Statistics – Computation
Scientific paper
Aug 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987apj...319..207b&link_type=abstract
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 319, Aug. 1, 1987, p. 207-214. Research supported by the Foundation for Bas
Statistics
Computation
19
Astrophysics, Computational Fluid Dynamics, Conservation Laws, Helical Flow, Magnetohydrodynamic Flow, Chiral Dynamics, Ideal Fluids, Kelvin-Helmholtz Instability, Potential Fields, Protostars, Pulsars
Scientific paper
Helicity conservation laws in fluid dynamics and magnetohydrodynamics are studied. The rate of fluid helicity dissipation in nonisentropic flow is derived, and the derivation is generalized, introducing the concept of chirality and reinterpreting the Ertel-Katz law as one of a family of laws dictating the variation of the rate of dissipation of some helicity along streamlines. Woltjer's two helicity conservation laws in MHD are reviewed, and the covariant derivation of the second is given. The two Oron helicities are introduced, their conserved character is established, and a type B law arising from the second Oron helicity's conservation is proved. Departures from perfect MHD are addressed, estimating the magnetic helicity (MH) dissipation in magnetized fluids with finite conductivity and deriving a type-B law for the MH dissipation rate in a particularly simple kind of imperfect MHD flow. An Ertel-Katz type law is derived for poorly conducting magnetized fluids.
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