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Prog. Theor. Phys. Vol. 127 No. 5 (2012) pp. 921-935
A Variational Principle for Dissipative Fluid Dynamics
Hiroki Fukagawa* and
Youhei Fujitani**
School of Fundamental Science and Technology, Keio University,
Yokohama 223-8522, Japan
(Received March 31, 2011; Revised March 26, 2012)
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.
Subject Index :
519
URL :
http://ptp.ipap.jp/link?PTP/127/921/
DOI : 10.1143/PTP.127.921
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