Skip to main content Accessibility help

Interaction of water waves with two closely spaced vertical obstacles

  • J. N. Newman (a1)


Two-dimensional waves are incident upon a pair of vertical flat plates intersecting the free surface in a fluid of infinite depth. An asymptotic theory is developed for the resulting wave reflexion and transmission, assuming that the separation between the plates is small. The fluid motion between the plates is a uniform vertical oscillation, matched to the outer wave field by a local flow at the opening beneath the plates. It is shown that the reflexion and transmission coefficients undergo rapid changes, ranging from complete reflexion to complete transmission, in the vicinity of a critical wavenumber where the fluid column between the obstacles is resonant.



Hide All
Evans, D. V. & Morris, C. A. N. 1972 Complementary approximations to the solution of a problem in water waves J. Inst. Math. Applics. 10, 19.
Isaacs, J. D. & Wiegel, R. L. 1949 The measurement of wave heights by means of a float in an open-end pipe Trans. Am. Geophy. Un. 30, 531506.
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.
Levine, H. & Rodemich, E. 1958 Scattering of surface waves on an ideal fluid. Appl. Math. & Stats Lab., Stanford University, Tech. Rep. no. 78.
Levine, H. & Schwinger, J. 1948 On the radiation of sound from an unflanged circular pipe Phys. Rev. 73, 383406.
Newman, J. N. 1963 The motions of a spar buoy in regular waves. David Taylor Model Basin, Washington, Rep. no. 1499.
Tuck, E. O. 1971 Transmission of water waves through small apertures J. Fluid Mech. 49, 6574.
Ursell, F. 1947 The effect of a fixed vertical barrier on surface waves in deep water Proc. Camb. Phil. Soc. 43, 347382.
Wang, S. & Wahab, R. 1971 Heaving oscillations of twin cylinders in a free surface J. Ship Res. 15, 3348.
Wehausen, J. V. & Laitone, E. V. 1960 Surface waves. In Handbuch der Physik IX. Fluid Dynamics, III, pp. 446778. Springer.
MathJax is a JavaScript display engine for mathematics. For more information see


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed