On a variational principle for Beltrami flows

 

Autores
<div class="autor_fcen" id="3892">González, R.</div>; Costa, A.; <div class="autor_fcen" id="7823">Santini, E.S.</div>
Tipo de recurso
artículo
Estado
Versión publicada
Año de publicación
2010
País
Argentina
Institución
Repositorio
Descripción
In a previous paper [R. González, L. G. Sarasua, and A. Costa, "Kelvin waves with helical Beltrami flow structure," Phys. Fluids20, 024106 (2008)] we analyzed the formation of Kelvin waves with a Beltrami flow structure in an ideal fluid. Here, taking into account the results of this paper, the topological analogy between the role of the magnetic field in Woltjer's theorem [L. Woltjer, "A theorem on force-free magnetic fields," Proc. Natl. Acad. Sci. U.S.A.44, 489 (1958)] and the role of the vorticity in the equivalent theorem is revisited. Via this analogy we identify the force-free equilibrium of the magnetohydrodynamics with the Beltrami flow equilibrium of the hydrodynamic. The stability of the last one is studied applying Arnold's theorem. We analyze the role of the enstrophy in the determination of the equilibrium and its stability. We show examples where the Beltrami flow equilibrium is stable under perturbations of the Beltrami flow type with the same eigenvalue as the basic flow one. The enstrophy variation results invariant with respect to a uniform rotating and translational frame and the stability is conserved when the flow experiences a transition from a Beltrami axisymmetric flow to a helical one of the same eigenvalue. These results are discussed in comparison with that given by Moffatt in 1986 [H. K. Moffatt, "Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology. Part 2. Stability considerations," J. Fluid Mech.166, 359 (1986)]. © 2010 American Institute of Physics.
Idioma
inglés
OAI Identifier
3573542d-782b-44a2-b2fd-eb61bd043713/snrd:HASH01aab4792cce62be89a5185d
Enlace del recurso
http://digital.bl.fcen.uba.ar/Download/paper/paper_10706631_v22_n7_p1_Gonzalez.pdf
Nivel de acceso
Acceso abierto
Materia
Arnold's theorem
Axisymmetric flow
Basic flow
Beltrami
Beltrami flow
Complex topology
Eigen-value
Enstrophy
Euler flows
Flow experience
Force-free magnetic fields
Ideal fluids
Kelvin waves
Variational principles
Eigenvalues and eigenfunctions
Flow structure
Gravity waves
Magnetic fields
Magnetohydrodynamics
Topology
Variational techniques
Stability