A new mechanism of the collapse in hydrodynamics is suggested, due to
breaking of continuously distributed vortex lines [1].
Collapse results in
formation of the point singularities of the vorticity field Omega.
At the collapse point, the value of the vorticity blows up as $(t_0-t)^{-1}$
where $t_0$ is a collapse time. The spatial structure of the collapsing
distribution approaches a pancake form: contraction occurs by the law
$l_1\sim(t_0-t)^{3/2}$ along the "soft" direction, the characteristic scales
vanish like $l_2\sim(t_0-t)^{1/2}$ along two other ("hard") directions.
This scenario of the collapse is shown to take place in the integrable
three-dimensional hydrodynamics with the Hamiltonian
${\cal H}=\int|{\bf\Omega}|d{\bf r}$. The conclusion about collapse made is based
on usage of the vortex line representation [2] according to
which each vortex line is labeled by two-dimensional Lagrangian marker and
 another coordinate coincides  with a curve parameter given the line.
Most numerical studies of collapse
in the Euler equation are in a good agreement with the proposed theory.
In particular, for the Euler equation in the vortex line representation
it is first demostrated [3] numerically appearance
of singularity of vorticity omega in one separate point which is not
connected with any symmetry of the initial distribution.

Sequences of such type of collapse are discussed for fully developed
hydrodynamic turbulence.

 

 
[1] E.A.Kuznetsov and V.P.Ruban,  JETP,  91, 775 (2000).
[2] E.A.Kuznetsov and V.P.Ruban, JETP Letters, {\bf 67}, 1076 (1998); Phys. Rev. E {\bf 61}, 831 (2000).
[3]V.A.Zheligovsky, E.A.Kuznetsov, O.M.Podvigina,  " Numerical modeling of collapse in ideal incompressible hydrodynamics " JETP Letters (accepted).