Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-28T21:55:29.916Z Has data issue: false hasContentIssue false
  • English
  • Français

The excitation of damped waves diffracted over a submerged circular sill

Published online by Cambridge University Press:  12 April 2006

H. D. Pite
H. D. Pite
Affiliation:
School of Mathematical Sciences, New South Wales Institute of Technology, Broadway, New South Wales 2007, Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

A mathematical model of rectilinear surface waves incident on a submerged circular sill is developed. The class of waves considered consists of those for which the ratio of wavelength to water depth is large but which do not necessarily belong in the longwave category. A friction damping term is introduced into the equations of motion and the solutions obtained for the regions over the sill and in the ocean are matched by assuming a continuous surface and energy flux at the sill edge. The results show large reductions in the Q-factor of the resonance peaks brought about by friction damping. It is also found that, except at low frequency, a large number of overlapping resonance peaks which are out of phase with one another occupy a relatively narrow frequency band such that these resonance peaks effectively cancel one another. Experiments were performed to determine the friction constant used in the equations of motion and, using this friction constant, the theoretical results of wave resonance are verified.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 82 , Issue 4 , 14 October 1977 , pp. 621 - 641
Copyright
© 1977 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

Abramowitz, M. & Stegun, I. A. (eds.) 1964 Handbook of Mathematical Functions. Washington: Nat. Bur. Stand.Google Scholar
Bartholomeusz, E. C. 1958 The reflection of long-waves at a step. Proc. Camb. Phil. Soc. 54, 106–118.Google Scholar
Biesel, F. 1949 Calculation of wave damping in a viscous liquid of known depth. Houille Blanche 4, 630–634.Google Scholar
Hilaly, N. 1967 Diffraction of water waves over bottom discontinuities. Hydraul. Engng Lab., Univ. California, Berkeley Tech. Rep. HEL-1–7.Google Scholar
Hough, S. S. 1897 On the influence of viscosity on waves and currents. Proc. Lond. Math. Soc. 28, 264–288.Google Scholar
Ippen, A. T. (ed.) 1966 Estuary and Coastline Hydrodynamics, pp. 71–77. McGraw-Hill.Google Scholar
Ippen, A. T. & Harleman, D. R. F. 1960 Analytical study of salinity intrusion in estuaries and canals. Comm. Tidal Hydraul., Corps Engrs, Vicksburg, Mississippi.Google Scholar
Iwagaki, Y., Tsuchiya, Y. & Chen, H. 1967 On the mechanism of laminar damping of oscillatory surface waves due to bottom friction. Bull. Disaster Prevention Res. Inst. 16(3). 49–75.Google Scholar
Iwagaki, Y. & Kakinuma, T. 1967 On the bottom friction factors off five Japanese coasts. Coastal Eng. Japan 10, 13–22.Google Scholar
Lamb, H. 1932 Hydrodynamics, 6th edn, pp. 262–263. Cambridge University Press.Google Scholar
Le Mehaute, B. 1960 Periodic gravity waves at discontinuity. J. Hydraul. Div., Proc. A.S.C.E. 86, 11–41.Google Scholar
Li, H. 1954 Stability of oscillatory laminar flow along a wall. U.S.A. Beach Erosion Bd Tech. Memo. no. 47, pp. 1–48.Google Scholar
Longuet-Higgins, M. S. 1967 On the trapping of wave energy round islands. J. Fluid Mech. 29, 781–821.Google Scholar
Mules, J. W. 1967 Surface wave scattering matrix for a shelf. J. Fluid Mech. 28, 755–767.Google Scholar
Newman, J. N. 1965 Propagation of water waves over an infinite step. J. Fluid Mech. 23, 399–415.Google Scholar
Pite, H. D. 1973 Studies in frictionally damped waves. Water Res. Lab., Univ. New South Wales Rep. no. 138, pp. 46–56, A7–5, 102–104.Google Scholar
Smith, R. & Sprinks, T. 1975 Scattering of surface waves by a conical island. J. Fluid Mech. 72, 373–384.Google Scholar
Summerfield, W. C. 1969 On the trapping of wave energy by bottom topography. Horace Lamb Centre Ocean. Res., Flinders Univ. Res. Paper no. 30, pp. 3–12, 89.Google Scholar
Van Dorn, W. G. 1966 Boundary dissipation of oscillatory waves. J. Fluid Mech. 24, 769–779.Google Scholar
Weenink, M. P. H. 1958 Meded Verk. k. ned met. Inst. 73, 87–88.Google Scholar
Wong, K. K., Ippen, A. T. & Harleman, D. R. F. 1963 Interaction of tsunami with oceanic islands and submarine topographies. M.I.T. Hydrodyn. Lab. Tech. Rep. no. 62, pp. 52–55.Google Scholar