Short surface waves in the presence of a finite dock. II

The generalized wave-making problem for the forced high-frequency oscillations of a finite dock is solved through use of the Green's function obtained in the first part of this paper. The specific cases of heave and roll are considered with particular reference to the forces on the dock and the amplitude and phase of the radiated waves. These results are then utilized to solve the problem of transmission of short waves under a fixed dock.

[1]  C. Wagner.  On the Solution of Fredholm Integral Equations of Second Kind by Iteration , 1951 .

[2]  F. Ursell,et al.  Short surface waves due to an oscillating immersed body , 1953, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[3]  F. Ursell,et al.  ON THE WAVES DUE TO THE ROLLING OF A SHIP , 1948 .

[4]  R. MacCamy.  On the heaving motion of cylinders of shallow draft , 1961 .

[5]  F. Ursell.  The transmission of surface waves under surface obstacles , 1961, Mathematical Proceedings of the Cambridge Philosophical Society.

[6]  W. R. Dean,et al.  The effect of a fixed vertical barrier on surface waves in deep water , 1947, Mathematical Proceedings of the Cambridge Philosophical Society.

[7]  F. Ursell,et al.  On the short-wave asymptotic theory of the wave equation (∇2 + k2)ø = 0 , 1957, Mathematical Proceedings of the Cambridge Philosophical Society.

[8]  H. Rubin.  The dock of finite extent , 1954 .

[9]  R. MacCamy.  On Babinet's Principle , 1958, Canadian Journal of Mathematics.

[10]  F. Ursell,et al.  WATER WAVES GENERATED BY OSCILLATING BODIES , 1954 .

[11]  S. Mikhlin.  CHAPTER III – SINGULAR INTEGRAL EQUATIONS , 1957 .

[12]  Fritz John,et al.  On the motion of floating bodies II. Simple harmonic motions , 1950 .