The complete second-order diffraction solution for an axisymmetric body Part 1. Monochromatic incident waves

The authors studied the diffraction, to second order, of plane monochromatic incident gravity waves by a vertically axisymmetric body. The second-order double-frequency diffraction potential is obtained explicitly. A sequence of one-dimensional integral equations along the generator of the body involving free-surface ring sources of general order are formulated and solved for the circumferential components of the second-order potential. The solution is expedited by analytic integrations in the entire local-wave-free outer field of a requisite free-surface integral. The method is validated by extensive convergence tests and comparisons to semi-analytic results for the second-order forces and moments on a uniform vertical circular cylinder. Complete second-order forces, moments, surface pressures and run-up on the vertical cylinder as well as a truncated vertical cone are presented. A summary is given of the most important findings.

[1]  Bernard Molin,et al.  Second-order diffraction loads upon three-dimensional bodies , 1979 .

[2]  S K Chakrabarti,et al.  COMMENTS ON SECOND-ORDER WAVE EFFECTS ON LARGE-DIAMETER VERTICAL CYLINDER , 1978 .

[3]  M. Rahman.  Wave diffraction by large offshore structures: an exact second-order theory , 1984 .

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

[5]  J. N. Newman.  Algorithms for the free-surface Green function , 1985 .

[6]  T. F. Ogilvie.  Second Order Hydrodynamic Effects on Ocean Platforms , 1983 .

[7]  Finn Gunnar Nielsen,et al.  Non-linear wave forces on a fixed vertical cylinder dueto the sum frequency of waves in irregular seas , 1986 .

[8]  R. E. Baddour,et al.  THE DIFFRACTION OF NONLINEAR PROGRESSIVE WAVES BY A VERTICAL CYLINDER , 1981 .

[9]  A. Hulme.  A ring-source/integral-equation method for the calculation of hydrodynamic forces exerted on floating bodies of revolution , 1983, Journal of Fluid Mechanics.

[10]  S. M. Hung,et al.  SECOND ORDER DIFFRACTION FORCES ON A VERTICAL CYLINDER IN REGULAR WAVES , 1987 .

[11]  J. N. Newman.  The Drift Force and Moment on Ships in Waves , 1967 .

[12]  A. B. Finkelstein.  The initial value problem for transient water waves , 1957 .

[13]  Chiang C. Mei,et al.  NUMERICAL METHODS IN WATER-WAVE DIFFRACTION AND RADIATION , 1978 .

[14]  F. John.  On the motion of floating bodies. I , 1949 .

[15]  Moo-Hyun Kim,et al.  THE NONLINEAR SUM-FREQUENCY WAVE EXCITATION AND RESPONSE OF A TENSION-LEG PLATFORM , 1988 .

[16]  John D. Fenton,et al.  Wave forces on vertical bodies of revolution , 1978, Journal of Fluid Mechanics.

[17]  Jared L. Black,et al.  Wave forces on vertical axisymmetric bodies , 1975, Journal of Fluid Mechanics.

[18]  Michael Isaacson,et al.  Nonlinear Wave Forces on Large Offshore Structures , 1977 .