Determination of nonlinear forces of the second-order arising from the interaction of waves and certain types of ship's motions in shallow water conditions
The article considers the definition of nonlinear second-order forces caused by the interaction of incoming, diffracted waves and waves caused by various types of motions based on the application of three-dimensional potential theory in the conditions of shallow water. To determine them, it is necessary to calculate the potentials of the second order of smallness. The presented solution is new in domestic practice. The problem is solved on the basis of small parameter methods and integral equations taking into account the nonlinear boundary condition on the free surface of the liquid. The paper shows the possibility of calculating the integrals over the free surface directly due to their convergence at an infinite distance from the ship. Nonlinear forces and moments are determined in the work using Green's function for a fluid of limited depth. The results of calculations of nonlinear forces and moments for different ships are presented. The calculations are presented in comparison with the calculations according to the twodimensional theory, performed also for the case of a liquid of limited depth. A good agreement of the results is shown among themselves in most cases. A significant effect of a decrease of relative depth on all components of non-linear forces without exception, regardless of the type of ship' motions and type of ship, is shown.