A numerical investigation of second-order difference-frequency forces and motions of a moored ship in shallow water

Abstract

A 3D time-domain Rankine source method is developed to study the hydrodynamic loads and motions of a moored ship in shallow water waves in head sea conditions. Both the wave steepness and ship motions relative to the ship’s draft are assumed small and the exact free-surface and body-boundary conditions are expanded about the mean surface by a Taylor series. A formulation correctly to second order in the wave steepness is adopted. A fourth-order Runge–Kutta method is used to time integrate the boundary conditions and the six degree of freedom motion equations. It is found that the water depth has significant effects on the hydrodynamic coefficients, especially on the vertical modes of motions. The linear horizontal motions of a moored ship have distinct increment in shallower water depth in the low-frequency domain. Further, the horizontal slow-drift excitation forces increase significantly with decreasing water depth and the second-order velocity potential gives dominant contribution in a frequency range of importance for moored ships in shallow water. Lastly, the slowly varying motions of an LNGC is simulated and the satisfactory agreements with experiments demonstrate that the present method can predict the slowly varying motions of a moored ship in finite-amplitude shallow water waves with acceptable results.