Second Order Difference Frequency Wave-Current Loading Using Kelvin-Newman Approximation

Kelvin & Newman introduced a linearization method to include the current (or forward speed) effect into the diffraction & radiation wave field for large-slender floating bodies. The K-N method assumes a steady far-field current while disregarding the steady potential field due to the presence of the body. The method is proven to be reliable when the Froude number is relatively small, the body shape is relatively slender (∂∂x≪∂∂y,∂∂z), and the sea condition is mild. This requirement is fulfilled for typical FPSOs and ship-shaped vessels in a typical current (or forward speed) condition. Several studies suggested that the presence of the current might change the first order hydrodynamic coefficients such as the first order diffraction force, added mass, and radiation damping. Currents also contributed to a change in the second-order slowly-varying drift force. However, the effect of current in the second-order difference-frequency force is yet to be investigated. By expanding the Kelvin-Newman approximation up to the second order, and solving the problem in the frequency domain, we can save computational time while expanding the accuracy of the scheme. The second order quadratic force is the main focus of this study, since it is the main contributor to the total second order difference frequency forces especially near the diagonal. By implementing the Kelvin-Newman wave current interaction approach up to the wave’s second order, we can assess the performance of the Kelvin-Newman wave current interaction formulation in various sea conditions.