# Diffraction of non-linear surface waves by a circular cylinder

TL;DR: In this paper, a nonlinear diffraction theory of periodic gravity waves due to their interaction with a circular cylinder which extends from the ocean bottom through the free surface is presented, where the velocity potential, free surface elevation and the frequency parameter are expanded as series in powers of a parameter which is the ratio of the amplitude to wave length.

Abstract: A non-linear diffraction theory of periodic gravity waves due to their interaction with a circular cylinder which extends from the ocean bottom through the free surface is presented. In order to obtain the solution, the velocity potential, the free surface elevation and the frequency parameter are expanded as series in powers of a parameter which is the ratio of the amplitude to wave length. Knowing the velocity potential of the incident wave, the velocity potential of the scattered wave for the corresponding order is obtained satisfying the proper boundary conditions and the radiation condition. The total potential governing the motion is thus obtained as a sum of incident and scattered potential for computing the pressures and forces on the cylinder.

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TL;DR: In this article, the authors applied diffraction to Stokes' fifth order gravity wave theory to obtain an expression for the velocity potential in the cylindrical polar coordinate system, based on which the dynamic pressure at the surface of a vertical cylinder and the total horizontal force on the cylinder in the direction of the wave propagation were determined.

Abstract: The method of diffraction is applied to Stokes' fifth order gravity wave theory to obtain an expression for the velocity potential in the cylindrical polar coordinate system. Based on this expression, the dynamic pressure at the surface of a vertical cylinder and the total horizontal force on the cylinder in the direction of the wave propagation are determined. The wave force is written in an equivalent form of the inertial part of Morison's equation and the effective inertial coefficients are shown to be functions of a single dimensionless quantity. The different parameters involved are plotted or tabulated so that forces on a vertical cylinder due to a nonlinear wave up to fifth order may be easily evaluated. Correlation of the theory with the available experimental data was found to be reasonably good.

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