Lagrangian and Dirac constraints for the ideal&nbsp;incompressible fluid and magnetohydrodynamics

Morrison, P. J.; Andreussi, T.; Pegoraro, F.

doi:10.1017/s0022377820000331

Lagrangian and Dirac constraints for the ideal incompressible fluid and magnetohydrodynamics

Journal Article · Wed May 13 00:00:00 EDT 2020 · Journal of Plasma Physics

DOI:https://doi.org/10.1017/s0022377820000331· OSTI ID:1800220

^[1]; Andreussi, T. ^[2]; ^[3]

Univ. of Texas, Austin, TX (United States); OSTI
SITAEL S.p.A., Pisa, (Italy)
Univ. of Pisa (Italy). Dipartimento di Fisica E. Fermi

The incompressibility constraint for fluid flow was imposed by Lagrange in the so-called Lagrangian variable description using his method of multipliers in the Lagrangian (variational) formulation. An alternative is the imposition of incompressibility in the Eulerian variable description by a generalization of Dirac’s constraint method using noncanonical Poisson brackets. Here it is shown how to impose the incompressibility constraint using Dirac’s method in terms of both the canonical Poisson brackets in the Lagrangian variable description and the noncanonical Poisson brackets in the Eulerian description, allowing for the advection of density. Both cases give the dynamics of infinite-dimensional geodesic flow on the group of volume preserving diffeomorphisms and explicit expressions for this dynamics in terms of the constraints and original variables is given. Since Lagrangian and Eulerian conservation laws are not identical, comparison of the various methods is made.

View Accepted Manuscript (DOE)

Research Organization:: University of Texas, Austin, TX (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: FG02-04ER54742

OSTI ID:: 1800220

Journal Information:: Journal of Plasma Physics, Journal Name: Journal of Plasma Physics Journal Issue: 3 Vol. 86; ISSN 0022-3778

Publisher:: Cambridge University PressCopyright Statement

Country of Publication:: United States

Language:: English

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