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

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Citation

Blender, R., & Badin, G. (2017). Viscous dissipation in 2D fluid dynamics as a symplectic process and its metriplectic representation. The European Physical Journal Plus, 132: 137. doi:10.1140/epjp/i2017-11440-x.


Cite as: https://hdl.handle.net/11858/00-001M-0000-002D-D884-4
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.