https://doi.org/10.1140/epjp/i2017-11440-x
Regular Article
Viscous dissipation in 2D fluid dynamics as a symplectic process and its metriplectic representation
1
Meteorological Institute, University of Hamburg, Hamburg, Germany
2
Institute of Oceanography, University of Hamburg, Hamburg, Germany
* e-mail: gualtiero.badin@uni-hamburg.de
Received:
16
January
2017
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
