Artículo
Abstract:
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.
Registro:
| Documento: | Artículo |
| Título: | On a variational principle for Beltrami flows |
| Autor: | González, R.; Costa, A.; Santini, E.S. |
| Filiación: | Instituto de Desarrollo Humano, Universidad Nacional de General Sarmiento, Buenos Aires 1613, Argentina Departimento de Física, FCEyN, Universidad de Buenos Aires, Buenos Aires 1613, Argentina Instituto de Astronomía Teórica y Experimental, Córdoba and Facultad de Ciencias Exactas, Físicas y Naturales, Universidad Nacional de Córdoba, Córdoba 5000, Argentina Instituto de Ciencias, Universidad Nacional de General Sarmiento, Buenos Aires 1613, Argentina ICRA-BR, Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro 22290-180, Brazil |
| Palabras clave: | 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 |
| Año: | 2010 |
| Volumen: | 22 |
| Número: | 7 |
| Página de inicio: | 1 |
| Página de fin: | 7 |
| DOI: | http://dx.doi.org/10.1063/1.3460297 |
| Título revista: | Physics of Fluids |
| Título revista abreviado: | Phys. Fluids |
| ISSN: | 10706631 |
| CODEN: | PHFLE |
| PDF: | https://bibliotecadigital.exactas.uba.ar/download/paper/paper_10706631_v22_n7_p1_Gonzalez.pdf |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10706631_v22_n7_p1_Gonzalez |
Referencias:
- González, R., Sarasua, L.G., Costa, A., Kelvin waves with helical Beltrami flow structure (2008) Phys. Fluids, 20, p. 024106. , PFLDAS, 0031-9171, 10.1063/1.2840196
- Woltjer, L., A theorem on force-free magnetic fields (1958) Proc. Natl. Acad. Sci. U.S.A., 44, p. 489. , PNASA6, 0027-8424, 10.1073/pnas.44.6.489
- Moffatt, H.K., Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology. Part 2. Stability considerations (1986) J. Fluid Mech., 166, p. 359. , JFLSA7, 0022-1120, 10.1017/S0022112086000198
- Moffatt, H.K., Tsinober, A., Helicity in laminar and turbulent flow (1992) Annu. Rev. Fluid Mech., 24, p. 281. , ARVFA3, 0066-4189, 10.1146/annurev.fl.24.010192.001433
- Moffatt, H.K., The degree of knottedness of tangled vortex lines (1969) J. Fluid Mech., 35, p. 117. , JFLSA7, 0022-1120, 10.1017/S0022112069000991
- Arnold, V.I., A variational principle for three-dimensional stationary flows of the ideal fluid (1965) Appl. Math. Mech., 29, p. 846. , AMMEEQ, 0253-4827
- Arnold, V.I., Sur un principe variationnel pour les écoulements stationnaires des liquides parfaits et ses applications aux problemes de stabilite non-linéaires (1966) J. Mech., 5, p. 24. , JMECB8, 0022-2569
- Wu, J.-.Z., Ma, H.-.Y., Zhou, M.-.D., (2006) Vorticity and Vortex Dynamics, , 10.1007/978-3-540-29028-5, Springer, Berlin
- Strictly, the procedure requires the addition of the gradient of a potential function: δv=(η×ωE)+∇φ. As the disturbance proposed is conditioned by the potential, we can choose φ to be a disturbance of the Beltrami flow type given in Eq. Another option is t; To denote the eigenvalues of the perturbation and equilibrium Beltrami flows, we use γ and α, respectively; Dritschel, D.G., Generalized helical Beltrami flows in hydrodynamics and magnetohydrodynamics (1991) J. Fluid Mech., 222, p. 525. , JFLSA7, 0022-1120, 10.1017/S0022112091001209
- Sarasúa, L.G., Sicardi Schifino, A.C., Gonzalez, R., The stability of steady, helical vortex filaments in a tube (1999) Phys. Fluids, 11, p. 1096. , PFLDAS, 0031-9171, 10.1063/1.869980
- Sarasua, L.G., Sicardi-Schifino, A.C., Gonzalez, R., The development of helical vortex filaments in a tube (2005) Phys. Fluids, 17, p. 044104. , PFLDAS, 0031-9171, 10.1063/1.1871713
- Batchelor, G.K., (1967) An Introduction to Fluids Dynamics, , (Cambridge University Press, Cambridge
- Hasimoto, H., Elementary aspects of vortex motion (1988) Fluid Dyn. Res., 3, p. 1. , FDRSEH, 0169-5983, 10.1016/0169-5983(88)90038-X
- For a Beltrami flow ω=ιv, then Φ=12∫(ω)2dV=12∫(ιv)2dV=ι2K. So, Φ is proportional to K; Saffman, P.G., (1992) Vortex Dynamics, , (Cambridge University Press, Cambridge
- Chandrasekhar, S., (1961) Hydrodynamic and Hydromagnetic Stability, , (Clarendon, Oxford
- θcc introduced in Paper I (p. 5) is the value of the Rossby number for which the basic flow is marginally stable, i.e., for this transition case, m=0 to m=1, if θ<θcc the flow is unstable and if θ>θcc it is stable; Chandrasekhar, S., Kendall, P.C., On force-free magnetic field (1957) A. Phys. J., 126, p. 457
Citas:
---------- APA ----------
González, R., Costa, A. & Santini, E.S. (2010) . On a variational principle for Beltrami flows. Physics of Fluids, 22(7), 1-7.http://dx.doi.org/10.1063/1.3460297
---------- CHICAGO ----------
González, R., Costa, A., Santini, E.S. "On a variational principle for Beltrami flows" . Physics of Fluids 22, no. 7 (2010) : 1-7.http://dx.doi.org/10.1063/1.3460297
---------- MLA ----------
González, R., Costa, A., Santini, E.S. "On a variational principle for Beltrami flows" . Physics of Fluids, vol. 22, no. 7, 2010, pp. 1-7.http://dx.doi.org/10.1063/1.3460297
---------- VANCOUVER ----------
González, R., Costa, A., Santini, E.S. On a variational principle for Beltrami flows. Phys. Fluids. 2010;22(7):1-7.http://dx.doi.org/10.1063/1.3460297
