Rayleigh-Bénard Convection as a Nambu-metriplectic problem

Details Rayleigh-Bénard Convection as a Nambu-metriplectic problem Rayleigh-Bénard Convection as a Nambu-metriplectic problem

2008-03-31

arxiv.org/abs/0803.4458v2

Physics

Fluid Dynamics

7 pages, extended and corrected version

Scientific paper

The traditional Hamiltonian structure of the equations governing conservative Rayleigh-B\'enard 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.

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