An analytical solution of second-order wave force on a vertical circular cylinder

Abstract

So far many investigations have been made on nonlinear wave diffraction problem for a large-diameter vertical circular cylinder. However, there are still some problems worthy to be further discussed. It includes that the second order radiation condition is not very clear and the inhomogeneous term of second order free surface boundary condition makes the calculation of second order wave force either not easier to be performed accurately due to its slowly decaying with radial distance or too complicated for practical application. In this paper, the second order radiation condition is posed for the circumferential Fourier components of second order potential, instead of the second order potential. It is found that the circumferenatial Fourier components of second order potential have to satisfy Sommerfeld radiation condition. By means of the mathematical formulae derived in this paper, the inhomogeneous term of second order free surface boundary condition were simplified and then an exact expression of second order wave force was obtained, which is simpler in form and easier to be used in practical calculation. The calculation results agree well with some experimental data.