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

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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Correspondence to Gualtiero Badin.

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Blender, R., Badin, G. Viscous dissipation in 2D fluid dynamics as a symplectic process and its metriplectic representation. Eur. Phys. J. Plus 132, 137 (2017). https://doi.org/10.1140/epjp/i2017-11440-x

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  • DOI: https://doi.org/10.1140/epjp/i2017-11440-x