Collapse of vortex lines in hydrodynamics

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 \Omega\ 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) proportional to (t(0) - t)(3/2) whereas in the other two "hard" directions it obeys l(2) proportional to (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 H = integral \Omega\ dr. (C) 2000 MAIK "Nauka/Interperiodica".