1970s

16. Moffatt, H.K. 1970  Turbulent dynamo action at low magnetic Reynolds number. J. Fluid Mech41, 435-452.

Helicity turned out to have immediate application for the turbulent dynamo.  The associated lack of mirror symmetry is also responsible for what Steenbeck et al. (1966) called the α-effect, whereby the mean electromotive force  generated by turbulence has a component parallel to the mean (large-scale) magnetic field.  This was a crucial breakthrough, which was to provide the starting point for nearly all subsequent theoretical and numerical investigations of planetary and astrophysical dynamos. 

 

My contribution here was to provide a proof of this dynamo effect when the magnetic Reynolds number R    based on the turbulent scale is small, provided the extent of the fluid region is sufficiently large.  This was very surprising at the time,  because it ran so counter to previous dynamo investigations. 

 

I came at this problem through my research student Glyn Roberts (PhD 1970), who wrote a brilliant PhD thesis on the theory of space-periodic dynamos.  I felt sure that this work could be adapted to the turbulent situation, and urged Glyn in this direction, but he chose to stay with the periodic case.  Glyn had met Fritz Krause at a meeting in Madrid (1969), and informed me of the work of the Potsdam group, which only achieved wide recognition in the West after translation into English by Paul Roberts and Michael Stix (1971).

m

Screen Shot 2013-08-17 at 07.18.00.png

Roberts, G.O. 1970 Spatially periodic dynamos. Phil. Trans. Roy. Soc. A266, 535-558 (also A271, 411-454).

Steenbeck, M., Krause, F. & Rädler, K.-H. 1966  Berechnung  der mittleren Lorentz-Felstärke für ein elektrisch leitendes Medium in turbulenter, durch Coriolis-Kräfte beeinfluβter Bewegung. Z.Naturforsch. 21a, 369-376. [English translation: Roberts, P.H. & Stix, M. 1971 Tech. Note 60, NCAR, Boulder, Colorado, USA.]

19. Moffatt, H.K. 1972 An approach to a dynamic theory of dynamo action in a rotating conducting fluid. J. Fluid Mech53, 385-399.

I believe this was the first paper to attempt a dynamically consistent dynamo theory, in which a ‘quenching effect’, which limits the dynamo growth of a magnetic field, was clearly identified. 

 

I presented a review of this work at the biennial Polish Fluid Mechanics Symposium 1973, held that year at a Conference centre in the wonderful forest of Białowieża in the far East of Poland. At this memorable meeting, I met two great Russian scientists, Ya. B. Zel'dovich and Olga Ladyzhenskaya. I gathered later that, on his return to Moscow, Zel’dovich communicated my result on the invariance of helicity to V.I.Arnol'd, who immediately developed the topic in characteristically rigorous manner (Arnol’d 1974).  I met Arnol’d much later in Moscow in 1982; he gave me a copy of his 1974 paper with the comment  that no-one in the West had read it (true beyond doubt)!  It was subsequently republished in English translation (Arnol’d 1986), and has since attracted the attention it always deserved. 

Arnol’d, V.I. (1974) The asymptotic Hopf invariant and its applications [in Russian]. Proc. Summer School in Differential Equations, Erevan, Armenian SSR Acad. Sci. [English translation: Sel.Math.Sov. 5 (1986), 327-345.]

26. Moffatt, H.K. 1977 Behaviour of a viscous film on the outer surface of a rotating cylinder. J. de Mécanique 16, 651-673.

If you dip a knife in a pot of syrup or any other very viscous fluid and pull it out, then you will instinctively hold the knife horizontally and rotate it to prevent the syrup falling off.  The question arises; what is the maximum load of syrup that can be supported by this simple technique?  I was stimulated to investigate this problem by a lecture at ICTP Trieste by V.V. Pukhnachov of the Lavrentyev Institute of Hydrodynamics, Novosibirsk.  Of course, it was natural to treat an idealised cylinder rather than a real knife -- Health and Safety might otherwise have intervened!  I found an expression for the critical load that can be supported, and explained the appearance of the characteristic lobes that appear in the experiment, which reveals a beautiful ‘syrup ring’ instability.   Application to industrial coating and rimming flow processes are multifarious.

Screen Shot 2013-08-17 at 10.02.00.png

Pukhnachov, V.V. 1977 Motion of a liquid film on the surface of a rotating cylinder in a gravitational field. Z.Prikl. Mekh. Tekh. Fiz. 3, 78-88.

For some subsequent developments, see also

Pukhnachov, V.V. 2005 Capillary/gravity film flows on the surface of a rotating cylinder. J.Math.Sci. 130, 4871-4891.

Hinch, E.J. & Kelmanson, M.A. 2003 On the decay and drift of free-surface perturbations in viscous thin-film flow exterior to a rotating cylinder. Proc.Roy.Soc. A 459, 1193-1213.

Kelmanson, M.A. 2009 On inertial effects in the Moffatt-Pukhnachov coating flow problem. J.Fluid Mech. 633, 327-353.

28. Moffatt, H.K. 1978 Magnetic field generation in electrically conducting fluids.(343 plus x pp) (Russian translation 1980, paperback edition 1983).

I wrote this monograph during a sabbatical year at the Université Pierre et Marie Curie, Paris, 1975/6.  It was the first book devoted to Dynamo Theory, although it was swiftly followed by others.  The time was ripe for such a book, because the basic principles governing the turbulent dynamo were by then well established, and subsequent work during the 1980s was to become heavily computational in nature.  Experimental confirmation of turbulent dynamo action had to wait a further 30 years (Monchaux et al 2007).  I believe that my book helped to stimulate much of the research activity in the field during these years.  The Russian translation was by Alexander Ruzmaikin, pupil and colleague of Ya. B. Zel'dovich.  An extended and updated version has been published  (Moffatt & Dormy 2019)

Monchaux, R., et al. . 2009. The von Kármán sodium experiment: turbulent dynamical dynamos. Phys. Fluids, 21, 035108.

Moffatt, H.K. & Dormy, E. 2019 Self-Exciting Fluid Dynamos. Cambridge texts in Applied Mathematics, CUP 520+xviii pp.