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Some developments in the theory of turbulence

Published online by Cambridge University Press:  20 April 2006

H. K. Moffatt
H. K. Moffatt
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge
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Abstract

This is in no way intended as a review of turbulence-the subject is far too big for adequate treatment within a reasonably finite number of pages; the monumental treatise of Monin & Yaglom (1971, 1975) bears witness to this statement. It is rather a discourse on those aspects of the problem of turbulence with which I have myself had contact over the last twenty years or so. My choice of topics therefore has a very personal bias - but that is perhaps consistent with the style and objectives of this rather unusual issue of JFM.

I have approached the dynamical problem of turbulence via two simpler (but nevertheless far from trivial) problems – viz the convection and diffusion of a passive scalar field and of a passive vector field by turbulence of known statistical properties. Particular emphasis is given to the method of successive averaging (a simplified version of the renormalization-group technique) which seems to me to have considerable potential. The difficulty of extending this method to the dynamical problem is discussed.

In a final section (§ 6) I have allowed myself the luxury of discussing a somewhat esoteric topic - the problem of inviscid invariants and their relationship with the topological structure of a complex vorticity field. The helicity invariant is the prototype; it is identifiable with the Hopf invariant (1931) and it may be obtained from appropriate manipulation of Noether's theorem (Moreau 1977). A suggestion is made concerning possible measurement of this fundamental measure of ‘lack of reflexional symmetry’ in a turbulent flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 106 , May 1981 , pp. 27 - 47
Copyright
© 1981 Cambridge University Press

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