Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-18T18:33:11.289Z Has data issue: false hasContentIssue false

The fundamental solution for small steady three-dimensional disturbances to a two-dimensional parallel shear flow

Published online by Cambridge University Press:  28 March 2006

M. J. Lighthill
Affiliation:
Department of Mathematics, University of Manchester

Abstract

In addition to the enormous aerodynamical literature concerned with the disturbances to a uniform stream produced by the presence of obstacles, there is a very extensive litrature on disturbances to irrotational non-uniform streams. The smaller body of work on disturbances to rotational streams is concerned principally with two-dimensional disturbances to a parallel shear flow; these are fairly easy to treat because the vortex lines are straight; they remain parallel and do not get stretched at all during the motion.

Type
Research Article
Copyright
© 1957 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Hall, I. M. 1956 J. Fluid Mech. 1, 142.
Hawthorne, W. R. 1951 Proc. Roy. Soc. A, 206, 374.
Hawthorne, W. R. 1954 J. Aero. Sci. 21, 588.
Hawthorne, W. R. & Martin, Moira E. 1955 Proc. Roy. Soc. A, 232, 184.
Kármán, Th. von & Tsien, H. S. 1945 Quart. Appl. Math. 3, 1.
Lighthill, M. J. 1953 Proc. Roy. Soc. A, 217, 478.
Lighthill, M. J. 1956 J. Fluid Mech. 1, 31, with corrigenda in the following reference.
Lighthill, M. J. 1957a J. Fluid Mech. 2, 311.
Lighthill, M. J. 1957b J. Fluid Mech. 2, 493.
Livesey, J. L. 1956 J. Aero. Sci. 23, 949.
Preston, J. H. 1954 Aero. Quart. 5, 218.
Squire, H. B. 1933 Proc. Roy. Soc. A, 142, 621.
Squire, H. B. & Winter, K. G. 1951 J. Aero. Sci. 18, 271.
Watson, G. N. 1944 Theory of Bessel Functions, 2nd Ed. Cambridge University Press.
Young, A. D. & Maas, J. N. 1936 Aero. Res. Counc., Lond., Rep. & Mem. no. 1770.