Determination of nonlinear second-order diffraction forces acting on a ship in shallow water conditions based on the use of three-dimensional potential theory

The article discusses a method for determining nonlinear diffraction forces acting on a ship in shallow water conditions on the basis of a three-dimensional potential theory. The influence of the relative depth of the fluid H/T on these nonlinear forces is assessed. To determine them, it is necessary to calculate the potentials of the second order of smallness. The solution of the problem is carried out on the basis of small parameter methods, Fredholm's integral equations and Green's function for a fluid of limited depth. The presented solution in national practice is new. During the determination of the second order potentials, nonlinear boundary conditions on the free surface of the liquid and on the wetted surface of the ship are taken into account on the basis of methods program was developed, considering various H/T. The results of calculations of the forces and moments for three types of different ships are presented. Comparison with calculations based on two-dimensional theory is given. Special attention is paid to taking into account the potential of the second-order of incoming wave. Its contribution to the formation of nonlinear diffraction forces is taken into account. A comparison of calculations with and without the influence of this potential is given