Abstract
A class of Euler flows of an ideal incompressible liquid is considered. The total kinetic helicity is invariant for barotropic inviscid flow under conservative body forces. The topological structure of vortex lines are classified by Hopf indices, Brouwer degrees and linking number in geometry. A new mechanism of generation and annihilation of a vortex line is given. The evolution equation of the vortex line has been given and its splitting behavior at the critical points is also discussed in detail. Three length approximation relations in the neighbourhood of singular points are given: l ∝ (t − t*)1/2, l ∝ t − t*, l= const.
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