Hostname: page-component-5c6d5d7d68-thh2z Total loading time: 0 Render date: 2024-08-16T07:11:30.409Z Has data issue: false hasContentIssue false
  • English
  • Français

Rectangular resonators on infinite and semi-infinite channels

Published online by Cambridge University Press:  29 March 2006

V. T. Buchwald  and
N. V. Williams
V. T. Buchwald
Affiliation:
School of Mathematics, University of New South Wales, Kensington
N. V. Williams
Affiliation:
School of Mathematics, University of New South Wales, Kensington
Get access Rights & Permissions [Opens in a new window]

Abstract

The surface elevations in a strip 0 < y < b and in a rectangle -d < y < 0, |x| < a are expressed as a Fourier integral and Fourier series respectively. Using a Galerkin technique to match boundary conditions, the solution to the general problem of the response of a rectangular resonator to inviscid shallow-water waves in infinite and semi-infinite channels is obtained.

Theoretical results are compared with laboratory experiments of James (1970, 1971a, b). Agreement is generally very good, except that the inviscid and linear theory does not predict the observed large energy losses in the resonator at resonance.

The theory is also applied to a geometry corresponding to the Gulf of Carpentaria, and the calculated response of the Gulf to semi-diurnal tides gives a zero response at Kuramba, in agreement with observations. The full response of the Gulf is calculated in subsequent work (Williams 1974) which takes the effects of the earth's rotation into account.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 67 , Issue 3 , 11 February 1975 , pp. 497 - 511
Copyright
© 1975 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

Bartholomeuzs, E. F. 1958 Reflexion of long waves at a step. Proc. Camb. Phil. Soc., 54, 106–118.Google Scholar
James, W. 1970 Resonators on narrow channels. J. Fluid Mech., 44, 615–621.Google Scholar
James, W. 1971a Response of rectangular resonators. Proc. Inc., & Civil Engrs, 48, 51–63.Google Scholar
James, W. 1971b Harbour resonators. Proc. A.X.C.E. 97 (WW1), 115–122.Google Scholar
Miles, J. W. 1947 Right angled joint in rectangular tube. J. Acoust. Soc. Am., 19, 572–579.Google Scholar
Miles, J. W. & Gilbert, F. 1968 The scattering of gravity waves. J. Fluid Mech., 34, 783–793.Google Scholar
Miles, J. W. & Munk, H. W. 1961 Harbour paradox. Proc. A.S.C.E. 87 (WW3), 111–130.Google Scholar
Valembois, J. 1953 Proc. Minnesota Int. Hydr. Conf., pp. 193–200.
Williams, N. V. 1973 The application of the resonator to problems in oceanography. Ph.D. dissertation, University of New South Wales.
Williams, N. V. 1974 The gulfs of Carpentaria and Thailand. (In preparation)