A Variational Principle for Dissipative Fluid Dynamics

Abstract In the variational principle leading to the Euler equation for a perfect fluid, we can use the method of undetermined multiplier for holonomic constraints representing mass conservation and adiabatic condition. For a dissipative fluid, the latter condition is replaced by the constraint spec...

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Bibliographic Details
Published in:Progress of theoretical physics 2012-05, Vol.127 (5), p.921-935
Main Authors: Fukagawa, Hiroki, Fujitani, Youhei
Format: Article
Language:English
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Summary:Abstract In the variational principle leading to the Euler equation for a perfect fluid, we can use the method of undetermined multiplier for holonomic constraints representing mass conservation and adiabatic condition. For a dissipative fluid, the latter condition is replaced by the constraint specifying how to dissipate. Noting that this constraint is nonholonomic, we can derive the balance equation of momentum for viscous and viscoelastic fluids by using a single variational principle. We can also derive the associated Hamiltonian formulation by regarding the velocity field as the input in the framework of control theory.
ISSN:0033-068X
1347-4081
DOI:10.1143/PTP.127.921