Capturing reconnection in Navier-Stokes and resistive MHD dynamics
Seminar Room 1, Newton Institute
In this work, the phenomena of vortex reconnection in Navier-Stokes (and magnetic reconnection in MHD), of importance in fully developed turbulence, are studied from the point of view of the Eulerian-Lagrangian representation. This representation is interpreted as a full characterization of fluid motion using only particle description. New generalized equations of motion for the Weber-Clebsch potentials associated to this representation are derived.
We perform direct numerical simulations in order to confirm the validity of the paradigm proposed by Constantin where particles will diffuse anomalously in the space -and time- vicinity of reconnection events. For Navier-Stokes, the generalized formalism captures the intense reconnection of vortices of the Boratav, Pelz and Zabusky flow, in agreement with the previous study by Ohkitani and Constantin. For MHD, the new formalism is used to detect magnetic reconnection in several flows: the 3D Arnold, Beltrami and Childress (ABC) flow and the (2D and 3D) Orszag-Tang vortex. It is concluded that periods of intense activity in the magnetic enstrophy are correlated with periods of increasingly frequent resettings. Finally, the positive correlation between the sharpness of the increase in resetting frequency and the spatial localization of the reconnection region is discussed.
* http://arxiv.org/abs/0804.3602v1 - ArXiv Preprint of Paper