Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-18T23:51:36.118Z Has data issue: false hasContentIssue false
  • English
  • Français

Long waves in a uniform channel of arbitrary cross-section

Published online by Cambridge University Press:  28 March 2006

D. H. Peregrine
D. H. Peregrine
Affiliation:
Department of Mathematics, University of Bristol
Get access Rights & Permissions [Opens in a new window]

Abstract

Equations of motion are derived for long gravity waves in a straight uniform channel. The cross-section of the channel may be of any shape provided that it does not have gently sloping banks and it is not very wide compared with its depth. The equations may be reduced to those for two-dimensional motion such as occurs in a rectangular channel. The order of approximation in these equations is sufficient to give the solitary wave as a solution.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 32 , Issue 2 , 3 May 1968 , pp. 353 - 365
Copyright
© 1968 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

Batchelor, G. K. 1956 J. Fluid Mech. 1, 177–90.
Burggraf, O. R. 1966 J. Fluid Mech. 24, 113–51.
Carslaw, H. S. & Jaeger, J. C. 1959 Conduction of Heat in Solids, 2nd ed. Oxford University Press.
Chao, B. T. 1962 Phys. Fluids, 5, 69–79.
Conkie, W. R. & Savic, P. 1953 Nat. Res. Coun. Can., Rept. no. MT-23.
Elzinga, E. R. & Banchero, J. T. 1961 A.I.Ch.E. J. 7, 394–9.
Garner, F. H. & Haycock, P. J. 1959 Proc. Roy. Soc A 252, 457–75.
Harper, J. F., Moore, D. W. & Pearson, J. R. A. 1967 J. Fluid Mech. 27, 361–6.
Harper, J. F. 1963 J. Fluid Mech. 17, 141–53.
Hill, M. J. M. 1894 Phil. Trans. Roy. Soc. 185, 213–45.
Hodgman, C. D. 1960 Handbook of Chemistry and Physics, 42nd ed. Chemical Rubber Publ. Co., Cleveland, Ohio.
Hu, S. & Kinter, R. C. 1955 A.I.Ch.E. J. 1, 42–8.
Keith, F. W. & Hixson, A. N. 1955 Ind. Engng Chem. 47, 258–67.
Klee, A. J. & Treybal, R. E. 1956 A.I.Ch.E. J. 2, 444–7.
Lamb, H. 1932 Hydrodyamics, 6th ed. Cambridge University Press.
Levich, V. G. 1949 Zhur. Exsp. I. Teoret. Fiz. 23, 71.
Licht, W. & Narasimhamurty, G. S. R. 1955 A.I.Ch.E. J. 1, 366–73.
Mills, R. D. 1965 J. Roy. Aeronaut. Soc. 69, 116–20.
Moore, D. W. 1959 J. Fluid Mech. 6, 113–30.
Moore, D. W. 1963 J. Fluid Mech. 16, 161–76.
Moore, D. W. 1965 J. Fluid Mech. 23, 747–66.
Watson, G. N. 1944 Theory of Bessel Functions, 2nd ed. Cambridge University Press.
Winnikow, S. & Chao, B. T. 1966 Phys. Fluids, 9, 50–61.