Title: Explicit formulae in the statistical equilibrium of nearly parallel vortex filaments

Speaker: Timothy Andersen, Rensselaer Polytechnic Institute Von Neumann Interview Candidate

Date/Time: Wednesday, January 10, 2007, 9:00 – 10:00 am

Location: CSRI Building, Room 90 (Sandia NM)

Brief Abstract:  Geophysical research has focused on flows, such as ocean currents, as two dimensional.  Two dimensional point or blob vortex models have the advantage of having a Hamiltonian, whereas 3D vortex filament or tube systems do not necessarily have one, although they do have action functionals. On the other hand, certain classes of 3D vortex models called nearly parallel vortex filament models do have a Hamiltonian and are more accurate descriptions of geophysical and atmospheric flows than purely 2D models, especially at smaller scales. In these ``quasi-2D'' models we replace 2D point vortices with vortex filaments that are very straight and nearly parallel but have Brownian variations along their lengths due to local self-induction. When very straight, quasi-2D filaments are expected to have virtually the same planar density distributions as 2D models. An open problem is when quasi-2D model statistics behave differently than those of the related 2D system and how this difference is manifested. In this talk I discuss the nearly parallel vortex filament model of Klein, Majda, Damodaran in statistical equilibrium, including a derivation for mean-field free-energy functionals and Monte Carlo results, which show the accuracy of these formulae.  I additionally discuss other applications besides geophysics such as plasmas and superfluid turbulence.