Generation and amplification of magnetic islands by drift interchange turbulence.

We investigate the multiscale nonlinear dynamics of a linearly stable or unstable tearing mode with small-scale interchange turbulence using 2D MHD numerical simulations. For a stable tearing mode, the nonlinear beating of the fastest growing small-scale interchange modes drives a magnetic island with an enhanced growth rate to a saturated size that is proportional to the turbulence generated anomalous diffusion. For a linearly unstable tearing mode the island saturation size scales inversely as one-fourth power of the linear tearing growth rate in accordance with weak turbulence theory predictions. Turbulence is also seen to introduce significant modifications in the flow patterns surrounding the magnetic island.

Nonlinear dynamics of magnetic islands imbedded in small-scale turbulence.

The nonlinear dynamics of magnetic tearing islands imbedded in a pressure gradient driven turbulence is investigated numerically in a reduced magnetohydrodynamic model. The study reveals regimes where the linear and nonlinear phases of the tearing instability are controlled by the properties of the pressure gradient. In these regimes, the interplay between the pressure and the magnetic flux determines the dynamics of the saturated state. A secondary instability can occur and strongly modify the magnetic island dynamics by triggering a poloidal rotation. It is shown that the complex nonlinear interaction between the islands and turbulence is nonlocal and involves small scales.

Effect of viscosity in the dynamics of two point vortices: exact results.

An exact, unstationary, two-dimensional solution of the Navier-Stokes equations for the flow generated by two point vortices is obtained. The viscosity nu is introduced as a Brownian motion in the Hamiltonian dynamics of point vortices. The point vortices execute a stochastic motion whose probability density can be computed from a Fokker-Planck equation, equivalent to the original Navier-Stokes equation. The derived solution describes, in particular, the merging process of two Lamb vortices, and the development of the characteristic spiral structure in the topology of the vorticity. The viscous effects are thoroughly investigated by an asymptotic analysis of the solution. In particular, the selection mechanism of a specific pattern among the infinity satisfying the nu=0 (Euler) equation is discussed.