2008/03/31 by Alexander Bihlo, Bihlo, Alexander
Computer Science · Engineering · Physics and Astronomy · #Atmospheric and Oceanic Physics (physics.ao-ph) #Cosmology and Gravitation Theories #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Nonlinear Dynamics and Pattern Formation #physics.ao-ph #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.0803.4458
7 pages, extended and corrected version
openalex publication_date 2008/03/31 · arxiv created 2008/05/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The traditional Hamiltonian structure of the equations governing conservative Rayleigh-Bénard convection (RBC) is singular, i.e. it's Poisson bracket possesses nontrivial Casimir functionals. We show that a special form of one of these Casimirs can be used to extend the bilinear Poisson bracket to a trilinear generalised Nambu bracket. It is further shown that the equations governing dissipative RBC can be written as the superposition of the conservative Nambu bracket with a dissipative symmetric bracket. This leads to a Nambu-metriplectic system, which completes the geometrical picture of RBC.