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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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References

1. Reynolds, O. Papers on Mechanical and Physical Subjects, Vol. 1, 1900, Vol. II, 1901, Vol. III, 1903. Cambridge University Press. See also: McDowell, D. M. & Jackson, J. D. (eds) Osborne Reynolds and Engineering Science Today, 1970. Manchester University Press.Google Scholar
2. Lamb, H. Hydrodynamics(6th Ed.), 1932. Cambridge University Press.Google Scholar
3. Goldstein, S. Mathieu functions. Trans Camb Phil Soc, 1927, 23, 303-336 (1927). See also six of his other papers: in Proc Camb Phil Soc, 1928, 24, 223-230, in Mon Not R Astron Soc (Geophys Suppl), 1928–29, 2, 44–56 and 213–231, in Proc Lond Math Soc, 1928, 28, (2), 81–90 and 91–101 and in Proc R Soc Edin A, 1929, 49, 210–223.Google Scholar
4. Goldstein, S. On the vortex theory of screw propellers. Proc R Soc A, 1929, 123, 440–465.Google Scholar
5. Goldstein, S. (ed) Modern Developments in Fluid Dynamics (2 vols), 1938. Oxford University Press.Google Scholar
6. Goldstein, S. On the stability of superposed streams of different densities. Proc R Soc A, 1931, 132, 524–548. For ydrodynamic stability, see also two of his other papers in Proc Camb Phil Soc, 1936, 32, 40–54 and 1937, 33, 41–61. Goldstein, S. A note on the measurement of total head and static pressure in a turbulent stream. Proc R Soc A, 1936, 155, 570–575. For turbulence, see also four of his other papers: in Proc Camb Phil Soc, 1935, 31, 232–241 and 351–359 and 1938, 34, 48–67 and 351–353.Google Scholar
7. Goldstein, S. On laminar boundary layer flow near a position of separation. Q J Mech Appl Math, 1948, 1, 43–69. See also: Brown S. N. and Stewartson, K. Laminar separation. Ann Rev Fluid Mech, 1969, 1, 45–72.Google Scholar
8. Goldstein, S. Low drag and suction aerofoils (Eleventh Wright Brothers Lecture). J Aero Sci, 1948, 15, 189–220.Google Scholar
9. Goldstein, S. and Ward, G. N. The linearised theory of conical fields in supersonic flow, with application to plane aerofoils. Aero Q, 1950, 2, 39–84. See also papers in Q J Mech Appl Math, 1948, 1, 216–219 and 344–357 and 1949, 2, 297–302.Google Scholar
10. Goldstein, S. On the law of decay of homogeneous isotropic turbulence and the theories of the equilibrium and similarity spectra. Proc Camb Phil Soc, 1950, 47, 554–574.Google Scholar
11. Pennycuick, C. J. Thermal soaring compared in three dissimilar tropical bird species, Fregata magnificens, Pelecanus occidentalis and Coragyps atratus . J Exper Biol, 1983, 102 , 307–325. For observations of soaring, see also (for example) his papers in J Exper Biol, 1971, 55, 39–46 and in Ibis, 1972,114,178–218 and (with Alerstam, T. and Larsson, B.) in Ornis Scandinavica 1979, 10, 241–251.Google Scholar
12. Pennycuick, C. J. A wind-tunnel study of gliding flight in the pigeon, Columba livia . J Exper Biol, 1968, 49, 509-26.Google Scholar
13. Rayner, J. M. V. Vertebrate flapping flight mechanics and aerodynamics and the evolution of flight in bats. Biona Rep, 1986, 5, 27–74. See also: Norberg, U. M. Vertebrate flight. 1989. Berlin. Springer.Google Scholar
14. Rayner, J. M. V. A vortex theory of animal flight. Parts 1 and 2. J Fluid Mech, 1979, 91, 697–763.Google Scholar
15. Kokshaysky, N. V. Tracing the wake of a flying bird. Nature, 1979, 279, 146–148.Google Scholar
16. Spedding, G. R., Rayner, J. M. V. and Pennycuick, C. J. Momentum and energy in the wake of a pigeon (Columba livia) in slow flight. J Exper Biol, 1984, 111, 81–102.Google Scholar
17. Spedding, G. R. The wake of a jackdaw (Corvus monedula) in slow flight. J Exper Biol, 1986, 125, 287–307.Google Scholar
18. Spedding, G. R. The wake of a kestrel (Falco tinnunculus) in flapping light. J Exper Biol, 1987, 127, 59–78.Google Scholar
19. Pennycuick, C. J. Bird Flight Performance, 1989. Oxford University Press.Google Scholar
20. Lighthill, J. Aerodynamics Aspects of Animal Flight, In: Wu, T. Y., Brokaw, C. J. and Brennen, C. (eds). Swimming and Flying in Nature, 1975, 423–491. New York: Plenum Press.Google Scholar
21. Marshall, N. B. The Life of Fishes. 1964. Weidenfeld and Nicholson.Google Scholar
22. Moulton, J. M. Swimming sounds and the schooling of fishes. Biol Bull, 1960, 119, 210–223.Google Scholar
23. Blaxter, J. H. S., Denton, E. J. and Gray, J. A. B. Acousticolateralis System in Clupeid Fishes. In: Tavolga, W. N., Popper, A. N. and Fay, R. R. (eds). Hearing and Sound Communication in Fishes, 1981. Springer-Verlag.Google Scholar
24. Denton, E. J. and SirGray, John. Mechanical factors in the excitation of clupeid lateral lines. Proc R Soc B, 1983, 218, 1–26.Google Scholar
25. Blaxter, J. H. S., Gray, J. A. B. and Denton, E. J. Sound and startle responses in herring shoals. J Mar Biol Ass UK, 1981, 61, 851–869.Google Scholar
26. Lighthill, James. An Informal Introduction to Theoretical Fluid Mechanics. 1986. Oxford University Press. See especially 133–136 and 210–215.Google Scholar