Representation of Viscous Dissipation in 2D Fluid Dynamics as a Symplectic Process and its Metriplectic Representation

Richard Blender; Gualtiero Badin

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arXiv · 1510.05846

Representation of Viscous Dissipation in 2D Fluid Dynamics as a Symplectic Process and its Metriplectic Representation

Richard Blender·Gualtiero Badin

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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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Richard Blender, Gualtiero Badin. 2017-02-15. Representation of Viscous Dissipation in 2D Fluid Dynamics as a Symplectic Process and its Metriplectic Representation. https://arxiv.org/abs/1510.05846

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