Viscous dissipation in 2D fluid dynamics as a symplectic process and its metriplectic representation

Richard Blender; Gualtiero Badin

doi:10.1140/epjp/i2017-11440-x

The European Physical Journal Plus

March 2017, 132:137

Viscous dissipation in 2D fluid dynamics as a symplectic process and its metriplectic representation

Authors
Authors and affiliations

Richard Blender
Gualtiero BadinEmail author

Regular Article

First Online:: 22 March 2017

Received:: 16 January 2017
Accepted:: 06 March 2017

DOI: 10.1140/epjp/i2017-11440-x

Cite this article as:: Blender, R. & Badin, G. Eur. Phys. J. Plus (2017) 132: 137. doi:10.1140/epjp/i2017-11440-x

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Abstract.

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.

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Authors and Affiliations

Richard Blender
- 1
Gualtiero Badin
- 2
Email authorView author's OrcID profile

1.Meteorological InstituteUniversity of HamburgHamburgGermany
2.Institute of OceanographyUniversity of HamburgHamburgGermany

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Viscous dissipation in 2D fluid dynamics as a symplectic process and its metriplectic representation

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