Formulation of wave and current forces acting on a body and resistance of ships

A general expression is formulated from the first principles for wave and current forces acting on a body. Morison's equation is recovered as a special case of the general formulation, thus establishing this heuristic-regarded equation on a firm theoretical ground. The drag force is clearly seen to be originating from the advective acceleration and the skin friction resistance, which is not explicitly represented in Morison's equation, is viewed as a small part of the drag force. For the special case of constant flow velocity the general expression is employed to derive a resistance formula for ships. The viscous term is handled through the use of Prandtl-Kármán formulation of friction drag due to a turbulent boundary layer. Conflict between Froude and Reynolds scaling is reconciled by allowing a deviation from the true partition of the corresponding forces but ensuring in return the correct scaling of the total resistance force for the model and ship. The performance of the resistance formula is checked against the experimental measurements of various ship forms. Finally, formulas for forces due to a current at an angle to a ship are suggested.