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.
| Original language | English |
|---|---|
| Pages (from-to) | 921-935 |
| Number of pages | 15 |
| Journal | Progress of Theoretical Physics |
| Volume | 127 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 2012 May |
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ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)
Cite this
A variational principle for dissipative fluid dynamics. / Fukagawa, Hiroki; Fujitani, Youhei.
In: Progress of Theoretical Physics, Vol. 127, No. 5, 05.2012, p. 921-935.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A variational principle for dissipative fluid dynamics
AU - Fukagawa, Hiroki
AU - Fujitani, Youhei
PY - 2012/5
Y1 - 2012/5
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84862532800&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84862532800&partnerID=8YFLogxK
U2 - 10.1143/PTP.127.921
DO - 10.1143/PTP.127.921
M3 - Article
AN - SCOPUS:84862532800
VL - 127
SP - 921
EP - 935
JO - Progress of Theoretical Physics
JF - Progress of Theoretical Physics
SN - 0033-068X
IS - 5
ER -