Algebraic construction of a Nambu bracket for the two-dimensional vorticity equation
Mathematical Physics
2015-05-27 v3 math.MP
Fluid Dynamics
Abstract
So far fluid mechanical Nambu brackets have mainly been given on an intuitive basis. Alternatively an algorithmic construction of such a bracket for the two-dimensional vorticity equation is presented here. Starting from the Lie--Poisson form and its algebraic properties it is shown how the Nambu representation can be explicitly constructed as the continuum limit from the structure preserving Zeitlin discretization.
Cite
@article{arxiv.1102.1298,
title = {Algebraic construction of a Nambu bracket for the two-dimensional vorticity equation},
author = {Matthias Sommer and Katharina Brazda and Michael Hantel},
journal= {arXiv preprint arXiv:1102.1298},
year = {2015}
}