obeys the law l 1 → (t 0 ? t)3/2 whereas in the other two “hard” directions it obeys l 2 → (t 0 ? t)1/2. It has been shown that this collapse scenario takes place in the general case for three-dimensional integrable hydrodynamics with the Hamiltonian ? = ∫|Ω| d r. |
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