Second-order wave force on a large cylinder

Summary A new technique has been developed for estimating the wave loadings on large circular cylinders. The theory, mainly due to Lighthill, has been applied to the case of large cylinders. Comparison with the previously reported experimental results shows favourable agreement for the range of parameters indicated in the graphs.Notations The following symbols are used in this paper a Wave amplitude - b Radius of the cylinder - D Diameter of the cylinder - F _l Linear force - F _d Dynamic force - F _q Quadratic force - F _w Water line force - g Acceleration due to gravity - h Depth of water - H=2a Total wave height - k Wave number,k=2/L - L Wave length - n Outward normal to body surface - n _x Direction cosine between the normaln and the given force - S Body surface - t Time - T Wave period - x, y, z Cartesian coordinates - r, ,z Cylindrical coordinates - W Vertical velocity of fluid - Density of fluid - Wave frequency, =2/T - Total velocity potential - _r , _z Partial derivatives with respect tor andz, respectively - ⁽¹⁾, _l Linear theory velocity potential - ⁽²⁾, _q Second-order velocity potential - Water surface elevation or wave height - _i Linear theory wave height - _q Quadratic theory wave height With 3 Figures