English

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

Fluid Dynamics 2017-02-16 v7 Mathematical Physics math.MP Atmospheric and Oceanic Physics

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.

Keywords

Cite

@article{arxiv.1510.05846,
  title  = {Representation of Viscous Dissipation in 2D Fluid Dynamics as a Symplectic Process and its Metriplectic Representation},
  author = {Richard Blender and Gualtiero Badin},
  journal= {arXiv preprint arXiv:1510.05846},
  year   = {2017}
}