2015/09/30 by Thiago F. Viscondi, Viscondi, Thiago F., Iberê L. Caldas +3
Mathematics · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Mathematical Physics (math-ph) #math-ph #math.MP #nlin.CD #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.1509.09247
27 pages, 1 figure; references added
arxiv created 2016/01/12 · arxiv updated 2016/01/13
A method for extracting finite-dimensional Hamiltonian systems from a class of 2+1 Hamiltonian mean field theories is presented. These theories possess noncanonical Poisson brackets, which normally resist Hamiltonian truncation, but a process of beatification by coordinate transformation near a reference state is described in order to perturbatively overcome this difficulty. Two examples of four-wave truncation of Euler's equation for scalar vortex dynamics are given and compared: one a direct non-Hamiltonian truncation of the equations of motion, the other obtained by beatifying the Poisson bracket and then truncating.