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.
@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}, }
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/
[1] 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] 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] The topological properties of magnetic helicity, J. Fluid Mech., Volume 147 (1984), pp. 133-148
[4] Stretch, Twist, Fold: The Fast Dynamo, Lecture Notes in Physics, Springer, 1995
[5] Existence of knotted vortex tubes in steady Euler flows, Acta Math., Volume 214 (2015) no. 1, pp. 61-134
[6] 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] A note on topology and magnetic energy in incompressible and perfectly conducting fluids, J. Fluid Mech., Volume 194 (1988), pp. 549-551
[8] Fast dynamo action in the Ponomarenko dynamo, Geophys. Astrophys. Fluid Dyn., Volume 44 (1988) no. 1–4, pp. 241-258
[9] Über Integrale der hydrodynamischen Gleichungen, welche der Wirbelbewegung entsprechen, J. Reine Angew. Math., Volume 55 (1858), pp. 25-55
[10] Creation and dynamics of knotted vortices, Nat. Phys., Volume 9 (2013) no. 4, pp. 253-258
[11] On the relationship of the properties of the elements to their atomic weights, Z. Chem., Volume 12 (1869), pp. 405-406
[12] The degree of knottedness of tangled vortex lines, J. Fluid Mech., Volume 35 (1969) no. 1, pp. 117-129
[13] Magnetic Field Generation in Electrically Conducting Fluids, Cambridge Monographs on Mechanics and Applied Mathematics, Cambridge University Press, 1978 (353 pp)
[14] Some developments in the theory of turbulence, J. Fluid Mech., Volume 106 ( May 1981 ), pp. 27-47
[15] Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology. 1. Fundamentals, J. Fluid Mech., Volume 159 (1985), pp. 359-378
[16] Magnetostrophic turbulence and the geodynamo, Nagoya University, Nagoya, Japan, 11–14 September 2006 (Y. Kaneda, ed.), Springer (2008), pp. 339-346
[17] Topological constraints associated with fast dynamo action, J. Fluid Mech., Volume 154 (1985), pp. 493-507
[18] Helicity and the Călugăreanu invariant, Proc. R. Soc. A, Volume 439 (1992), pp. 411-429
[19] et al. The von Kármán sodium experiment: turbulent dynamical dynamos, Phys. Fluids, Volume 21 (2009)
[20] Constantes d'un îlot tourbillonnaire en fluid parfait barotrope, C. R. hebd. séances Acad. sci. Paris, Volume 252 (1961), pp. 2810-2812
[21] Theory of the hydromagnetic generator, J. Appl. Mech. Tech. Phys., Volume 14 (1973) no. 6, pp. 775-778
[22] 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] Ideal Knots, vol. 19, World Scientific, 1998
[24] 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] On vortex motion, Trans. R. Soc. Edinb., Volume 25 (1869), pp. 217-260
[27] Origin of magnetic fields in astrophysics, Sov. Phys. Usp., Volume 15 (1972), pp. 159-172
[28] A theorem on force-free magnetic fields, Proc. Natl. Acad. Sci. USA, Volume 44 (1958), pp. 489-491
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