DIRECT NUMERICAL SIMULATIONS OF THE BATCHELOR TRAILING VORTEX BY A SPECTRAL METHOD

The nonlinear vorticity dynamics of the Batchelor trailing vortex is p resented. Direct numerical simulations of the three-dimensional, incom pressible, Navier-Stokes equations by a spectral method are used. It i s shown that the initial vortex core is subjected to three transformat ions: a twisting phase, a lateral expansion of its cross section and f ormation of a spiral structure. These transformations are accompanied by a gradual deceleration of axial velocity. Mean kinetic energy is th en transferred to radial velocity. When the transfer is maximum a seco ndary instability is initiated leading to the spiral structure. These transformations are in agreement with vortex breakdown observed in rec ent experiments. (C) 1998 American Institute of Physics. [S1070-6631(9 8)00402-4].