On the Effect of Non-Linear Boundary Conditions on the Wave Disturbance and Hydrodynamic Forces of Underwater Vehicles Travelling Near the Free-Surface

This study compares the effect of non-linear free-surface boundary conditions for a high-order non-linear free-surface Rankine-source boundary element method on wave disturbance and hydrodynamic forces acting on an underwater vehicle travelling near a calm free-surface. In particular, simulations for a steady nonaxisymmetric prolate spheroid using different basis flows and linearization techniques were compared to an analytical method achieved by Chatjigeorgiou using a multipole expansion of Green’s functions. It appears that at low Froude numbers, the basis flow used in the formulation contributes significantly to differences in the steady solutions for wave resistance and pitch, whereas for higher Froude numbers the linearization technique becomes a more defining feature. Upon observation of the analytical solution for wave resistance, one can see that it was formed under a Neumann-Kelvin formulation and this is supported by the Neumann-Kelvin simulations converging well to the analytical solution. Further comparisons were made using a wave directional energy spectrum gathered from transverse wave cuts of the free wave pattern. The spectral analysis allows for a higher level of comparison between all of the different cases, establishing a direct relation between the change in wave resistance and the energy content variation of the particular wave spectrum components.