Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-28T13:55:26.805Z Has data issue: false hasContentIssue false
  • English
  • Français

A theory of the propagation of bores in channels and rivers

Published online by Cambridge University Press:  24 October 2008

M. R. Abbott  and
M. J. Lighthill
M. R. Abbott
Affiliation:
National Gas Turbine EstablishmentFarnboroughHampshire
Get access Rights & Permissions [Opens in a new window]

Abstract

A theory is presented of the non-linear propagation of waves and bores in channels of varying cross-section with a basic steady flow governed by frictional resistance; this corresponds to the flow in tidal rivers. The theory provides a condition on the tidal range required to produce a bore, in terms of the geometry and friction parameters of the river, and the propagation of such a bore is then described. The theory is applied to the River Severn and the results agree satisfactorily with observation. The results for the special case of waves moving into still water in a channel of varying section are also noted in detail.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 52 , Issue 2 , April 1956 , pp. 344 - 362
Copyright
Copyright © Cambridge Philosophical Society 1956

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

REFERENCES

(1)Cornish, V.Waves of the sea and other water waves (London, 1910), pp. 230–62.CrossRefGoogle Scholar
(2)Gibson, A. H.Hydraulics and its applications (London, 1930), pp. 285–95.Google Scholar
(3)Gibson, A. H.Construction and operation of a tidal model of the Severn estuary (H.M.S.O., London, 1933), pp. 65–82 and 150, 151.Google Scholar
(4)Green, G.On the motion of waves in a variable canal of small depth and width. Trans. Camb. Phil. Soc. 6 (1837), 457–62.Google Scholar
(5)Lamb, H.Hydrodynamics (Cambridge, 1916), pp. 265, 266 and 272.Google Scholar
(6)Prandtl, L.The essentials of fluid dynamics (London, 1952), pp. 161–2.Google Scholar
(7)Whitham, G. B.The flow pattern of a supersonic projectile. Commun. pure appl. Math. 5 (1952), 301–48.CrossRefGoogle Scholar
(8)Whitham, G. B.The propagation of weak spherical shocks in stars. Commun. pure appl. Math. 6 (1953), 397–414.CrossRefGoogle Scholar