The second-order solution for wave interaction with a submergered cylinder

The second-order solution of the problem of the interaction of a train of regular waves with a completely submerged, horizontal circular cylinder in water of finite depth is presented for two-dimensional flow. The incident wave is developed as a second-order Stokes' wave by use of a perturbation method and the solution of both the first-order and second-order scatter potentials is obtained numerically using the Green's function approach. The hydrodynamic pressure and resulting first-order and second-order force coefficients are determined numerically and presented for various values of water depth, cylinder depth of submergence and wave length.