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Author: Philip J Morrison
Requested Type: Poster
Submitted: 2018-03-01 17:43:15

Co-authors: T. Andreussi, F. Pegoraro

Contact Info:
University of Texas at Austin
2515 Speedway
Austin, TX   78712

Abstract Text:
The imposition of the incompressibility constraint in fluid flow was imposed by Lagrange in the so-called Lagrangian variable description using his method of multipliers in a variational formulation [1]. An alternative is the imposition of this constraint in the Eulerian variable description by a generalization of Dirac's constraint method [2,3] using noncanonical Poisson brackets [4]. It will be shown how to impose the compressibility constraint using Dirac's method in terms of canonical Poisson brackets, and a comparison emphasizing the pros and cons of the various methods will be discussed. In addition the definition and use of energy for stability will be described along with the extension to magnetofluid dynamics.

* Supported by U.S. Dept. of Energy Contract # DE-FG05-80ET-53088.

[1] J. L. Lagrange, {Me'canique Analytique (Ve Courcier, Paris, 1788).
[2] P. J. Morrison et al., Ann. Phys. 324, 1747 (2009).
[3] C. Chandre et al., Phys.~Lett. A 376, 737 (2012).
[4] P. J. Morrison, Rev. Mod. Phys. 70, 467 (1998).