Helicity

H. Keith Moffatt

doi:10.1016/j.crme.2017.12.002

The legacy of Jean-Jacques Moreau in mechanics

Helicity

H. Keith Moffatt ¹

¹ Department of Applied Mathematics and Theoretical Physics, Wilberforce Road, Cambridge, CB3 0WA, UK

Comptes Rendus. Mécanique, Volume 346 (2018) no. 3, pp. 165-169.

Abstract

This short review is a contribution to an issue of Comptes Rendus Mécanique commemorating the scientific work of Jean-Jacques Moreau (1923–2014). His main contribution to fluid mechanics appeared in a brief paper in the Comptes Rendus à l'Académie des Sciences in 1961, but was not recognised till much later. It may now be seen as a significant milestone in advancing the theory of ideal fluid flow as described by Euler's equations.

Received: 2017-05-20
Accepted: 2017-10-11
Published online: 2017-12-07

DOI: 10.1016/j.crme.2017.12.002

Keywords: Knotted vortices, Magnetic relaxation, Dynamo

Author's affiliations:

H. Keith Moffatt ¹

¹ Department of Applied Mathematics and Theoretical Physics, Wilberforce Road, Cambridge, CB3 0WA, UK

@article{CRMECA_2018__346_3_165_0,
     author = {H. Keith Moffatt},
     title = {Helicity},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {165--169},
     publisher = {Elsevier},
     volume = {346},
     number = {3},
     year = {2018},
     doi = {10.1016/j.crme.2017.12.002},
     language = {en},
}

TY  - JOUR
AU  - H. Keith Moffatt
TI  - Helicity
JO  - Comptes Rendus. Mécanique
PY  - 2018
SP  - 165
EP  - 169
VL  - 346
IS  - 3
PB  - Elsevier
DO  - 10.1016/j.crme.2017.12.002
LA  - en
ID  - CRMECA_2018__346_3_165_0
ER  -

%0 Journal Article
%A H. Keith Moffatt
%T Helicity
%J Comptes Rendus. Mécanique
%D 2018
%P 165-169
%V 346
%N 3
%I Elsevier
%R 10.1016/j.crme.2017.12.002
%G en
%F CRMECA_2018__346_3_165_0

H. Keith Moffatt. Helicity. Comptes Rendus. Mécanique, Volume 346 (2018) no. 3, pp. 165-169. doi : 10.1016/j.crme.2017.12.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2017.12.002/

References
Cited by

[1] V.I. Arnold Variational principle for three-dimensional steady-state flows of an ideal fluid, J. Appl. Math. Mech., Volume 29 (1965) no. 5, pp. 1002-1008

[2] V.I. Arnold The asymptotic Hopf invariant and its applications, Dilizhan, Erevan, Armenia, Volume 5 (1974), pp. 229-256 (in Russian). English translation: Sel. Math. Sov., 1986, pp. 327-345

[3] M.A. Berger; G.B. Field The topological properties of magnetic helicity, J. Fluid Mech., Volume 147 (1984), pp. 133-148

[4] S. Childress; A.D. Gilbert Stretch, Twist, Fold: The Fast Dynamo, Lecture Notes in Physics, Springer, 1995

[5] A. Enciso; D. Peralta-Salas Existence of knotted vortex tubes in steady Euler flows, Acta Math., Volume 214 (2015) no. 1, pp. 61-134

[6] A. Flammini; A. Maritan; A. Stasiak Simulations of action of DNA topoisomerases to investigate boundaries and shapes of spaces of knots, Biophys. J., Volume 87 (2004) no. 5, pp. 2968-2975

[7] M.H. Freedman A note on topology and magnetic energy in incompressible and perfectly conducting fluids, J. Fluid Mech., Volume 194 (1988), pp. 549-551

[8] A.D. Gilbert Fast dynamo action in the Ponomarenko dynamo, Geophys. Astrophys. Fluid Dyn., Volume 44 (1988) no. 1–4, pp. 241-258

[9] H.v. Helmholtz Über Integrale der hydrodynamischen Gleichungen, welche der Wirbelbewegung entsprechen, J. Reine Angew. Math., Volume 55 (1858), pp. 25-55

[10] D. Kleckner; W.T.M. Irvine Creation and dynamics of knotted vortices, Nat. Phys., Volume 9 (2013) no. 4, pp. 253-258

[11] D.D. Mendeleev On the relationship of the properties of the elements to their atomic weights, Z. Chem., Volume 12 (1869), pp. 405-406

[12] H.K. Moffatt The degree of knottedness of tangled vortex lines, J. Fluid Mech., Volume 35 (1969) no. 1, pp. 117-129

[13] H.K. Moffatt Magnetic Field Generation in Electrically Conducting Fluids, Cambridge Monographs on Mechanics and Applied Mathematics, Cambridge University Press, 1978 (353 pp)

[14] H.K. Moffatt Some developments in the theory of turbulence, J. Fluid Mech., Volume 106 ( May 1981 ), pp. 27-47

[15] H.K. Moffatt Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology. 1. Fundamentals, J. Fluid Mech., Volume 159 (1985), pp. 359-378

[16] H.K. Moffatt Magnetostrophic turbulence and the geodynamo, Nagoya University, Nagoya, Japan, 11–14 September 2006 (Y. Kaneda, ed.), Springer (2008), pp. 339-346

[17] H.K. Moffatt; M.R.E. Proctor Topological constraints associated with fast dynamo action, J. Fluid Mech., Volume 154 (1985), pp. 493-507

[18] H.K. Moffatt; R.L. Ricca Helicity and the Călugăreanu invariant, Proc. R. Soc. A, Volume 439 (1992), pp. 411-429

[19] R. Monchaux; M. Berhanu; S. Aumaître et al. The von Kármán sodium experiment: turbulent dynamical dynamos, Phys. Fluids, Volume 21 (2009)

[20] J.-J. Moreau Constantes d'un îlot tourbillonnaire en fluid parfait barotrope, C. R. hebd. séances Acad. sci. Paris, Volume 252 (1961), pp. 2810-2812

[21] Yu.B. Ponomarenko Theory of the hydromagnetic generator, J. Appl. Mech. Tech. Phys., Volume 14 (1973) no. 6, pp. 775-778

[22] P. Rouchon On the Arnol'd stability criterion for steady-state flows of an ideal fluid, Eur. J. Mech. B, Fluids, Volume 10 (1991) no. 6, pp. 651-661

[23] A. Stasiak; V. Katritch; L.H. Kauffman Ideal Knots, vol. 19, World Scientific, 1998

[24] P.G. Tait LXIII. On integrals of the hydrodynamical equations, which express vortex-motion, Philos. Mag., Volume 33 (1867) no. 226, pp. 485-512 translation of Helmholtz (1858)

[25] P.G. Tait, On knots, I, II, III, Scientific Papers, 1898, p. 1.

[26] W. Thomson On vortex motion, Trans. R. Soc. Edinb., Volume 25 (1869), pp. 217-260

[27] S.I. Vainshtein; Ya.B. Zel'dovich Origin of magnetic fields in astrophysics, Sov. Phys. Usp., Volume 15 (1972), pp. 159-172

[28] L. Woltjer A theorem on force-free magnetic fields, Proc. Natl. Acad. Sci. USA, Volume 44 (1958), pp. 489-491

Cited by Sources:

Comments - Policy