Viscous dissipation in 2D fluid dynamics as a symplectic process and its metriplectic representation
Meteorological Institute, University of Hamburg, Hamburg, Germany
2 Institute of Oceanography, University of Hamburg, Hamburg, Germany
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Accepted: 6 March 2017
Published online: 22 March 2017
Dissipation can be represented in Hamiltonian mechanics in an extended phase space as a symplectic process. The method uses an auxiliary variable which represents the excitation of unresolved dynamics and a Hamiltonian for the interaction between the resolved dynamics and the auxiliary variable. This method is applied to viscous dissipation (including hyper-viscosity) in a two-dimensional fluid, for which the dynamics is non-canonical. We derive a metriplectic representation and suggest a measure for the entropy of the system.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2017