Breaking of vortex and magnetic field lines in hydrodynamics and MHD

Abstract

A new description of vortex lines dynamics is suggested as a motion of a compressible charged fluid driving by effective self‐consistent electromagnetic field. Transition to the Lagrangian description in a new hydrodynamics is equivalent for the original Euler equations to the mixed Lagrangian‐Eulerian description — the vortex line representation (VLR). As a sequence of compressibility of new hydrodynamics breaking of continuously distributed vortex lines is possible that results in formation of the point singularities of the vorticity field . Behavior of the maximum of vorticity near the collapse point closely follows the dependence (t0 − t)−1, where t0 is the time of collapse. This is in correspondence with the numerics performed within the vortex line representation as well as with many other numerical evidences of collapse in the 3D Euler equations. Sequences of such type of collapse are discussed for fully developed hydrodynamic turbulence, in particular for the Kolmorogov spectrum. It is also demons...