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The Inaugural Goldstein Memorial Lecture — Some challenging new applications for basic mathematical methods in the mechanics of fluids that were originally pursued with aeronautical aims

Published online by Cambridge University Press:  04 July 2016

James Lighthill
James Lighthill*
Affiliation:
Department of Mathematics, University College, London
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Abstract

The lecture recalls great Manchester traditions in the mechanics of fluids and in related areas of mathematics which were brilliantly renewed from 1945 onwards through Sydney Goldstein’s work as Beyer Professor of Applied Mathematics. Goldstein brought to this important task not only his own personal distinction in those fields but also his great experience in leading interacting groups working in experimental and theoretical fluid dynamics with largely aeronautical objectives. The University has continued strongly to maintain these traditions.

The lecture celebrates also two fine pieces of research where gifted biologists have successfully used certain key mathematical ideas and methods in the mechanics of fluids to solve problems of importance in the field of animal locomotion. The first example is the work of C. J. Pennycuick, J. M. V. Rayner and G. R. Spedding in determining the character of the vortex wake behind a steadily moving bird in horizontal flapping flight. Typically, this takes the form of a “concertina wake” of fluctuating width but approximately constant circulation, exerting forces which are greater in the downstroke (which sheds a wide wake) and less in the upstroke (which sheds a narrower wake). Some notable advantages of the concertina wake are indicated.

Finally, work by Sir Eric Denton, Sir John Gray and Dr J. H. S. Blaxter on schooling behaviour in herrings and other clupeoid fishes is described. These fishes’ mechanisms for advantageously maintaining well coordinated motion of the school as a whole depend not only on eye vision but also on certain specialised organs admirably fitted to the sensing of hydrodynamic pressure fields (associated with the motions of other fishes) and of their lateral and longitudinal gradients.

Type
Research Article
Information
The Aeronautical Journal , Volume 94 , Issue 932 , February 1990 , pp. 41 - 52
Copyright
Copyright © Royal Aeronautical Society 1990 

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