Nambu brackets in fluid dynamics and magnetohydrodynamics

by Michael Kurgansky (A.M. Obukhov Institute of Atmospheric Physics of the Russian Academy of Sciences)

Thursday 31 Mar 2011, 16:00 → 18:00 Europe/Rome

Aula Conversi (Dipartimento di Fisica - Ed. G. Marconi)

Nambu formalism in classical mechanics and ideal fluid dynamics (Nambu 1973; Novir and Blender 1993) is overviewed and concrete examples of the construction of Nambu brackets for equations of motion (both 3D and 2D) of Boussinesq stratified fluids and also for magnetohydrodynamical (MHD) equations are given. It serves a generalization of Hamiltonian formulation for the considered equations of motion. Two alternative Nambu formulations are proposed, first by using fluid dynamical (kinematic) helicity in 3D and enstrophy in 2D as constitutive elements a! nd second, by using the existing conservation laws of the governing equations.